Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(43,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.s (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.127 |
Dual form | 546.2.s.d.43.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 2.73205i | − | 1.22181i | −0.791704 | − | 0.610905i | \(-0.790806\pi\) | ||
0.791704 | − | 0.610905i | \(-0.209194\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.36603 | − | 2.36603i | −0.431975 | − | 0.748203i | ||||
\(11\) | 0.232051 | − | 0.133975i | 0.0699660 | − | 0.0403949i | −0.464609 | − | 0.885516i | \(-0.653805\pi\) |
0.534575 | + | 0.845121i | \(0.320472\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.866025 | − | 3.50000i | 0.240192 | − | 0.970725i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.36603 | − | 1.36603i | 0.610905 | − | 0.352706i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.86603 | − | 3.23205i | 0.452578 | − | 0.783887i | −0.545968 | − | 0.837806i | \(-0.683838\pi\) |
0.998545 | + | 0.0539188i | \(0.0171712\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.13397 | + | 1.23205i | 0.489567 | + | 0.282652i | 0.724395 | − | 0.689385i | \(-0.242119\pi\) |
−0.234828 | + | 0.972037i | \(0.575453\pi\) | |||||||
\(20\) | −2.36603 | − | 1.36603i | −0.529059 | − | 0.305453i | ||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | 0.133975 | − | 0.232051i | 0.0285635 | − | 0.0494734i | ||||
\(23\) | −1.73205 | − | 3.00000i | −0.361158 | − | 0.625543i | 0.626994 | − | 0.779024i | \(-0.284285\pi\) |
−0.988152 | + | 0.153481i | \(0.950952\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | −1.00000 | − | 3.46410i | −0.196116 | − | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.866025 | + | 0.500000i | −0.163663 | + | 0.0944911i | ||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | 1.36603 | − | 2.36603i | 0.249401 | − | 0.431975i | ||||
\(31\) | 9.66025i | 1.73503i | 0.497409 | + | 0.867516i | \(0.334285\pi\) | ||||
−0.497409 | + | 0.867516i | \(0.665715\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0.232051 | + | 0.133975i | 0.0403949 | + | 0.0233220i | ||||
\(34\) | − | 3.73205i | − | 0.640041i | ||||||
\(35\) | −1.36603 | + | 2.36603i | −0.230900 | + | 0.399931i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −4.09808 | + | 2.36603i | −0.673720 | + | 0.388972i | −0.797485 | − | 0.603339i | \(-0.793836\pi\) |
0.123765 | + | 0.992312i | \(0.460503\pi\) | |||||||
\(38\) | 2.46410 | 0.399730 | ||||||||
\(39\) | 3.46410 | − | 1.00000i | 0.554700 | − | 0.160128i | ||||
\(40\) | −2.73205 | −0.431975 | ||||||||
\(41\) | 6.06218 | − | 3.50000i | 0.946753 | − | 0.546608i | 0.0546823 | − | 0.998504i | \(-0.482585\pi\) |
0.892071 | + | 0.451896i | \(0.149252\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | −1.36603 | + | 2.36603i | −0.208317 | + | 0.360815i | −0.951184 | − | 0.308623i | \(-0.900132\pi\) |
0.742868 | + | 0.669438i | \(0.233465\pi\) | |||||||
\(44\) | − | 0.267949i | − | 0.0403949i | ||||||
\(45\) | 2.36603 | + | 1.36603i | 0.352706 | + | 0.203635i | ||||
\(46\) | −3.00000 | − | 1.73205i | −0.442326 | − | 0.255377i | ||||
\(47\) | − | 2.46410i | − | 0.359426i | −0.983719 | − | 0.179713i | \(-0.942483\pi\) | ||
0.983719 | − | 0.179713i | \(-0.0575169\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −2.13397 | + | 1.23205i | −0.301790 | + | 0.174238i | ||||
\(51\) | 3.73205 | 0.522592 | ||||||||
\(52\) | −2.59808 | − | 2.50000i | −0.360288 | − | 0.346688i | ||||
\(53\) | −3.53590 | −0.485693 | −0.242846 | − | 0.970065i | \(-0.578081\pi\) | ||||
−0.242846 | + | 0.970065i | \(0.578081\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −0.366025 | − | 0.633975i | −0.0493549 | − | 0.0854851i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | 2.46410i | 0.326378i | ||||||||
\(58\) | 2.59808 | + | 1.50000i | 0.341144 | + | 0.196960i | ||||
\(59\) | 11.1962 | + | 6.46410i | 1.45761 | + | 0.841554i | 0.998894 | − | 0.0470259i | \(-0.0149743\pi\) |
0.458721 | + | 0.888580i | \(0.348308\pi\) | |||||||
\(60\) | − | 2.73205i | − | 0.352706i | ||||||
\(61\) | 4.13397 | − | 7.16025i | 0.529301 | − | 0.916777i | −0.470115 | − | 0.882605i | \(-0.655787\pi\) |
0.999416 | − | 0.0341713i | \(-0.0108792\pi\) | |||||||
\(62\) | 4.83013 | + | 8.36603i | 0.613427 | + | 1.06249i | ||||
\(63\) | 0.866025 | − | 0.500000i | 0.109109 | − | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −9.56218 | − | 2.36603i | −1.18604 | − | 0.293469i | ||||
\(66\) | 0.267949 | 0.0329823 | ||||||||
\(67\) | −0.803848 | + | 0.464102i | −0.0982056 | + | 0.0566990i | −0.548298 | − | 0.836283i | \(-0.684724\pi\) |
0.450093 | + | 0.892982i | \(0.351391\pi\) | |||||||
\(68\) | −1.86603 | − | 3.23205i | −0.226289 | − | 0.391944i | ||||
\(69\) | 1.73205 | − | 3.00000i | 0.208514 | − | 0.361158i | ||||
\(70\) | 2.73205i | 0.326543i | ||||||||
\(71\) | 7.09808 | + | 4.09808i | 0.842387 | + | 0.486352i | 0.858075 | − | 0.513525i | \(-0.171661\pi\) |
−0.0156881 | + | 0.999877i | \(0.504994\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 13.4641i | 1.57585i | 0.615769 | + | 0.787927i | \(0.288846\pi\) | ||||
−0.615769 | + | 0.787927i | \(0.711154\pi\) | |||||||
\(74\) | −2.36603 | + | 4.09808i | −0.275045 | + | 0.476392i | ||||
\(75\) | −1.23205 | − | 2.13397i | −0.142265 | − | 0.246410i | ||||
\(76\) | 2.13397 | − | 1.23205i | 0.244784 | − | 0.141326i | ||||
\(77\) | −0.267949 | −0.0305356 | ||||||||
\(78\) | 2.50000 | − | 2.59808i | 0.283069 | − | 0.294174i | ||||
\(79\) | −16.8564 | −1.89649 | −0.948247 | − | 0.317534i | \(-0.897145\pi\) | ||||
−0.948247 | + | 0.317534i | \(0.897145\pi\) | |||||||
\(80\) | −2.36603 | + | 1.36603i | −0.264530 | + | 0.152726i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.50000 | − | 6.06218i | 0.386510 | − | 0.669456i | ||||
\(83\) | 11.6603i | 1.27988i | 0.768425 | + | 0.639940i | \(0.221041\pi\) | ||||
−0.768425 | + | 0.639940i | \(0.778959\pi\) | |||||||
\(84\) | −0.866025 | − | 0.500000i | −0.0944911 | − | 0.0545545i | ||||
\(85\) | −8.83013 | − | 5.09808i | −0.957762 | − | 0.552964i | ||||
\(86\) | 2.73205i | 0.294605i | ||||||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | −0.133975 | − | 0.232051i | −0.0142817 | − | 0.0247367i | ||||
\(89\) | 0.401924 | − | 0.232051i | 0.0426038 | − | 0.0245973i | −0.478547 | − | 0.878062i | \(-0.658836\pi\) |
0.521151 | + | 0.853465i | \(0.325503\pi\) | |||||||
\(90\) | 2.73205 | 0.287983 | ||||||||
\(91\) | −2.50000 | + | 2.59808i | −0.262071 | + | 0.272352i | ||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | −8.36603 | + | 4.83013i | −0.867516 | + | 0.500861i | ||||
\(94\) | −1.23205 | − | 2.13397i | −0.127076 | − | 0.220103i | ||||
\(95\) | 3.36603 | − | 5.83013i | 0.345347 | − | 0.598158i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 2.36603 | + | 1.36603i | 0.240233 | + | 0.138699i | 0.615284 | − | 0.788305i | \(-0.289041\pi\) |
−0.375051 | + | 0.927004i | \(0.622375\pi\) | |||||||
\(98\) | 0.866025 | + | 0.500000i | 0.0874818 | + | 0.0505076i | ||||
\(99\) | 0.267949i | 0.0269299i | ||||||||
\(100\) | −1.23205 | + | 2.13397i | −0.123205 | + | 0.213397i | ||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | 3.23205 | − | 1.86603i | 0.320021 | − | 0.184764i | ||||
\(103\) | 1.80385 | 0.177738 | 0.0888692 | − | 0.996043i | \(-0.471675\pi\) | ||||
0.0888692 | + | 0.996043i | \(0.471675\pi\) | |||||||
\(104\) | −3.50000 | − | 0.866025i | −0.343203 | − | 0.0849208i | ||||
\(105\) | −2.73205 | −0.266621 | ||||||||
\(106\) | −3.06218 | + | 1.76795i | −0.297425 | + | 0.171718i | ||||
\(107\) | 4.23205 | + | 7.33013i | 0.409128 | + | 0.708630i | 0.994792 | − | 0.101923i | \(-0.0324997\pi\) |
−0.585664 | + | 0.810554i | \(0.699166\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 13.6603i | 1.30842i | 0.756315 | + | 0.654208i | \(0.226998\pi\) | ||||
−0.756315 | + | 0.654208i | \(0.773002\pi\) | |||||||
\(110\) | −0.633975 | − | 0.366025i | −0.0604471 | − | 0.0348992i | ||||
\(111\) | −4.09808 | − | 2.36603i | −0.388972 | − | 0.224573i | ||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | −0.0980762 | + | 0.169873i | −0.00922623 | + | 0.0159803i | −0.870602 | − | 0.491989i | \(-0.836270\pi\) |
0.861375 | + | 0.507969i | \(0.169604\pi\) | |||||||
\(114\) | 1.23205 | + | 2.13397i | 0.115392 | + | 0.199865i | ||||
\(115\) | −8.19615 | + | 4.73205i | −0.764295 | + | 0.441266i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 2.59808 | + | 2.50000i | 0.240192 | + | 0.231125i | ||||
\(118\) | 12.9282 | 1.19014 | ||||||||
\(119\) | −3.23205 | + | 1.86603i | −0.296282 | + | 0.171058i | ||||
\(120\) | −1.36603 | − | 2.36603i | −0.124700 | − | 0.215988i | ||||
\(121\) | −5.46410 | + | 9.46410i | −0.496737 | + | 0.860373i | ||||
\(122\) | − | 8.26795i | − | 0.748545i | ||||||
\(123\) | 6.06218 | + | 3.50000i | 0.546608 | + | 0.315584i | ||||
\(124\) | 8.36603 | + | 4.83013i | 0.751291 | + | 0.433758i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0.500000 | − | 0.866025i | 0.0445435 | − | 0.0771517i | ||||
\(127\) | −9.73205 | − | 16.8564i | −0.863580 | − | 1.49576i | −0.868450 | − | 0.495776i | \(-0.834884\pi\) |
0.00487054 | − | 0.999988i | \(-0.498450\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −2.73205 | −0.240544 | ||||||||
\(130\) | −9.46410 | + | 2.73205i | −0.830057 | + | 0.239617i | ||||
\(131\) | 5.07180 | 0.443125 | 0.221562 | − | 0.975146i | \(-0.428884\pi\) | ||||
0.221562 | + | 0.975146i | \(0.428884\pi\) | |||||||
\(132\) | 0.232051 | − | 0.133975i | 0.0201974 | − | 0.0116610i | ||||
\(133\) | −1.23205 | − | 2.13397i | −0.106832 | − | 0.185039i | ||||
\(134\) | −0.464102 | + | 0.803848i | −0.0400923 | + | 0.0694419i | ||||
\(135\) | 2.73205i | 0.235137i | ||||||||
\(136\) | −3.23205 | − | 1.86603i | −0.277146 | − | 0.160010i | ||||
\(137\) | −7.39230 | − | 4.26795i | −0.631567 | − | 0.364636i | 0.149792 | − | 0.988718i | \(-0.452140\pi\) |
−0.781359 | + | 0.624082i | \(0.785473\pi\) | |||||||
\(138\) | − | 3.46410i | − | 0.294884i | ||||||
\(139\) | −3.06218 | + | 5.30385i | −0.259731 | + | 0.449866i | −0.966170 | − | 0.257907i | \(-0.916967\pi\) |
0.706439 | + | 0.707774i | \(0.250300\pi\) | |||||||
\(140\) | 1.36603 | + | 2.36603i | 0.115450 | + | 0.199966i | ||||
\(141\) | 2.13397 | − | 1.23205i | 0.179713 | − | 0.103757i | ||||
\(142\) | 8.19615 | 0.687806 | ||||||||
\(143\) | −0.267949 | − | 0.928203i | −0.0224070 | − | 0.0776203i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.09808 | − | 4.09808i | 0.589463 | − | 0.340327i | ||||
\(146\) | 6.73205 | + | 11.6603i | 0.557148 | + | 0.965009i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | 4.73205i | 0.388972i | ||||||||
\(149\) | 4.39230 | + | 2.53590i | 0.359832 | + | 0.207749i | 0.669007 | − | 0.743256i | \(-0.266720\pi\) |
−0.309175 | + | 0.951005i | \(0.600053\pi\) | |||||||
\(150\) | −2.13397 | − | 1.23205i | −0.174238 | − | 0.100597i | ||||
\(151\) | 2.80385i | 0.228174i | 0.993471 | + | 0.114087i | \(0.0363942\pi\) | ||||
−0.993471 | + | 0.114087i | \(0.963606\pi\) | |||||||
\(152\) | 1.23205 | − | 2.13397i | 0.0999325 | − | 0.173088i | ||||
\(153\) | 1.86603 | + | 3.23205i | 0.150859 | + | 0.261296i | ||||
\(154\) | −0.232051 | + | 0.133975i | −0.0186992 | + | 0.0107960i | ||||
\(155\) | 26.3923 | 2.11988 | ||||||||
\(156\) | 0.866025 | − | 3.50000i | 0.0693375 | − | 0.280224i | ||||
\(157\) | −8.53590 | −0.681239 | −0.340619 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340619 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(158\) | −14.5981 | + | 8.42820i | −1.16136 | + | 0.670512i | ||||
\(159\) | −1.76795 | − | 3.06218i | −0.140207 | − | 0.242846i | ||||
\(160\) | −1.36603 | + | 2.36603i | −0.107994 | + | 0.187051i | ||||
\(161\) | 3.46410i | 0.273009i | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 15.7583 | + | 9.09808i | 1.23429 | + | 0.712616i | 0.967921 | − | 0.251255i | \(-0.0808434\pi\) |
0.266367 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(164\) | − | 7.00000i | − | 0.546608i | ||||||
\(165\) | 0.366025 | − | 0.633975i | 0.0284950 | − | 0.0493549i | ||||
\(166\) | 5.83013 | + | 10.0981i | 0.452506 | + | 0.783763i | ||||
\(167\) | 18.9282 | − | 10.9282i | 1.46471 | − | 0.845650i | 0.465485 | − | 0.885056i | \(-0.345880\pi\) |
0.999223 | + | 0.0394060i | \(0.0125466\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −11.5000 | − | 6.06218i | −0.884615 | − | 0.466321i | ||||
\(170\) | −10.1962 | −0.782009 | ||||||||
\(171\) | −2.13397 | + | 1.23205i | −0.163189 | + | 0.0942173i | ||||
\(172\) | 1.36603 | + | 2.36603i | 0.104158 | + | 0.180408i | ||||
\(173\) | 8.63397 | − | 14.9545i | 0.656429 | − | 1.13697i | −0.325105 | − | 0.945678i | \(-0.605400\pi\) |
0.981534 | − | 0.191290i | \(-0.0612672\pi\) | |||||||
\(174\) | 3.00000i | 0.227429i | ||||||||
\(175\) | 2.13397 | + | 1.23205i | 0.161313 | + | 0.0931343i | ||||
\(176\) | −0.232051 | − | 0.133975i | −0.0174915 | − | 0.0100987i | ||||
\(177\) | 12.9282i | 0.971743i | ||||||||
\(178\) | 0.232051 | − | 0.401924i | 0.0173929 | − | 0.0301255i | ||||
\(179\) | 0.803848 | + | 1.39230i | 0.0600824 | + | 0.104066i | 0.894502 | − | 0.447064i | \(-0.147530\pi\) |
−0.834420 | + | 0.551130i | \(0.814197\pi\) | |||||||
\(180\) | 2.36603 | − | 1.36603i | 0.176353 | − | 0.101818i | ||||
\(181\) | 9.19615 | 0.683545 | 0.341772 | − | 0.939783i | \(-0.388973\pi\) | ||||
0.341772 | + | 0.939783i | \(0.388973\pi\) | |||||||
\(182\) | −0.866025 | + | 3.50000i | −0.0641941 | + | 0.259437i | ||||
\(183\) | 8.26795 | 0.611184 | ||||||||
\(184\) | −3.00000 | + | 1.73205i | −0.221163 | + | 0.127688i | ||||
\(185\) | 6.46410 | + | 11.1962i | 0.475250 | + | 0.823157i | ||||
\(186\) | −4.83013 | + | 8.36603i | −0.354162 | + | 0.613427i | ||||
\(187\) | − | 1.00000i | − | 0.0731272i | ||||||
\(188\) | −2.13397 | − | 1.23205i | −0.155636 | − | 0.0898565i | ||||
\(189\) | 0.866025 | + | 0.500000i | 0.0629941 | + | 0.0363696i | ||||
\(190\) | − | 6.73205i | − | 0.488394i | ||||||
\(191\) | −3.09808 | + | 5.36603i | −0.224169 | + | 0.388272i | −0.956070 | − | 0.293139i | \(-0.905300\pi\) |
0.731901 | + | 0.681411i | \(0.238633\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.89230 | − | 3.40192i | 0.424137 | − | 0.244876i | −0.272709 | − | 0.962097i | \(-0.587919\pi\) |
0.696846 | + | 0.717221i | \(0.254586\pi\) | |||||||
\(194\) | 2.73205 | 0.196150 | ||||||||
\(195\) | −2.73205 | − | 9.46410i | −0.195646 | − | 0.677738i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.96410 | + | 2.86603i | −0.353678 | + | 0.204196i | −0.666304 | − | 0.745680i | \(-0.732125\pi\) |
0.312626 | + | 0.949876i | \(0.398791\pi\) | |||||||
\(198\) | 0.133975 | + | 0.232051i | 0.00952116 | + | 0.0164911i | ||||
\(199\) | 3.09808 | − | 5.36603i | 0.219617 | − | 0.380387i | −0.735074 | − | 0.677987i | \(-0.762853\pi\) |
0.954691 | + | 0.297599i | \(0.0961860\pi\) | |||||||
\(200\) | 2.46410i | 0.174238i | ||||||||
\(201\) | −0.803848 | − | 0.464102i | −0.0566990 | − | 0.0327352i | ||||
\(202\) | −8.66025 | − | 5.00000i | −0.609333 | − | 0.351799i | ||||
\(203\) | − | 3.00000i | − | 0.210559i | ||||||
\(204\) | 1.86603 | − | 3.23205i | 0.130648 | − | 0.226289i | ||||
\(205\) | −9.56218 | − | 16.5622i | −0.667851 | − | 1.15675i | ||||
\(206\) | 1.56218 | − | 0.901924i | 0.108842 | − | 0.0628400i | ||||
\(207\) | 3.46410 | 0.240772 | ||||||||
\(208\) | −3.46410 | + | 1.00000i | −0.240192 | + | 0.0693375i | ||||
\(209\) | 0.660254 | 0.0456707 | ||||||||
\(210\) | −2.36603 | + | 1.36603i | −0.163271 | + | 0.0942647i | ||||
\(211\) | −5.92820 | − | 10.2679i | −0.408114 | − | 0.706875i | 0.586564 | − | 0.809903i | \(-0.300480\pi\) |
−0.994678 | + | 0.103028i | \(0.967147\pi\) | |||||||
\(212\) | −1.76795 | + | 3.06218i | −0.121423 | + | 0.210311i | ||||
\(213\) | 8.19615i | 0.561591i | ||||||||
\(214\) | 7.33013 | + | 4.23205i | 0.501077 | + | 0.289297i | ||||
\(215\) | 6.46410 | + | 3.73205i | 0.440848 | + | 0.254524i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 4.83013 | − | 8.36603i | 0.327890 | − | 0.567923i | ||||
\(218\) | 6.83013 | + | 11.8301i | 0.462595 | + | 0.801237i | ||||
\(219\) | −11.6603 | + | 6.73205i | −0.787927 | + | 0.454910i | ||||
\(220\) | −0.732051 | −0.0493549 | ||||||||
\(221\) | −9.69615 | − | 9.33013i | −0.652234 | − | 0.627612i | ||||
\(222\) | −4.73205 | −0.317594 | ||||||||
\(223\) | 10.7321 | − | 6.19615i | 0.718671 | − | 0.414925i | −0.0955922 | − | 0.995421i | \(-0.530474\pi\) |
0.814263 | + | 0.580496i | \(0.197141\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 1.23205 | − | 2.13397i | 0.0821367 | − | 0.142265i | ||||
\(226\) | 0.196152i | 0.0130479i | ||||||||
\(227\) | −13.3923 | − | 7.73205i | −0.888878 | − | 0.513194i | −0.0153030 | − | 0.999883i | \(-0.504871\pi\) |
−0.873575 | + | 0.486689i | \(0.838205\pi\) | |||||||
\(228\) | 2.13397 | + | 1.23205i | 0.141326 | + | 0.0815946i | ||||
\(229\) | 24.3205i | 1.60714i | 0.595207 | + | 0.803572i | \(0.297070\pi\) | ||||
−0.595207 | + | 0.803572i | \(0.702930\pi\) | |||||||
\(230\) | −4.73205 | + | 8.19615i | −0.312022 | + | 0.540438i | ||||
\(231\) | −0.133975 | − | 0.232051i | −0.00881488 | − | 0.0152678i | ||||
\(232\) | 2.59808 | − | 1.50000i | 0.170572 | − | 0.0984798i | ||||
\(233\) | 8.19615 | 0.536948 | 0.268474 | − | 0.963287i | \(-0.413481\pi\) | ||||
0.268474 | + | 0.963287i | \(0.413481\pi\) | |||||||
\(234\) | 3.50000 | + | 0.866025i | 0.228802 | + | 0.0566139i | ||||
\(235\) | −6.73205 | −0.439151 | ||||||||
\(236\) | 11.1962 | − | 6.46410i | 0.728807 | − | 0.420777i | ||||
\(237\) | −8.42820 | − | 14.5981i | −0.547471 | − | 0.948247i | ||||
\(238\) | −1.86603 | + | 3.23205i | −0.120956 | + | 0.209503i | ||||
\(239\) | − | 24.1962i | − | 1.56512i | −0.622576 | − | 0.782559i | \(-0.713914\pi\) | ||
0.622576 | − | 0.782559i | \(-0.286086\pi\) | |||||||
\(240\) | −2.36603 | − | 1.36603i | −0.152726 | − | 0.0881766i | ||||
\(241\) | −24.9282 | − | 14.3923i | −1.60577 | − | 0.927090i | −0.990303 | − | 0.138925i | \(-0.955635\pi\) |
−0.615464 | − | 0.788165i | \(-0.711031\pi\) | |||||||
\(242\) | 10.9282i | 0.702492i | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −4.13397 | − | 7.16025i | −0.264651 | − | 0.458388i | ||||
\(245\) | 2.36603 | − | 1.36603i | 0.151160 | − | 0.0872722i | ||||
\(246\) | 7.00000 | 0.446304 | ||||||||
\(247\) | 6.16025 | − | 6.40192i | 0.391968 | − | 0.407345i | ||||
\(248\) | 9.66025 | 0.613427 | ||||||||
\(249\) | −10.0981 | + | 5.83013i | −0.639940 | + | 0.369469i | ||||
\(250\) | −3.46410 | − | 6.00000i | −0.219089 | − | 0.379473i | ||||
\(251\) | 3.90192 | − | 6.75833i | 0.246287 | − | 0.426582i | −0.716205 | − | 0.697889i | \(-0.754123\pi\) |
0.962493 | + | 0.271307i | \(0.0874560\pi\) | |||||||
\(252\) | − | 1.00000i | − | 0.0629941i | ||||||
\(253\) | −0.803848 | − | 0.464102i | −0.0505375 | − | 0.0291778i | ||||
\(254\) | −16.8564 | − | 9.73205i | −1.05767 | − | 0.610643i | ||||
\(255\) | − | 10.1962i | − | 0.638508i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −13.5263 | − | 23.4282i | −0.843746 | − | 1.46141i | −0.886706 | − | 0.462334i | \(-0.847012\pi\) |
0.0429595 | − | 0.999077i | \(-0.486321\pi\) | |||||||
\(258\) | −2.36603 | + | 1.36603i | −0.147302 | + | 0.0850450i | ||||
\(259\) | 4.73205 | 0.294035 | ||||||||
\(260\) | −6.83013 | + | 7.09808i | −0.423586 | + | 0.440204i | ||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | 4.39230 | − | 2.53590i | 0.271357 | − | 0.156668i | ||||
\(263\) | 7.63397 | + | 13.2224i | 0.470731 | + | 0.815330i | 0.999440 | − | 0.0334733i | \(-0.0106569\pi\) |
−0.528709 | + | 0.848803i | \(0.677324\pi\) | |||||||
\(264\) | 0.133975 | − | 0.232051i | 0.00824557 | − | 0.0142817i | ||||
\(265\) | 9.66025i | 0.593425i | ||||||||
\(266\) | −2.13397 | − | 1.23205i | −0.130842 | − | 0.0755419i | ||||
\(267\) | 0.401924 | + | 0.232051i | 0.0245973 | + | 0.0142013i | ||||
\(268\) | 0.928203i | 0.0566990i | ||||||||
\(269\) | −15.8564 | + | 27.4641i | −0.966782 | + | 1.67452i | −0.262033 | + | 0.965059i | \(0.584393\pi\) |
−0.704749 | + | 0.709457i | \(0.748940\pi\) | |||||||
\(270\) | 1.36603 | + | 2.36603i | 0.0831337 | + | 0.143992i | ||||
\(271\) | 20.3660 | − | 11.7583i | 1.23715 | − | 0.714268i | 0.268638 | − | 0.963241i | \(-0.413427\pi\) |
0.968510 | + | 0.248974i | \(0.0800932\pi\) | |||||||
\(272\) | −3.73205 | −0.226289 | ||||||||
\(273\) | −3.50000 | − | 0.866025i | −0.211830 | − | 0.0524142i | ||||
\(274\) | −8.53590 | −0.515672 | ||||||||
\(275\) | −0.571797 | + | 0.330127i | −0.0344806 | + | 0.0199074i | ||||
\(276\) | −1.73205 | − | 3.00000i | −0.104257 | − | 0.180579i | ||||
\(277\) | −2.80385 | + | 4.85641i | −0.168467 | + | 0.291793i | −0.937881 | − | 0.346957i | \(-0.887215\pi\) |
0.769414 | + | 0.638750i | \(0.220548\pi\) | |||||||
\(278\) | 6.12436i | 0.367314i | ||||||||
\(279\) | −8.36603 | − | 4.83013i | −0.500861 | − | 0.289172i | ||||
\(280\) | 2.36603 | + | 1.36603i | 0.141397 | + | 0.0816356i | ||||
\(281\) | 7.80385i | 0.465539i | 0.972532 | + | 0.232769i | \(0.0747787\pi\) | ||||
−0.972532 | + | 0.232769i | \(0.925221\pi\) | |||||||
\(282\) | 1.23205 | − | 2.13397i | 0.0733676 | − | 0.127076i | ||||
\(283\) | −4.53590 | − | 7.85641i | −0.269631 | − | 0.467015i | 0.699135 | − | 0.714989i | \(-0.253568\pi\) |
−0.968767 | + | 0.247974i | \(0.920235\pi\) | |||||||
\(284\) | 7.09808 | − | 4.09808i | 0.421193 | − | 0.243176i | ||||
\(285\) | 6.73205 | 0.398772 | ||||||||
\(286\) | −0.696152 | − | 0.669873i | −0.0411644 | − | 0.0396104i | ||||
\(287\) | −7.00000 | −0.413197 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 1.53590 | + | 2.66025i | 0.0903470 | + | 0.156486i | ||||
\(290\) | 4.09808 | − | 7.09808i | 0.240647 | − | 0.416813i | ||||
\(291\) | 2.73205i | 0.160156i | ||||||||
\(292\) | 11.6603 | + | 6.73205i | 0.682365 | + | 0.393963i | ||||
\(293\) | −24.9282 | − | 14.3923i | −1.45632 | − | 0.840807i | −0.457493 | − | 0.889213i | \(-0.651253\pi\) |
−0.998828 | + | 0.0484056i | \(0.984586\pi\) | |||||||
\(294\) | 1.00000i | 0.0583212i | ||||||||
\(295\) | 17.6603 | − | 30.5885i | 1.02822 | − | 1.78093i | ||||
\(296\) | 2.36603 | + | 4.09808i | 0.137522 | + | 0.238196i | ||||
\(297\) | −0.232051 | + | 0.133975i | −0.0134650 | + | 0.00777399i | ||||
\(298\) | 5.07180 | 0.293801 | ||||||||
\(299\) | −12.0000 | + | 3.46410i | −0.693978 | + | 0.200334i | ||||
\(300\) | −2.46410 | −0.142265 | ||||||||
\(301\) | 2.36603 | − | 1.36603i | 0.136375 | − | 0.0787364i | ||||
\(302\) | 1.40192 | + | 2.42820i | 0.0806716 | + | 0.139727i | ||||
\(303\) | 5.00000 | − | 8.66025i | 0.287242 | − | 0.497519i | ||||
\(304\) | − | 2.46410i | − | 0.141326i | ||||||
\(305\) | −19.5622 | − | 11.2942i | −1.12013 | − | 0.646706i | ||||
\(306\) | 3.23205 | + | 1.86603i | 0.184764 | + | 0.106674i | ||||
\(307\) | 7.78461i | 0.444291i | 0.975014 | + | 0.222146i | \(0.0713060\pi\) | ||||
−0.975014 | + | 0.222146i | \(0.928694\pi\) | |||||||
\(308\) | −0.133975 | + | 0.232051i | −0.00763391 | + | 0.0132223i | ||||
\(309\) | 0.901924 | + | 1.56218i | 0.0513087 | + | 0.0888692i | ||||
\(310\) | 22.8564 | − | 13.1962i | 1.29816 | − | 0.749491i | ||||
\(311\) | 8.80385 | 0.499220 | 0.249610 | − | 0.968346i | \(-0.419698\pi\) | ||||
0.249610 | + | 0.968346i | \(0.419698\pi\) | |||||||
\(312\) | −1.00000 | − | 3.46410i | −0.0566139 | − | 0.196116i | ||||
\(313\) | 12.1962 | 0.689367 | 0.344684 | − | 0.938719i | \(-0.387986\pi\) | ||||
0.344684 | + | 0.938719i | \(0.387986\pi\) | |||||||
\(314\) | −7.39230 | + | 4.26795i | −0.417172 | + | 0.240854i | ||||
\(315\) | −1.36603 | − | 2.36603i | −0.0769668 | − | 0.133310i | ||||
\(316\) | −8.42820 | + | 14.5981i | −0.474123 | + | 0.821206i | ||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | −3.06218 | − | 1.76795i | −0.171718 | − | 0.0991417i | ||||
\(319\) | 0.696152 | + | 0.401924i | 0.0389771 | + | 0.0225034i | ||||
\(320\) | 2.73205i | 0.152726i | ||||||||
\(321\) | −4.23205 | + | 7.33013i | −0.236210 | + | 0.409128i | ||||
\(322\) | 1.73205 | + | 3.00000i | 0.0965234 | + | 0.167183i | ||||
\(323\) | 7.96410 | − | 4.59808i | 0.443134 | − | 0.255844i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −2.13397 | + | 8.62436i | −0.118372 | + | 0.478393i | ||||
\(326\) | 18.1962 | 1.00779 | ||||||||
\(327\) | −11.8301 | + | 6.83013i | −0.654208 | + | 0.377707i | ||||
\(328\) | −3.50000 | − | 6.06218i | −0.193255 | − | 0.334728i | ||||
\(329\) | −1.23205 | + | 2.13397i | −0.0679252 | + | 0.117650i | ||||
\(330\) | − | 0.732051i | − | 0.0402981i | ||||||
\(331\) | 2.66025 | + | 1.53590i | 0.146221 | + | 0.0844206i | 0.571325 | − | 0.820724i | \(-0.306429\pi\) |
−0.425105 | + | 0.905144i | \(0.639763\pi\) | |||||||
\(332\) | 10.0981 | + | 5.83013i | 0.554204 | + | 0.319970i | ||||
\(333\) | − | 4.73205i | − | 0.259315i | ||||||
\(334\) | 10.9282 | − | 18.9282i | 0.597965 | − | 1.03571i | ||||
\(335\) | 1.26795 | + | 2.19615i | 0.0692755 | + | 0.119989i | ||||
\(336\) | −0.866025 | + | 0.500000i | −0.0472456 | + | 0.0272772i | ||||
\(337\) | 13.7846 | 0.750896 | 0.375448 | − | 0.926844i | \(-0.377489\pi\) | ||||
0.375448 | + | 0.926844i | \(0.377489\pi\) | |||||||
\(338\) | −12.9904 | + | 0.500000i | −0.706584 | + | 0.0271964i | ||||
\(339\) | −0.196152 | −0.0106535 | ||||||||
\(340\) | −8.83013 | + | 5.09808i | −0.478881 | + | 0.276482i | ||||
\(341\) | 1.29423 | + | 2.24167i | 0.0700864 | + | 0.121393i | ||||
\(342\) | −1.23205 | + | 2.13397i | −0.0666217 | + | 0.115392i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 2.36603 | + | 1.36603i | 0.127568 | + | 0.0736512i | ||||
\(345\) | −8.19615 | − | 4.73205i | −0.441266 | − | 0.254765i | ||||
\(346\) | − | 17.2679i | − | 0.928331i | ||||||
\(347\) | 2.42820 | − | 4.20577i | 0.130353 | − | 0.225778i | −0.793460 | − | 0.608623i | \(-0.791722\pi\) |
0.923813 | + | 0.382845i | \(0.125056\pi\) | |||||||
\(348\) | 1.50000 | + | 2.59808i | 0.0804084 | + | 0.139272i | ||||
\(349\) | 27.4641 | − | 15.8564i | 1.47012 | − | 0.848774i | 0.470682 | − | 0.882303i | \(-0.344008\pi\) |
0.999438 | + | 0.0335290i | \(0.0106746\pi\) | |||||||
\(350\) | 2.46410 | 0.131712 | ||||||||
\(351\) | −0.866025 | + | 3.50000i | −0.0462250 | + | 0.186816i | ||||
\(352\) | −0.267949 | −0.0142817 | ||||||||
\(353\) | −4.73205 | + | 2.73205i | −0.251862 | + | 0.145412i | −0.620616 | − | 0.784114i | \(-0.713118\pi\) |
0.368755 | + | 0.929527i | \(0.379784\pi\) | |||||||
\(354\) | 6.46410 | + | 11.1962i | 0.343563 | + | 0.595069i | ||||
\(355\) | 11.1962 | − | 19.3923i | 0.594230 | − | 1.02924i | ||||
\(356\) | − | 0.464102i | − | 0.0245973i | ||||||
\(357\) | −3.23205 | − | 1.86603i | −0.171058 | − | 0.0987605i | ||||
\(358\) | 1.39230 | + | 0.803848i | 0.0735856 | + | 0.0424847i | ||||
\(359\) | 26.1962i | 1.38258i | 0.722577 | + | 0.691290i | \(0.242957\pi\) | ||||
−0.722577 | + | 0.691290i | \(0.757043\pi\) | |||||||
\(360\) | 1.36603 | − | 2.36603i | 0.0719959 | − | 0.124700i | ||||
\(361\) | −6.46410 | − | 11.1962i | −0.340216 | − | 0.589271i | ||||
\(362\) | 7.96410 | − | 4.59808i | 0.418584 | − | 0.241670i | ||||
\(363\) | −10.9282 | −0.573582 | ||||||||
\(364\) | 1.00000 | + | 3.46410i | 0.0524142 | + | 0.181568i | ||||
\(365\) | 36.7846 | 1.92539 | ||||||||
\(366\) | 7.16025 | − | 4.13397i | 0.374272 | − | 0.216086i | ||||
\(367\) | 16.1244 | + | 27.9282i | 0.841685 | + | 1.45784i | 0.888470 | + | 0.458935i | \(0.151769\pi\) |
−0.0467851 | + | 0.998905i | \(0.514898\pi\) | |||||||
\(368\) | −1.73205 | + | 3.00000i | −0.0902894 | + | 0.156386i | ||||
\(369\) | 7.00000i | 0.364405i | ||||||||
\(370\) | 11.1962 | + | 6.46410i | 0.582060 | + | 0.336053i | ||||
\(371\) | 3.06218 | + | 1.76795i | 0.158980 | + | 0.0917873i | ||||
\(372\) | 9.66025i | 0.500861i | ||||||||
\(373\) | −5.29423 | + | 9.16987i | −0.274125 | + | 0.474798i | −0.969914 | − | 0.243448i | \(-0.921721\pi\) |
0.695789 | + | 0.718246i | \(0.255055\pi\) | |||||||
\(374\) | −0.500000 | − | 0.866025i | −0.0258544 | − | 0.0447811i | ||||
\(375\) | 6.00000 | − | 3.46410i | 0.309839 | − | 0.178885i | ||||
\(376\) | −2.46410 | −0.127076 | ||||||||
\(377\) | 10.3923 | − | 3.00000i | 0.535231 | − | 0.154508i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −14.3660 | + | 8.29423i | −0.737933 | + | 0.426046i | −0.821317 | − | 0.570472i | \(-0.806760\pi\) |
0.0833842 | + | 0.996517i | \(0.473427\pi\) | |||||||
\(380\) | −3.36603 | − | 5.83013i | −0.172673 | − | 0.299079i | ||||
\(381\) | 9.73205 | − | 16.8564i | 0.498588 | − | 0.863580i | ||||
\(382\) | 6.19615i | 0.317023i | ||||||||
\(383\) | −30.6506 | − | 17.6962i | −1.56617 | − | 0.904231i | −0.996609 | − | 0.0822852i | \(-0.973778\pi\) |
−0.569565 | − | 0.821946i | \(-0.692888\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0.732051i | 0.0373088i | ||||||||
\(386\) | 3.40192 | − | 5.89230i | 0.173153 | − | 0.299910i | ||||
\(387\) | −1.36603 | − | 2.36603i | −0.0694390 | − | 0.120272i | ||||
\(388\) | 2.36603 | − | 1.36603i | 0.120117 | − | 0.0693494i | ||||
\(389\) | −29.1769 | −1.47933 | −0.739664 | − | 0.672976i | \(-0.765016\pi\) | ||||
−0.739664 | + | 0.672976i | \(0.765016\pi\) | |||||||
\(390\) | −7.09808 | − | 6.83013i | −0.359425 | − | 0.345857i | ||||
\(391\) | −12.9282 | −0.653807 | ||||||||
\(392\) | 0.866025 | − | 0.500000i | 0.0437409 | − | 0.0252538i | ||||
\(393\) | 2.53590 | + | 4.39230i | 0.127919 | + | 0.221562i | ||||
\(394\) | −2.86603 | + | 4.96410i | −0.144388 | + | 0.250088i | ||||
\(395\) | 46.0526i | 2.31716i | ||||||||
\(396\) | 0.232051 | + | 0.133975i | 0.0116610 | + | 0.00673248i | ||||
\(397\) | 8.25833 | + | 4.76795i | 0.414474 | + | 0.239297i | 0.692710 | − | 0.721216i | \(-0.256417\pi\) |
−0.278236 | + | 0.960513i | \(0.589750\pi\) | |||||||
\(398\) | − | 6.19615i | − | 0.310585i | ||||||
\(399\) | 1.23205 | − | 2.13397i | 0.0616797 | − | 0.106832i | ||||
\(400\) | 1.23205 | + | 2.13397i | 0.0616025 | + | 0.106699i | ||||
\(401\) | 8.66025 | − | 5.00000i | 0.432472 | − | 0.249688i | −0.267927 | − | 0.963439i | \(-0.586339\pi\) |
0.700399 | + | 0.713751i | \(0.253005\pi\) | |||||||
\(402\) | −0.928203 | −0.0462946 | ||||||||
\(403\) | 33.8109 | + | 8.36603i | 1.68424 | + | 0.416741i | ||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | −2.36603 | + | 1.36603i | −0.117569 | + | 0.0678783i | ||||
\(406\) | −1.50000 | − | 2.59808i | −0.0744438 | − | 0.128940i | ||||
\(407\) | −0.633975 | + | 1.09808i | −0.0314250 | + | 0.0544296i | ||||
\(408\) | − | 3.73205i | − | 0.184764i | ||||||
\(409\) | −14.4904 | − | 8.36603i | −0.716503 | − | 0.413673i | 0.0969611 | − | 0.995288i | \(-0.469088\pi\) |
−0.813464 | + | 0.581615i | \(0.802421\pi\) | |||||||
\(410\) | −16.5622 | − | 9.56218i | −0.817948 | − | 0.472242i | ||||
\(411\) | − | 8.53590i | − | 0.421045i | ||||||
\(412\) | 0.901924 | − | 1.56218i | 0.0444346 | − | 0.0769630i | ||||
\(413\) | −6.46410 | − | 11.1962i | −0.318078 | − | 0.550927i | ||||
\(414\) | 3.00000 | − | 1.73205i | 0.147442 | − | 0.0851257i | ||||
\(415\) | 31.8564 | 1.56377 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | −6.12436 | −0.299911 | ||||||||
\(418\) | 0.571797 | − | 0.330127i | 0.0279675 | − | 0.0161470i | ||||
\(419\) | −2.09808 | − | 3.63397i | −0.102498 | − | 0.177531i | 0.810215 | − | 0.586132i | \(-0.199350\pi\) |
−0.912713 | + | 0.408601i | \(0.866017\pi\) | |||||||
\(420\) | −1.36603 | + | 2.36603i | −0.0666552 | + | 0.115450i | ||||
\(421\) | 6.39230i | 0.311542i | 0.987793 | + | 0.155771i | \(0.0497862\pi\) | ||||
−0.987793 | + | 0.155771i | \(0.950214\pi\) | |||||||
\(422\) | −10.2679 | − | 5.92820i | −0.499836 | − | 0.288580i | ||||
\(423\) | 2.13397 | + | 1.23205i | 0.103757 | + | 0.0599044i | ||||
\(424\) | 3.53590i | 0.171718i | ||||||||
\(425\) | −4.59808 | + | 7.96410i | −0.223039 | + | 0.386316i | ||||
\(426\) | 4.09808 | + | 7.09808i | 0.198552 | + | 0.343903i | ||||
\(427\) | −7.16025 | + | 4.13397i | −0.346509 | + | 0.200057i | ||||
\(428\) | 8.46410 | 0.409128 | ||||||||
\(429\) | 0.669873 | − | 0.696152i | 0.0323418 | − | 0.0336106i | ||||
\(430\) | 7.46410 | 0.359951 | ||||||||
\(431\) | 2.70577 | − | 1.56218i | 0.130332 | − | 0.0752475i | −0.433416 | − | 0.901194i | \(-0.642692\pi\) |
0.563749 | + | 0.825946i | \(0.309359\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −2.46410 | + | 4.26795i | −0.118417 | + | 0.205105i | −0.919141 | − | 0.393930i | \(-0.871115\pi\) |
0.800723 | + | 0.599034i | \(0.204449\pi\) | |||||||
\(434\) | − | 9.66025i | − | 0.463707i | ||||||
\(435\) | 7.09808 | + | 4.09808i | 0.340327 | + | 0.196488i | ||||
\(436\) | 11.8301 | + | 6.83013i | 0.566560 | + | 0.327104i | ||||
\(437\) | − | 8.53590i | − | 0.408327i | ||||||
\(438\) | −6.73205 | + | 11.6603i | −0.321670 | + | 0.557148i | ||||
\(439\) | 2.19615 | + | 3.80385i | 0.104817 | + | 0.181548i | 0.913663 | − | 0.406472i | \(-0.133241\pi\) |
−0.808847 | + | 0.588020i | \(0.799908\pi\) | |||||||
\(440\) | −0.633975 | + | 0.366025i | −0.0302236 | + | 0.0174496i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −13.0622 | − | 3.23205i | −0.621304 | − | 0.153733i | ||||
\(443\) | −10.6077 | −0.503987 | −0.251993 | − | 0.967729i | \(-0.581086\pi\) | ||||
−0.251993 | + | 0.967729i | \(0.581086\pi\) | |||||||
\(444\) | −4.09808 | + | 2.36603i | −0.194486 | + | 0.112287i | ||||
\(445\) | −0.633975 | − | 1.09808i | −0.0300533 | − | 0.0520538i | ||||
\(446\) | 6.19615 | − | 10.7321i | 0.293396 | − | 0.508177i | ||||
\(447\) | 5.07180i | 0.239888i | ||||||||
\(448\) | 0.866025 | + | 0.500000i | 0.0409159 | + | 0.0236228i | ||||
\(449\) | 6.29423 | + | 3.63397i | 0.297043 | + | 0.171498i | 0.641114 | − | 0.767446i | \(-0.278473\pi\) |
−0.344071 | + | 0.938944i | \(0.611806\pi\) | |||||||
\(450\) | − | 2.46410i | − | 0.116159i | ||||||
\(451\) | 0.937822 | − | 1.62436i | 0.0441603 | − | 0.0764879i | ||||
\(452\) | 0.0980762 | + | 0.169873i | 0.00461312 | + | 0.00799015i | ||||
\(453\) | −2.42820 | + | 1.40192i | −0.114087 | + | 0.0658681i | ||||
\(454\) | −15.4641 | −0.725766 | ||||||||
\(455\) | 7.09808 | + | 6.83013i | 0.332763 | + | 0.320201i | ||||
\(456\) | 2.46410 | 0.115392 | ||||||||
\(457\) | 30.1244 | − | 17.3923i | 1.40916 | − | 0.813578i | 0.413851 | − | 0.910345i | \(-0.364183\pi\) |
0.995307 | + | 0.0967670i | \(0.0308502\pi\) | |||||||
\(458\) | 12.1603 | + | 21.0622i | 0.568211 | + | 0.984171i | ||||
\(459\) | −1.86603 | + | 3.23205i | −0.0870986 | + | 0.150859i | ||||
\(460\) | 9.46410i | 0.441266i | ||||||||
\(461\) | −24.0000 | − | 13.8564i | −1.11779 | − | 0.645357i | −0.176955 | − | 0.984219i | \(-0.556625\pi\) |
−0.940836 | + | 0.338862i | \(0.889958\pi\) | |||||||
\(462\) | −0.232051 | − | 0.133975i | −0.0107960 | − | 0.00623306i | ||||
\(463\) | 9.19615i | 0.427381i | 0.976901 | + | 0.213691i | \(0.0685485\pi\) | ||||
−0.976901 | + | 0.213691i | \(0.931452\pi\) | |||||||
\(464\) | 1.50000 | − | 2.59808i | 0.0696358 | − | 0.120613i | ||||
\(465\) | 13.1962 | + | 22.8564i | 0.611957 | + | 1.05994i | ||||
\(466\) | 7.09808 | − | 4.09808i | 0.328812 | − | 0.189840i | ||||
\(467\) | −17.8564 | −0.826296 | −0.413148 | − | 0.910664i | \(-0.635571\pi\) | ||||
−0.413148 | + | 0.910664i | \(0.635571\pi\) | |||||||
\(468\) | 3.46410 | − | 1.00000i | 0.160128 | − | 0.0462250i | ||||
\(469\) | 0.928203 | 0.0428604 | ||||||||
\(470\) | −5.83013 | + | 3.36603i | −0.268924 | + | 0.155263i | ||||
\(471\) | −4.26795 | − | 7.39230i | −0.196657 | − | 0.340619i | ||||
\(472\) | 6.46410 | − | 11.1962i | 0.297534 | − | 0.515345i | ||||
\(473\) | 0.732051i | 0.0336597i | ||||||||
\(474\) | −14.5981 | − | 8.42820i | −0.670512 | − | 0.387120i | ||||
\(475\) | −5.25833 | − | 3.03590i | −0.241269 | − | 0.139297i | ||||
\(476\) | 3.73205i | 0.171058i | ||||||||
\(477\) | 1.76795 | − | 3.06218i | 0.0809488 | − | 0.140207i | ||||
\(478\) | −12.0981 | − | 20.9545i | −0.553353 | − | 0.958436i | ||||
\(479\) | −9.18653 | + | 5.30385i | −0.419743 | + | 0.242339i | −0.694968 | − | 0.719041i | \(-0.744581\pi\) |
0.275224 | + | 0.961380i | \(0.411248\pi\) | |||||||
\(480\) | −2.73205 | −0.124700 | ||||||||
\(481\) | 4.73205 | + | 16.3923i | 0.215763 | + | 0.747425i | ||||
\(482\) | −28.7846 | −1.31110 | ||||||||
\(483\) | −3.00000 | + | 1.73205i | −0.136505 | + | 0.0788110i | ||||
\(484\) | 5.46410 | + | 9.46410i | 0.248368 | + | 0.430186i | ||||
\(485\) | 3.73205 | − | 6.46410i | 0.169464 | − | 0.293520i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −9.35641 | − | 5.40192i | −0.423979 | − | 0.244785i | 0.272799 | − | 0.962071i | \(-0.412051\pi\) |
−0.696778 | + | 0.717286i | \(0.745384\pi\) | |||||||
\(488\) | −7.16025 | − | 4.13397i | −0.324129 | − | 0.187136i | ||||
\(489\) | 18.1962i | 0.822858i | ||||||||
\(490\) | 1.36603 | − | 2.36603i | 0.0617107 | − | 0.106886i | ||||
\(491\) | −6.12436 | − | 10.6077i | −0.276388 | − | 0.478719i | 0.694096 | − | 0.719882i | \(-0.255804\pi\) |
−0.970484 | + | 0.241164i | \(0.922471\pi\) | |||||||
\(492\) | 6.06218 | − | 3.50000i | 0.273304 | − | 0.157792i | ||||
\(493\) | 11.1962 | 0.504249 | ||||||||
\(494\) | 2.13397 | − | 8.62436i | 0.0960121 | − | 0.388028i | ||||
\(495\) | 0.732051 | 0.0329032 | ||||||||
\(496\) | 8.36603 | − | 4.83013i | 0.375646 | − | 0.216879i | ||||
\(497\) | −4.09808 | − | 7.09808i | −0.183824 | − | 0.318392i | ||||
\(498\) | −5.83013 | + | 10.0981i | −0.261254 | + | 0.452506i | ||||
\(499\) | 38.9808i | 1.74502i | 0.488598 | + | 0.872509i | \(0.337509\pi\) | ||||
−0.488598 | + | 0.872509i | \(0.662491\pi\) | |||||||
\(500\) | −6.00000 | − | 3.46410i | −0.268328 | − | 0.154919i | ||||
\(501\) | 18.9282 | + | 10.9282i | 0.845650 | + | 0.488236i | ||||
\(502\) | − | 7.80385i | − | 0.348303i | ||||||
\(503\) | −15.8564 | + | 27.4641i | −0.707002 | + | 1.22456i | 0.258962 | + | 0.965888i | \(0.416620\pi\) |
−0.965964 | + | 0.258676i | \(0.916714\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | −23.6603 | + | 13.6603i | −1.05287 | + | 0.607873i | ||||
\(506\) | −0.928203 | −0.0412637 | ||||||||
\(507\) | −0.500000 | − | 12.9904i | −0.0222058 | − | 0.576923i | ||||
\(508\) | −19.4641 | −0.863580 | ||||||||
\(509\) | −10.4378 | + | 6.02628i | −0.462648 | + | 0.267110i | −0.713157 | − | 0.701004i | \(-0.752735\pi\) |
0.250509 | + | 0.968114i | \(0.419402\pi\) | |||||||
\(510\) | −5.09808 | − | 8.83013i | −0.225747 | − | 0.391005i | ||||
\(511\) | 6.73205 | − | 11.6603i | 0.297808 | − | 0.515819i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.13397 | − | 1.23205i | −0.0942173 | − | 0.0543964i | ||||
\(514\) | −23.4282 | − | 13.5263i | −1.03337 | − | 0.596619i | ||||
\(515\) | − | 4.92820i | − | 0.217163i | ||||||
\(516\) | −1.36603 | + | 2.36603i | −0.0601359 | + | 0.104158i | ||||
\(517\) | −0.330127 | − | 0.571797i | −0.0145190 | − | 0.0251476i | ||||
\(518\) | 4.09808 | − | 2.36603i | 0.180059 | − | 0.103957i | ||||
\(519\) | 17.2679 | 0.757979 | ||||||||
\(520\) | −2.36603 | + | 9.56218i | −0.103757 | + | 0.419329i | ||||
\(521\) | −5.73205 | −0.251126 | −0.125563 | − | 0.992086i | \(-0.540074\pi\) | ||||
−0.125563 | + | 0.992086i | \(0.540074\pi\) | |||||||
\(522\) | −2.59808 | + | 1.50000i | −0.113715 | + | 0.0656532i | ||||
\(523\) | 14.5981 | + | 25.2846i | 0.638329 | + | 1.10562i | 0.985799 | + | 0.167928i | \(0.0537075\pi\) |
−0.347470 | + | 0.937691i | \(0.612959\pi\) | |||||||
\(524\) | 2.53590 | − | 4.39230i | 0.110781 | − | 0.191879i | ||||
\(525\) | 2.46410i | 0.107542i | ||||||||
\(526\) | 13.2224 | + | 7.63397i | 0.576525 | + | 0.332857i | ||||
\(527\) | 31.2224 | + | 18.0263i | 1.36007 | + | 0.785237i | ||||
\(528\) | − | 0.267949i | − | 0.0116610i | ||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | 4.83013 | + | 8.36603i | 0.209807 | + | 0.363397i | ||||
\(531\) | −11.1962 | + | 6.46410i | −0.485872 | + | 0.280518i | ||||
\(532\) | −2.46410 | −0.106832 | ||||||||
\(533\) | −7.00000 | − | 24.2487i | −0.303204 | − | 1.05033i | ||||
\(534\) | 0.464102 | 0.0200836 | ||||||||
\(535\) | 20.0263 | − | 11.5622i | 0.865812 | − | 0.499877i | ||||
\(536\) | 0.464102 | + | 0.803848i | 0.0200461 | + | 0.0347209i | ||||
\(537\) | −0.803848 | + | 1.39230i | −0.0346886 | + | 0.0600824i | ||||
\(538\) | 31.7128i | 1.36724i | ||||||||
\(539\) | 0.232051 | + | 0.133975i | 0.00999514 | + | 0.00577069i | ||||
\(540\) | 2.36603 | + | 1.36603i | 0.101818 | + | 0.0587844i | ||||
\(541\) | 19.8038i | 0.851434i | 0.904856 | + | 0.425717i | \(0.139978\pi\) | ||||
−0.904856 | + | 0.425717i | \(0.860022\pi\) | |||||||
\(542\) | 11.7583 | − | 20.3660i | 0.505064 | − | 0.874796i | ||||
\(543\) | 4.59808 | + | 7.96410i | 0.197322 | + | 0.341772i | ||||
\(544\) | −3.23205 | + | 1.86603i | −0.138573 | + | 0.0800052i | ||||
\(545\) | 37.3205 | 1.59863 | ||||||||
\(546\) | −3.46410 | + | 1.00000i | −0.148250 | + | 0.0427960i | ||||
\(547\) | −37.1244 | −1.58732 | −0.793661 | − | 0.608360i | \(-0.791828\pi\) | ||||
−0.793661 | + | 0.608360i | \(0.791828\pi\) | |||||||
\(548\) | −7.39230 | + | 4.26795i | −0.315784 | + | 0.182318i | ||||
\(549\) | 4.13397 | + | 7.16025i | 0.176434 | + | 0.305592i | ||||
\(550\) | −0.330127 | + | 0.571797i | −0.0140767 | + | 0.0243815i | ||||
\(551\) | 7.39230i | 0.314923i | ||||||||
\(552\) | −3.00000 | − | 1.73205i | −0.127688 | − | 0.0737210i | ||||
\(553\) | 14.5981 | + | 8.42820i | 0.620773 | + | 0.358404i | ||||
\(554\) | 5.60770i | 0.238248i | ||||||||
\(555\) | −6.46410 | + | 11.1962i | −0.274386 | + | 0.475250i | ||||
\(556\) | 3.06218 | + | 5.30385i | 0.129865 | + | 0.224933i | ||||
\(557\) | −16.7487 | + | 9.66987i | −0.709666 | + | 0.409726i | −0.810937 | − | 0.585133i | \(-0.801042\pi\) |
0.101272 | + | 0.994859i | \(0.467709\pi\) | |||||||
\(558\) | −9.66025 | −0.408951 | ||||||||
\(559\) | 7.09808 | + | 6.83013i | 0.300217 | + | 0.288884i | ||||
\(560\) | 2.73205 | 0.115450 | ||||||||
\(561\) | 0.866025 | − | 0.500000i | 0.0365636 | − | 0.0211100i | ||||
\(562\) | 3.90192 | + | 6.75833i | 0.164593 | + | 0.285083i | ||||
\(563\) | −18.3660 | + | 31.8109i | −0.774036 | + | 1.34067i | 0.161299 | + | 0.986906i | \(0.448432\pi\) |
−0.935335 | + | 0.353764i | \(0.884902\pi\) | |||||||
\(564\) | − | 2.46410i | − | 0.103757i | ||||||
\(565\) | 0.464102 | + | 0.267949i | 0.0195249 | + | 0.0112727i | ||||
\(566\) | −7.85641 | − | 4.53590i | −0.330229 | − | 0.190658i | ||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 4.09808 | − | 7.09808i | 0.171951 | − | 0.297829i | ||||
\(569\) | 9.63397 | + | 16.6865i | 0.403877 | + | 0.699536i | 0.994190 | − | 0.107639i | \(-0.0343290\pi\) |
−0.590313 | + | 0.807175i | \(0.700996\pi\) | |||||||
\(570\) | 5.83013 | − | 3.36603i | 0.244197 | − | 0.140987i | ||||
\(571\) | −30.1962 | −1.26367 | −0.631835 | − | 0.775103i | \(-0.717698\pi\) | ||||
−0.631835 | + | 0.775103i | \(0.717698\pi\) | |||||||
\(572\) | −0.937822 | − | 0.232051i | −0.0392123 | − | 0.00970253i | ||||
\(573\) | −6.19615 | −0.258848 | ||||||||
\(574\) | −6.06218 | + | 3.50000i | −0.253030 | + | 0.146087i | ||||
\(575\) | 4.26795 | + | 7.39230i | 0.177986 | + | 0.308280i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 16.7321i | − | 0.696564i | −0.937390 | − | 0.348282i | \(-0.886765\pi\) | ||
0.937390 | − | 0.348282i | \(-0.113235\pi\) | |||||||
\(578\) | 2.66025 | + | 1.53590i | 0.110652 | + | 0.0638850i | ||||
\(579\) | 5.89230 | + | 3.40192i | 0.244876 | + | 0.141379i | ||||
\(580\) | − | 8.19615i | − | 0.340327i | ||||||
\(581\) | 5.83013 | − | 10.0981i | 0.241874 | − | 0.418939i | ||||
\(582\) | 1.36603 | + | 2.36603i | 0.0566236 | + | 0.0980749i | ||||
\(583\) | −0.820508 | + | 0.473721i | −0.0339820 | + | 0.0196195i | ||||
\(584\) | 13.4641 | 0.557148 | ||||||||
\(585\) | 6.83013 | − | 7.09808i | 0.282391 | − | 0.293469i | ||||
\(586\) | −28.7846 | −1.18908 | ||||||||
\(587\) | −35.8301 | + | 20.6865i | −1.47887 | + | 0.853825i | −0.999714 | − | 0.0239066i | \(-0.992390\pi\) |
−0.479153 | + | 0.877731i | \(0.659056\pi\) | |||||||
\(588\) | 0.500000 | + | 0.866025i | 0.0206197 | + | 0.0357143i | ||||
\(589\) | −11.9019 | + | 20.6147i | −0.490410 | + | 0.849415i | ||||
\(590\) | − | 35.3205i | − | 1.45412i | ||||||
\(591\) | −4.96410 | − | 2.86603i | −0.204196 | − | 0.117893i | ||||
\(592\) | 4.09808 | + | 2.36603i | 0.168430 | + | 0.0972430i | ||||
\(593\) | 48.3205i | 1.98429i | 0.125111 | + | 0.992143i | \(0.460071\pi\) | ||||
−0.125111 | + | 0.992143i | \(0.539929\pi\) | |||||||
\(594\) | −0.133975 | + | 0.232051i | −0.00549704 | + | 0.00952116i | ||||
\(595\) | 5.09808 | + | 8.83013i | 0.209001 | + | 0.362000i | ||||
\(596\) | 4.39230 | − | 2.53590i | 0.179916 | − | 0.103874i | ||||
\(597\) | 6.19615 | 0.253592 | ||||||||
\(598\) | −8.66025 | + | 9.00000i | −0.354144 | + | 0.368037i | ||||
\(599\) | 33.7128 | 1.37747 | 0.688734 | − | 0.725014i | \(-0.258167\pi\) | ||||
0.688734 | + | 0.725014i | \(0.258167\pi\) | |||||||
\(600\) | −2.13397 | + | 1.23205i | −0.0871191 | + | 0.0502983i | ||||
\(601\) | 18.5622 | + | 32.1506i | 0.757167 | + | 1.31145i | 0.944290 | + | 0.329115i | \(0.106750\pi\) |
−0.187123 | + | 0.982337i | \(0.559916\pi\) | |||||||
\(602\) | 1.36603 | − | 2.36603i | 0.0556750 | − | 0.0964320i | ||||
\(603\) | − | 0.928203i | − | 0.0377994i | ||||||
\(604\) | 2.42820 | + | 1.40192i | 0.0988022 | + | 0.0570435i | ||||
\(605\) | 25.8564 | + | 14.9282i | 1.05121 | + | 0.606918i | ||||
\(606\) | − | 10.0000i | − | 0.406222i | ||||||
\(607\) | 12.9545 | − | 22.4378i | 0.525806 | − | 0.910723i | −0.473742 | − | 0.880664i | \(-0.657097\pi\) |
0.999548 | − | 0.0300594i | \(-0.00956963\pi\) | |||||||
\(608\) | −1.23205 | − | 2.13397i | −0.0499663 | − | 0.0865441i | ||||
\(609\) | 2.59808 | − | 1.50000i | 0.105279 | − | 0.0607831i | ||||
\(610\) | −22.5885 | −0.914580 | ||||||||
\(611\) | −8.62436 | − | 2.13397i | −0.348904 | − | 0.0863314i | ||||
\(612\) | 3.73205 | 0.150859 | ||||||||
\(613\) | −12.2487 | + | 7.07180i | −0.494721 | + | 0.285627i | −0.726531 | − | 0.687134i | \(-0.758869\pi\) |
0.231810 | + | 0.972761i | \(0.425535\pi\) | |||||||
\(614\) | 3.89230 | + | 6.74167i | 0.157081 | + | 0.272072i | ||||
\(615\) | 9.56218 | − | 16.5622i | 0.385584 | − | 0.667851i | ||||
\(616\) | 0.267949i | 0.0107960i | ||||||||
\(617\) | 3.04552 | + | 1.75833i | 0.122608 | + | 0.0707877i | 0.560050 | − | 0.828459i | \(-0.310782\pi\) |
−0.437442 | + | 0.899247i | \(0.644115\pi\) | |||||||
\(618\) | 1.56218 | + | 0.901924i | 0.0628400 | + | 0.0362807i | ||||
\(619\) | − | 32.3205i | − | 1.29907i | −0.760331 | − | 0.649535i | \(-0.774963\pi\) | ||
0.760331 | − | 0.649535i | \(-0.225037\pi\) | |||||||
\(620\) | 13.1962 | − | 22.8564i | 0.529970 | − | 0.917935i | ||||
\(621\) | 1.73205 | + | 3.00000i | 0.0695048 | + | 0.120386i | ||||
\(622\) | 7.62436 | − | 4.40192i | 0.305709 | − | 0.176501i | ||||
\(623\) | −0.464102 | −0.0185938 | ||||||||
\(624\) | −2.59808 | − | 2.50000i | −0.104006 | − | 0.100080i | ||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 10.5622 | − | 6.09808i | 0.422150 | − | 0.243728i | ||||
\(627\) | 0.330127 | + | 0.571797i | 0.0131840 | + | 0.0228354i | ||||
\(628\) | −4.26795 | + | 7.39230i | −0.170310 | + | 0.294985i | ||||
\(629\) | 17.6603i | 0.704160i | ||||||||
\(630\) | −2.36603 | − | 1.36603i | −0.0942647 | − | 0.0544238i | ||||
\(631\) | −31.1603 | − | 17.9904i | −1.24047 | − | 0.716186i | −0.271280 | − | 0.962500i | \(-0.587447\pi\) |
−0.969190 | + | 0.246315i | \(0.920780\pi\) | |||||||
\(632\) | 16.8564i | 0.670512i | ||||||||
\(633\) | 5.92820 | − | 10.2679i | 0.235625 | − | 0.408114i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | −46.0526 | + | 26.5885i | −1.82754 | + | 1.05513i | ||||
\(636\) | −3.53590 | −0.140207 | ||||||||
\(637\) | 3.46410 | − | 1.00000i | 0.137253 | − | 0.0396214i | ||||
\(638\) | 0.803848 | 0.0318246 | ||||||||
\(639\) | −7.09808 | + | 4.09808i | −0.280796 | + | 0.162117i | ||||
\(640\) | 1.36603 | + | 2.36603i | 0.0539969 | + | 0.0935254i | ||||
\(641\) | 16.1244 | − | 27.9282i | 0.636874 | − | 1.10310i | −0.349241 | − | 0.937033i | \(-0.613561\pi\) |
0.986115 | − | 0.166065i | \(-0.0531061\pi\) | |||||||
\(642\) | 8.46410i | 0.334051i | ||||||||
\(643\) | −31.4545 | − | 18.1603i | −1.24044 | − | 0.716171i | −0.271259 | − | 0.962506i | \(-0.587440\pi\) |
−0.969185 | + | 0.246336i | \(0.920773\pi\) | |||||||
\(644\) | 3.00000 | + | 1.73205i | 0.118217 | + | 0.0682524i | ||||
\(645\) | 7.46410i | 0.293899i | ||||||||
\(646\) | 4.59808 | − | 7.96410i | 0.180909 | − | 0.313343i | ||||
\(647\) | −0.866025 | − | 1.50000i | −0.0340470 | − | 0.0589711i | 0.848500 | − | 0.529196i | \(-0.177506\pi\) |
−0.882547 | + | 0.470225i | \(0.844173\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 3.46410 | 0.135978 | ||||||||
\(650\) | 2.46410 | + | 8.53590i | 0.0966500 | + | 0.334805i | ||||
\(651\) | 9.66025 | 0.378615 | ||||||||
\(652\) | 15.7583 | − | 9.09808i | 0.617144 | − | 0.356308i | ||||
\(653\) | −23.1603 | − | 40.1147i | −0.906331 | − | 1.56981i | −0.819121 | − | 0.573621i | \(-0.805538\pi\) |
−0.0872099 | − | 0.996190i | \(-0.527795\pi\) | |||||||
\(654\) | −6.83013 | + | 11.8301i | −0.267079 | + | 0.462595i | ||||
\(655\) | − | 13.8564i | − | 0.541415i | ||||||
\(656\) | −6.06218 | − | 3.50000i | −0.236688 | − | 0.136652i | ||||
\(657\) | −11.6603 | − | 6.73205i | −0.454910 | − | 0.262642i | ||||
\(658\) | 2.46410i | 0.0960607i | ||||||||
\(659\) | −10.0359 | + | 17.3827i | −0.390943 | + | 0.677133i | −0.992574 | − | 0.121641i | \(-0.961184\pi\) |
0.601631 | + | 0.798774i | \(0.294518\pi\) | |||||||
\(660\) | −0.366025 | − | 0.633975i | −0.0142475 | − | 0.0246774i | ||||
\(661\) | −41.9090 | + | 24.1962i | −1.63007 | + | 0.941121i | −0.646000 | + | 0.763337i | \(0.723560\pi\) |
−0.984070 | + | 0.177784i | \(0.943107\pi\) | |||||||
\(662\) | 3.07180 | 0.119389 | ||||||||
\(663\) | 3.23205 | − | 13.0622i | 0.125522 | − | 0.507293i | ||||
\(664\) | 11.6603 | 0.452506 | ||||||||
\(665\) | −5.83013 | + | 3.36603i | −0.226083 | + | 0.130529i | ||||
\(666\) | −2.36603 | − | 4.09808i | −0.0916816 | − | 0.158797i | ||||
\(667\) | 5.19615 | − | 9.00000i | 0.201196 | − | 0.348481i | ||||
\(668\) | − | 21.8564i | − | 0.845650i | ||||||
\(669\) | 10.7321 | + | 6.19615i | 0.414925 | + | 0.239557i | ||||
\(670\) | 2.19615 | + | 1.26795i | 0.0848448 | + | 0.0489852i | ||||
\(671\) | − | 2.21539i | − | 0.0855242i | ||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | −17.0359 | − | 29.5070i | −0.656686 | − | 1.13741i | −0.981468 | − | 0.191624i | \(-0.938625\pi\) |
0.324783 | − | 0.945789i | \(-0.394709\pi\) | |||||||
\(674\) | 11.9378 | − | 6.89230i | 0.459828 | − | 0.265482i | ||||
\(675\) | 2.46410 | 0.0948433 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | 45.7654 | 1.75891 | 0.879453 | − | 0.475986i | \(-0.157909\pi\) | ||||
0.879453 | + | 0.475986i | \(0.157909\pi\) | |||||||
\(678\) | −0.169873 | + | 0.0980762i | −0.00652393 | + | 0.00376659i | ||||
\(679\) | −1.36603 | − | 2.36603i | −0.0524232 | − | 0.0907997i | ||||
\(680\) | −5.09808 | + | 8.83013i | −0.195502 | + | 0.338620i | ||||
\(681\) | − | 15.4641i | − | 0.592586i | ||||||
\(682\) | 2.24167 | + | 1.29423i | 0.0858380 | + | 0.0495586i | ||||
\(683\) | 4.85641 | + | 2.80385i | 0.185825 | + | 0.107286i | 0.590027 | − | 0.807384i | \(-0.299117\pi\) |
−0.404201 | + | 0.914670i | \(0.632451\pi\) | |||||||
\(684\) | 2.46410i | 0.0942173i | ||||||||
\(685\) | −11.6603 | + | 20.1962i | −0.445515 | + | 0.771655i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | −21.0622 | + | 12.1603i | −0.803572 | + | 0.463943i | ||||
\(688\) | 2.73205 | 0.104158 | ||||||||
\(689\) | −3.06218 | + | 12.3756i | −0.116660 | + | 0.471475i | ||||
\(690\) | −9.46410 | −0.360292 | ||||||||
\(691\) | 0.679492 | − | 0.392305i | 0.0258491 | − | 0.0149240i | −0.487020 | − | 0.873391i | \(-0.661916\pi\) |
0.512869 | + | 0.858467i | \(0.328583\pi\) | |||||||
\(692\) | −8.63397 | − | 14.9545i | −0.328214 | − | 0.568484i | ||||
\(693\) | 0.133975 | − | 0.232051i | 0.00508927 | − | 0.00881488i | ||||
\(694\) | − | 4.85641i | − | 0.184347i | ||||||
\(695\) | 14.4904 | + | 8.36603i | 0.549651 | + | 0.317341i | ||||
\(696\) | 2.59808 | + | 1.50000i | 0.0984798 | + | 0.0568574i | ||||
\(697\) | − | 26.1244i | − | 0.989531i | ||||||
\(698\) | 15.8564 | − | 27.4641i | 0.600174 | − | 1.03953i | ||||
\(699\) | 4.09808 | + | 7.09808i | 0.155003 | + | 0.268474i | ||||
\(700\) | 2.13397 | − | 1.23205i | 0.0806567 | − | 0.0465671i | ||||
\(701\) | 20.3205 | 0.767495 | 0.383747 | − | 0.923438i | \(-0.374633\pi\) | ||||
0.383747 | + | 0.923438i | \(0.374633\pi\) | |||||||
\(702\) | 1.00000 | + | 3.46410i | 0.0377426 | + | 0.130744i | ||||
\(703\) | −11.6603 | −0.439775 | ||||||||
\(704\) | −0.232051 | + | 0.133975i | −0.00874574 | + | 0.00504936i | ||||
\(705\) | −3.36603 | − | 5.83013i | −0.126772 | − | 0.219575i | ||||
\(706\) | −2.73205 | + | 4.73205i | −0.102822 | + | 0.178093i | ||||
\(707\) | 10.0000i | 0.376089i | ||||||||
\(708\) | 11.1962 | + | 6.46410i | 0.420777 | + | 0.242936i | ||||
\(709\) | 12.1699 | + | 7.02628i | 0.457049 | + | 0.263877i | 0.710803 | − | 0.703391i | \(-0.248332\pi\) |
−0.253754 | + | 0.967269i | \(0.581665\pi\) | |||||||
\(710\) | − | 22.3923i | − | 0.840368i | ||||||
\(711\) | 8.42820 | − | 14.5981i | 0.316082 | − | 0.547471i | ||||
\(712\) | −0.232051 | − | 0.401924i | −0.00869647 | − | 0.0150627i | ||||
\(713\) | 28.9808 | − | 16.7321i | 1.08534 | − | 0.626620i | ||||
\(714\) | −3.73205 | −0.139668 | ||||||||
\(715\) | −2.53590 | + | 0.732051i | −0.0948372 | + | 0.0273771i | ||||
\(716\) | 1.60770 | 0.0600824 | ||||||||
\(717\) | 20.9545 | − | 12.0981i | 0.782559 | − | 0.451811i | ||||
\(718\) | 13.0981 | + | 22.6865i | 0.488816 | + | 0.846654i | ||||
\(719\) | −17.5263 | + | 30.3564i | −0.653620 | + | 1.13210i | 0.328618 | + | 0.944463i | \(0.393417\pi\) |
−0.982238 | + | 0.187640i | \(0.939916\pi\) | |||||||
\(720\) | − | 2.73205i | − | 0.101818i | ||||||
\(721\) | −1.56218 | − | 0.901924i | −0.0581785 | − | 0.0335894i | ||||
\(722\) | −11.1962 | − | 6.46410i | −0.416678 | − | 0.240569i | ||||
\(723\) | − | 28.7846i | − | 1.07051i | ||||||
\(724\) | 4.59808 | − | 7.96410i | 0.170886 | − | 0.295984i | ||||
\(725\) | −3.69615 | − | 6.40192i | −0.137272 | − | 0.237761i | ||||
\(726\) | −9.46410 | + | 5.46410i | −0.351246 | + | 0.202792i | ||||
\(727\) | 5.46410 | 0.202652 | 0.101326 | − | 0.994853i | \(-0.467691\pi\) | ||||
0.101326 | + | 0.994853i | \(0.467691\pi\) | |||||||
\(728\) | 2.59808 | + | 2.50000i | 0.0962911 | + | 0.0926562i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 31.8564 | − | 18.3923i | 1.17906 | − | 0.680730i | ||||
\(731\) | 5.09808 | + | 8.83013i | 0.188559 | + | 0.326594i | ||||
\(732\) | 4.13397 | − | 7.16025i | 0.152796 | − | 0.264651i | ||||
\(733\) | 20.8564i | 0.770349i | 0.922844 | + | 0.385174i | \(0.125859\pi\) | ||||
−0.922844 | + | 0.385174i | \(0.874141\pi\) | |||||||
\(734\) | 27.9282 | + | 16.1244i | 1.03085 | + | 0.595161i | ||||
\(735\) | 2.36603 | + | 1.36603i | 0.0872722 | + | 0.0503866i | ||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | −0.124356 | + | 0.215390i | −0.00458070 | + | 0.00793400i | ||||
\(738\) | 3.50000 | + | 6.06218i | 0.128837 | + | 0.223152i | ||||
\(739\) | 12.4641 | − | 7.19615i | 0.458499 | − | 0.264715i | −0.252914 | − | 0.967489i | \(-0.581389\pi\) |
0.711413 | + | 0.702774i | \(0.248056\pi\) | |||||||
\(740\) | 12.9282 | 0.475250 | ||||||||
\(741\) | 8.62436 | + | 2.13397i | 0.316824 | + | 0.0783935i | ||||
\(742\) | 3.53590 | 0.129807 | ||||||||
\(743\) | −22.0981 | + | 12.7583i | −0.810700 | + | 0.468058i | −0.847199 | − | 0.531276i | \(-0.821713\pi\) |
0.0364990 | + | 0.999334i | \(0.488379\pi\) | |||||||
\(744\) | 4.83013 | + | 8.36603i | 0.177081 | + | 0.306713i | ||||
\(745\) | 6.92820 | − | 12.0000i | 0.253830 | − | 0.439646i | ||||
\(746\) | 10.5885i | 0.387671i | ||||||||
\(747\) | −10.0981 | − | 5.83013i | −0.369469 | − | 0.213313i | ||||
\(748\) | −0.866025 | − | 0.500000i | −0.0316650 | − | 0.0182818i | ||||
\(749\) | − | 8.46410i | − | 0.309272i | ||||||
\(750\) | 3.46410 | − | 6.00000i | 0.126491 | − | 0.219089i | ||||
\(751\) | 10.4282 | + | 18.0622i | 0.380531 | + | 0.659098i | 0.991138 | − | 0.132835i | \(-0.0424081\pi\) |
−0.610608 | + | 0.791933i | \(0.709075\pi\) | |||||||
\(752\) | −2.13397 | + | 1.23205i | −0.0778180 | + | 0.0449283i | ||||
\(753\) | 7.80385 | 0.284388 | ||||||||
\(754\) | 7.50000 | − | 7.79423i | 0.273134 | − | 0.283849i | ||||
\(755\) | 7.66025 | 0.278785 | ||||||||
\(756\) | 0.866025 | − | 0.500000i | 0.0314970 | − | 0.0181848i | ||||
\(757\) | −0.0262794 | − | 0.0455173i | −0.000955143 | − | 0.00165436i | 0.865547 | − | 0.500827i | \(-0.166971\pi\) |
−0.866503 | + | 0.499173i | \(0.833637\pi\) | |||||||
\(758\) | −8.29423 | + | 14.3660i | −0.301260 | + | 0.521798i | ||||
\(759\) | − | 0.928203i | − | 0.0336916i | ||||||
\(760\) | −5.83013 | − | 3.36603i | −0.211481 | − | 0.122099i | ||||
\(761\) | 30.5885 | + | 17.6603i | 1.10883 | + | 0.640184i | 0.938526 | − | 0.345208i | \(-0.112192\pi\) |
0.170304 | + | 0.985391i | \(0.445525\pi\) | |||||||
\(762\) | − | 19.4641i | − | 0.705110i | ||||||
\(763\) | 6.83013 | − | 11.8301i | 0.247267 | − | 0.428279i | ||||
\(764\) | 3.09808 | + | 5.36603i | 0.112084 | + | 0.194136i | ||||
\(765\) | 8.83013 | − | 5.09808i | 0.319254 | − | 0.184321i | ||||
\(766\) | −35.3923 | −1.27878 | ||||||||
\(767\) | 32.3205 | − | 33.5885i | 1.16703 | − | 1.21281i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 29.8301 | − | 17.2224i | 1.07570 | − | 0.621057i | 0.145968 | − | 0.989289i | \(-0.453370\pi\) |
0.929734 | + | 0.368233i | \(0.120037\pi\) | |||||||
\(770\) | 0.366025 | + | 0.633975i | 0.0131906 | + | 0.0228469i | ||||
\(771\) | 13.5263 | − | 23.4282i | 0.487137 | − | 0.843746i | ||||
\(772\) | − | 6.80385i | − | 0.244876i | ||||||
\(773\) | −18.7128 | − | 10.8038i | −0.673053 | − | 0.388587i | 0.124179 | − | 0.992260i | \(-0.460370\pi\) |
−0.797232 | + | 0.603672i | \(0.793704\pi\) | |||||||
\(774\) | −2.36603 | − | 1.36603i | −0.0850450 | − | 0.0491008i | ||||
\(775\) | − | 23.8038i | − | 0.855059i | ||||||
\(776\) | 1.36603 | − | 2.36603i | 0.0490375 | − | 0.0849354i | ||||
\(777\) | 2.36603 | + | 4.09808i | 0.0848807 | + | 0.147018i | ||||
\(778\) | −25.2679 | + | 14.5885i | −0.905900 | + | 0.523022i | ||||
\(779\) | 17.2487 | 0.617999 | ||||||||
\(780\) | −9.56218 | − | 2.36603i | −0.342381 | − | 0.0847173i | ||||
\(781\) | 2.19615 | 0.0785845 | ||||||||
\(782\) | −11.1962 | + | 6.46410i | −0.400374 | + | 0.231156i | ||||
\(783\) | −1.50000 | − | 2.59808i | −0.0536056 | − | 0.0928477i | ||||
\(784\) | 0.500000 | − | 0.866025i | 0.0178571 | − | 0.0309295i | ||||
\(785\) | 23.3205i | 0.832345i | ||||||||
\(786\) | 4.39230 | + | 2.53590i | 0.156668 | + | 0.0904525i | ||||
\(787\) | 12.3109 | + | 7.10770i | 0.438836 | + | 0.253362i | 0.703104 | − | 0.711087i | \(-0.251797\pi\) |
−0.264268 | + | 0.964449i | \(0.585130\pi\) | |||||||
\(788\) | 5.73205i | 0.204196i | ||||||||
\(789\) | −7.63397 | + | 13.2224i | −0.271777 | + | 0.470731i | ||||
\(790\) | 23.0263 | + | 39.8827i | 0.819238 | + | 1.41896i | ||||
\(791\) | 0.169873 | − | 0.0980762i | 0.00603999 | − | 0.00348719i | ||||
\(792\) | 0.267949 | 0.00952116 | ||||||||
\(793\) | −21.4808 | − | 20.6699i | −0.762804 | − | 0.734009i | ||||
\(794\) | 9.53590 | 0.338416 | ||||||||
\(795\) | −8.36603 | + | 4.83013i | −0.296712 | + | 0.171307i | ||||
\(796\) | −3.09808 | − | 5.36603i | −0.109808 | − | 0.190194i | ||||
\(797\) | 1.36603 | − | 2.36603i | 0.0483871 | − | 0.0838089i | −0.840817 | − | 0.541319i | \(-0.817925\pi\) |
0.889205 | + | 0.457510i | \(0.151259\pi\) | |||||||
\(798\) | − | 2.46410i | − | 0.0872283i | ||||||
\(799\) | −7.96410 | − | 4.59808i | −0.281750 | − | 0.162668i | ||||
\(800\) | 2.13397 | + | 1.23205i | 0.0754474 | + | 0.0435596i | ||||
\(801\) | 0.464102i | 0.0163982i | ||||||||
\(802\) | 5.00000 | − | 8.66025i | 0.176556 | − | 0.305804i | ||||
\(803\) | 1.80385 | + | 3.12436i | 0.0636564 | + | 0.110256i | ||||
\(804\) | −0.803848 | + | 0.464102i | −0.0283495 | + | 0.0163676i | ||||
\(805\) | 9.46410 | 0.333566 | ||||||||
\(806\) | 33.4641 | − | 9.66025i | 1.17872 | − | 0.340268i | ||||
\(807\) | −31.7128 | −1.11634 | ||||||||
\(808\) | −8.66025 | + | 5.00000i | −0.304667 | + | 0.175899i | ||||
\(809\) | −5.09808 | − | 8.83013i | −0.179239 | − | 0.310451i | 0.762381 | − | 0.647128i | \(-0.224030\pi\) |
−0.941620 | + | 0.336677i | \(0.890697\pi\) | |||||||
\(810\) | −1.36603 | + | 2.36603i | −0.0479972 | + | 0.0831337i | ||||
\(811\) | − | 8.53590i | − | 0.299736i | −0.988706 | − | 0.149868i | \(-0.952115\pi\) | ||
0.988706 | − | 0.149868i | \(-0.0478849\pi\) | |||||||
\(812\) | −2.59808 | − | 1.50000i | −0.0911746 | − | 0.0526397i | ||||
\(813\) | 20.3660 | + | 11.7583i | 0.714268 | + | 0.412383i | ||||
\(814\) | 1.26795i | 0.0444416i | ||||||||
\(815\) | 24.8564 | − | 43.0526i | 0.870682 | − | 1.50807i | ||||
\(816\) | −1.86603 | − | 3.23205i | −0.0653240 | − | 0.113144i | ||||
\(817\) | −5.83013 | + | 3.36603i | −0.203970 | + | 0.117762i | ||||
\(818\) | −16.7321 | −0.585022 | ||||||||
\(819\) | −1.00000 | − | 3.46410i | −0.0349428 | − | 0.121046i | ||||
\(820\) | −19.1244 | −0.667851 | ||||||||
\(821\) | 12.4808 | − | 7.20577i | 0.435582 | − | 0.251483i | −0.266140 | − | 0.963934i | \(-0.585748\pi\) |
0.701722 | + | 0.712451i | \(0.252415\pi\) | |||||||
\(822\) | −4.26795 | − | 7.39230i | −0.148862 | − | 0.257836i | ||||
\(823\) | 10.4641 | − | 18.1244i | 0.364756 | − | 0.631775i | −0.623981 | − | 0.781439i | \(-0.714486\pi\) |
0.988737 | + | 0.149664i | \(0.0478192\pi\) | |||||||
\(824\) | − | 1.80385i | − | 0.0628400i | ||||||
\(825\) | −0.571797 | − | 0.330127i | −0.0199074 | − | 0.0114935i | ||||
\(826\) | −11.1962 | − | 6.46410i | −0.389564 | − | 0.224915i | ||||
\(827\) | − | 40.3923i | − | 1.40458i | −0.711892 | − | 0.702289i | \(-0.752161\pi\) | ||
0.711892 | − | 0.702289i | \(-0.247839\pi\) | |||||||
\(828\) | 1.73205 | − | 3.00000i | 0.0601929 | − | 0.104257i | ||||
\(829\) | −0.330127 | − | 0.571797i | −0.0114658 | − | 0.0198593i | 0.860236 | − | 0.509897i | \(-0.170316\pi\) |
−0.871701 | + | 0.490037i | \(0.836983\pi\) | |||||||
\(830\) | 27.5885 | − | 15.9282i | 0.957609 | − | 0.552876i | ||||
\(831\) | −5.60770 | −0.194529 | ||||||||
\(832\) | −0.866025 | + | 3.50000i | −0.0300240 | + | 0.121341i | ||||
\(833\) | 3.73205 | 0.129308 | ||||||||
\(834\) | −5.30385 | + | 3.06218i | −0.183657 | + | 0.106035i | ||||
\(835\) | −29.8564 | − | 51.7128i | −1.03322 | − | 1.78960i | ||||
\(836\) | 0.330127 | − | 0.571797i | 0.0114177 | − | 0.0197760i | ||||
\(837\) | − | 9.66025i | − | 0.333907i | ||||||
\(838\) | −3.63397 | − | 2.09808i | −0.125534 | − | 0.0724768i | ||||
\(839\) | 12.4641 | + | 7.19615i | 0.430309 | + | 0.248439i | 0.699478 | − | 0.714654i | \(-0.253416\pi\) |
−0.269170 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(840\) | 2.73205i | 0.0942647i | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 3.19615 | + | 5.53590i | 0.110147 | + | 0.190780i | ||||
\(843\) | −6.75833 | + | 3.90192i | −0.232769 | + | 0.134389i | ||||
\(844\) | −11.8564 | −0.408114 | ||||||||
\(845\) | −16.5622 | + | 31.4186i | −0.569756 | + | 1.08083i | ||||
\(846\) | 2.46410 | 0.0847176 | ||||||||
\(847\) | 9.46410 | − | 5.46410i | 0.325190 | − | 0.187749i | ||||
\(848\) | 1.76795 | + | 3.06218i | 0.0607116 | + | 0.105156i | ||||
\(849\) | 4.53590 | − | 7.85641i | 0.155672 | − | 0.269631i | ||||
\(850\) | 9.19615i | 0.315425i | ||||||||
\(851\) | 14.1962 | + | 8.19615i | 0.486638 | + | 0.280960i | ||||
\(852\) | 7.09808 | + | 4.09808i | 0.243176 | + | 0.140398i | ||||
\(853\) | 33.3923i | 1.14333i | 0.820487 | + | 0.571665i | \(0.193702\pi\) | ||||
−0.820487 | + | 0.571665i | \(0.806298\pi\) | |||||||
\(854\) | −4.13397 | + | 7.16025i | −0.141462 | + | 0.245019i | ||||
\(855\) | 3.36603 | + | 5.83013i | 0.115116 | + | 0.199386i | ||||
\(856\) | 7.33013 | − | 4.23205i | 0.250539 | − | 0.144649i | ||||
\(857\) | 21.6077 | 0.738105 | 0.369052 | − | 0.929409i | \(-0.379682\pi\) | ||||
0.369052 | + | 0.929409i | \(0.379682\pi\) | |||||||
\(858\) | 0.232051 | − | 0.937822i | 0.00792208 | − | 0.0320167i | ||||
\(859\) | −45.0526 | −1.53717 | −0.768587 | − | 0.639746i | \(-0.779040\pi\) | ||||
−0.768587 | + | 0.639746i | \(0.779040\pi\) | |||||||
\(860\) | 6.46410 | − | 3.73205i | 0.220424 | − | 0.127262i | ||||
\(861\) | −3.50000 | − | 6.06218i | −0.119280 | − | 0.206598i | ||||
\(862\) | 1.56218 | − | 2.70577i | 0.0532080 | − | 0.0921589i | ||||
\(863\) | − | 28.6410i | − | 0.974952i | −0.873137 | − | 0.487476i | \(-0.837918\pi\) | ||
0.873137 | − | 0.487476i | \(-0.162082\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −40.8564 | − | 23.5885i | −1.38916 | − | 0.802032i | ||||
\(866\) | 4.92820i | 0.167467i | ||||||||
\(867\) | −1.53590 | + | 2.66025i | −0.0521618 | + | 0.0903470i | ||||
\(868\) | −4.83013 | − | 8.36603i | −0.163945 | − | 0.283961i | ||||
\(869\) | −3.91154 | + | 2.25833i | −0.132690 | + | 0.0766086i | ||||
\(870\) | 8.19615 | 0.277876 | ||||||||
\(871\) | 0.928203 | + | 3.21539i | 0.0314510 | + | 0.108949i | ||||
\(872\) | 13.6603 | 0.462595 | ||||||||
\(873\) | −2.36603 | + | 1.36603i | −0.0800778 | + | 0.0462330i | ||||
\(874\) | −4.26795 | − | 7.39230i | −0.144366 | − | 0.250048i | ||||
\(875\) | −3.46410 | + | 6.00000i | −0.117108 | + | 0.202837i | ||||
\(876\) | 13.4641i | 0.454910i | ||||||||
\(877\) | 31.4378 | + | 18.1506i | 1.06158 | + | 0.612903i | 0.925869 | − | 0.377845i | \(-0.123335\pi\) |
0.135711 | + | 0.990748i | \(0.456668\pi\) | |||||||
\(878\) | 3.80385 | + | 2.19615i | 0.128374 | + | 0.0741166i | ||||
\(879\) | − | 28.7846i | − | 0.970881i | ||||||
\(880\) | −0.366025 | + | 0.633975i | −0.0123387 | + | 0.0213713i | ||||
\(881\) | 0.535898 | + | 0.928203i | 0.0180549 | + | 0.0312720i | 0.874912 | − | 0.484283i | \(-0.160919\pi\) |
−0.856857 | + | 0.515554i | \(0.827586\pi\) | |||||||
\(882\) | −0.866025 | + | 0.500000i | −0.0291606 | + | 0.0168359i | ||||
\(883\) | −34.4449 | −1.15916 | −0.579581 | − | 0.814915i | \(-0.696784\pi\) | ||||
−0.579581 | + | 0.814915i | \(0.696784\pi\) | |||||||
\(884\) | −12.9282 | + | 3.73205i | −0.434823 | + | 0.125522i | ||||
\(885\) | 35.3205 | 1.18729 | ||||||||
\(886\) | −9.18653 | + | 5.30385i | −0.308628 | + | 0.178186i | ||||
\(887\) | −22.5263 | − | 39.0167i | −0.756358 | − | 1.31005i | −0.944696 | − | 0.327947i | \(-0.893643\pi\) |
0.188338 | − | 0.982104i | \(-0.439690\pi\) | |||||||
\(888\) | −2.36603 | + | 4.09808i | −0.0793986 | + | 0.137522i | ||||
\(889\) | 19.4641i | 0.652805i | ||||||||
\(890\) | −1.09808 | − | 0.633975i | −0.0368076 | − | 0.0212509i | ||||
\(891\) | −0.232051 | − | 0.133975i | −0.00777399 | − | 0.00448832i | ||||
\(892\) | − | 12.3923i | − | 0.414925i | ||||||
\(893\) | 3.03590 | − | 5.25833i | 0.101592 | − | 0.175963i | ||||
\(894\) | 2.53590 | + | 4.39230i | 0.0848131 | + | 0.146901i | ||||
\(895\) | 3.80385 | − | 2.19615i | 0.127149 | − | 0.0734093i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −9.00000 | − | 8.66025i | −0.300501 | − | 0.289157i | ||||
\(898\) | 7.26795 | 0.242535 | ||||||||
\(899\) | −25.0981 | + | 14.4904i | −0.837068 | + | 0.483281i | ||||
\(900\) | −1.23205 | − | 2.13397i | −0.0410684 | − | 0.0711325i | ||||
\(901\) | −6.59808 | + | 11.4282i | −0.219814 | + | 0.380729i | ||||
\(902\) | − | 1.87564i | − | 0.0624521i | ||||||
\(903\) | 2.36603 | + | 1.36603i | 0.0787364 | + | 0.0454585i | ||||
\(904\) | 0.169873 | + | 0.0980762i | 0.00564989 | + | 0.00326197i | ||||
\(905\) | − | 25.1244i | − | 0.835162i | ||||||
\(906\) | −1.40192 | + | 2.42820i | −0.0465758 | + | 0.0806716i | ||||
\(907\) | −13.7321 | − | 23.7846i | −0.455965 | − | 0.789755i | 0.542778 | − | 0.839876i | \(-0.317373\pi\) |
−0.998743 | + | 0.0501213i | \(0.984039\pi\) | |||||||
\(908\) | −13.3923 | + | 7.73205i | −0.444439 | + | 0.256597i | ||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 9.56218 | + | 2.36603i | 0.316983 | + | 0.0784330i | ||||
\(911\) | −0.0525589 | −0.00174135 | −0.000870677 | − | 1.00000i | \(-0.500277\pi\) | ||||
−0.000870677 | 1.00000i | \(0.500277\pi\) | ||||||||
\(912\) | 2.13397 | − | 1.23205i | 0.0706630 | − | 0.0407973i | ||||
\(913\) | 1.56218 | + | 2.70577i | 0.0517005 | + | 0.0895480i | ||||
\(914\) | 17.3923 | − | 30.1244i | 0.575286 | − | 0.996425i | ||||
\(915\) | − | 22.5885i | − | 0.746751i | ||||||
\(916\) | 21.0622 | + | 12.1603i | 0.695914 | + | 0.401786i | ||||
\(917\) | −4.39230 | − | 2.53590i | −0.145047 | − | 0.0837427i | ||||
\(918\) | 3.73205i | 0.123176i | ||||||||
\(919\) | −20.8205 | + | 36.0622i | −0.686805 | + | 1.18958i | 0.286061 | + | 0.958212i | \(0.407654\pi\) |
−0.972866 | + | 0.231370i | \(0.925679\pi\) | |||||||
\(920\) | 4.73205 | + | 8.19615i | 0.156011 | + | 0.270219i | ||||
\(921\) | −6.74167 | + | 3.89230i | −0.222146 | + | 0.128256i | ||||
\(922\) | −27.7128 | −0.912673 | ||||||||
\(923\) | 20.4904 | − | 21.2942i | 0.674449 | − | 0.700908i | ||||
\(924\) | −0.267949 | −0.00881488 | ||||||||
\(925\) | 10.0981 | − | 5.83013i | 0.332023 | − | 0.191693i | ||||
\(926\) | 4.59808 | + | 7.96410i | 0.151102 | + | 0.261717i | ||||
\(927\) | −0.901924 | + | 1.56218i | −0.0296231 | + | 0.0513087i | ||||
\(928\) | − | 3.00000i | − | 0.0984798i | ||||||
\(929\) | −37.7032 | − | 21.7679i | −1.23700 | − | 0.714183i | −0.268521 | − | 0.963274i | \(-0.586535\pi\) |
−0.968480 | + | 0.249090i | \(0.919868\pi\) | |||||||
\(930\) | 22.8564 | + | 13.1962i | 0.749491 | + | 0.432719i | ||||
\(931\) | 2.46410i | 0.0807577i | ||||||||
\(932\) | 4.09808 | − | 7.09808i | 0.134237 | − | 0.232505i | ||||
\(933\) | 4.40192 | + | 7.62436i | 0.144113 | + | 0.249610i | ||||
\(934\) | −15.4641 | + | 8.92820i | −0.506001 | + | 0.292140i | ||||
\(935\) | −2.73205 | −0.0893476 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | 45.5692 | 1.48868 | 0.744341 | − | 0.667800i | \(-0.232764\pi\) | ||||
0.744341 | + | 0.667800i | \(0.232764\pi\) | |||||||
\(938\) | 0.803848 | − | 0.464102i | 0.0262466 | − | 0.0151535i | ||||
\(939\) | 6.09808 | + | 10.5622i | 0.199003 | + | 0.344684i | ||||
\(940\) | −3.36603 | + | 5.83013i | −0.109788 | + | 0.190158i | ||||
\(941\) | − | 49.1769i | − | 1.60312i | −0.597913 | − | 0.801561i | \(-0.704003\pi\) | ||
0.597913 | − | 0.801561i | \(-0.295997\pi\) | |||||||
\(942\) | −7.39230 | − | 4.26795i | −0.240854 | − | 0.139057i | ||||
\(943\) | −21.0000 | − | 12.1244i | −0.683854 | − | 0.394823i | ||||
\(944\) | − | 12.9282i | − | 0.420777i | ||||||
\(945\) | 1.36603 | − | 2.36603i | 0.0444368 | − | 0.0769668i | ||||
\(946\) | 0.366025 | + | 0.633975i | 0.0119005 | + | 0.0206123i | ||||
\(947\) | 11.2128 | − | 6.47372i | 0.364367 | − | 0.210368i | −0.306627 | − | 0.951830i | \(-0.599201\pi\) |
0.670995 | + | 0.741462i | \(0.265867\pi\) | |||||||
\(948\) | −16.8564 | −0.547471 | ||||||||
\(949\) | 47.1244 | + | 11.6603i | 1.52972 | + | 0.378508i | ||||
\(950\) | −6.07180 | −0.196995 | ||||||||
\(951\) | 15.5885 | − | 9.00000i | 0.505490 | − | 0.291845i | ||||
\(952\) | 1.86603 | + | 3.23205i | 0.0604782 | + | 0.104751i | ||||
\(953\) | −10.6865 | + | 18.5096i | −0.346171 | + | 0.599585i | −0.985566 | − | 0.169293i | \(-0.945852\pi\) |
0.639395 | + | 0.768878i | \(0.279185\pi\) | |||||||
\(954\) | − | 3.53590i | − | 0.114479i | ||||||
\(955\) | 14.6603 | + | 8.46410i | 0.474395 | + | 0.273892i | ||||
\(956\) | −20.9545 | − | 12.0981i | −0.677716 | − | 0.391280i | ||||
\(957\) | 0.803848i | 0.0259847i | ||||||||
\(958\) | −5.30385 | + | 9.18653i | −0.171360 | + | 0.296803i | ||||
\(959\) | 4.26795 | + | 7.39230i | 0.137819 | + | 0.238710i | ||||
\(960\) | −2.36603 | + | 1.36603i | −0.0763631 | + | 0.0440883i | ||||
\(961\) | −62.3205 | −2.01034 | ||||||||
\(962\) | 12.2942 | + | 11.8301i | 0.396382 | + | 0.381419i | ||||
\(963\) | −8.46410 | −0.272752 | ||||||||
\(964\) | −24.9282 | + | 14.3923i | −0.802883 | + | 0.463545i | ||||
\(965\) | −9.29423 | − | 16.0981i | −0.299192 | − | 0.518215i | ||||
\(966\) | −1.73205 | + | 3.00000i | −0.0557278 | + | 0.0965234i | ||||
\(967\) | 36.0000i | 1.15768i | 0.815440 | + | 0.578841i | \(0.196495\pi\) | ||||
−0.815440 | + | 0.578841i | \(0.803505\pi\) | |||||||
\(968\) | 9.46410 | + | 5.46410i | 0.304188 | + | 0.175623i | ||||
\(969\) | 7.96410 | + | 4.59808i | 0.255844 | + | 0.147711i | ||||
\(970\) | − | 7.46410i | − | 0.239658i | ||||||
\(971\) | 2.12436 | − | 3.67949i | 0.0681738 | − | 0.118081i | −0.829924 | − | 0.557877i | \(-0.811616\pi\) |
0.898097 | + | 0.439796i | \(0.144949\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 5.30385 | − | 3.06218i | 0.170034 | − | 0.0981689i | ||||
\(974\) | −10.8038 | −0.346178 | ||||||||
\(975\) | −8.53590 | + | 2.46410i | −0.273368 | + | 0.0789144i | ||||
\(976\) | −8.26795 | −0.264651 | ||||||||
\(977\) | 26.1962 | − | 15.1244i | 0.838089 | − | 0.483871i | −0.0185251 | − | 0.999828i | \(-0.505897\pi\) |
0.856614 | + | 0.515957i | \(0.172564\pi\) | |||||||
\(978\) | 9.09808 | + | 15.7583i | 0.290924 | + | 0.503896i | ||||
\(979\) | 0.0621778 | − | 0.107695i | 0.00198721 | − | 0.00344195i | ||||
\(980\) | − | 2.73205i | − | 0.0872722i | ||||||
\(981\) | −11.8301 | − | 6.83013i | −0.377707 | − | 0.218069i | ||||
\(982\) | −10.6077 | − | 6.12436i | −0.338505 | − | 0.195436i | ||||
\(983\) | − | 55.8564i | − | 1.78154i | −0.454452 | − | 0.890771i | \(-0.650165\pi\) | ||
0.454452 | − | 0.890771i | \(-0.349835\pi\) | |||||||
\(984\) | 3.50000 | − | 6.06218i | 0.111576 | − | 0.193255i | ||||
\(985\) | 7.83013 | + | 13.5622i | 0.249489 | + | 0.432127i | ||||
\(986\) | 9.69615 | − | 5.59808i | 0.308788 | − | 0.178279i | ||||
\(987\) | −2.46410 | −0.0784332 | ||||||||
\(988\) | −2.46410 | − | 8.53590i | −0.0783935 | − | 0.271563i | ||||
\(989\) | 9.46410 | 0.300941 | ||||||||
\(990\) | 0.633975 | − | 0.366025i | 0.0201490 | − | 0.0116331i | ||||
\(991\) | 12.6962 | + | 21.9904i | 0.403307 | + | 0.698547i | 0.994123 | − | 0.108259i | \(-0.0345275\pi\) |
−0.590816 | + | 0.806806i | \(0.701194\pi\) | |||||||
\(992\) | 4.83013 | − | 8.36603i | 0.153357 | − | 0.265622i | ||||
\(993\) | 3.07180i | 0.0974805i | ||||||||
\(994\) | −7.09808 | − | 4.09808i | −0.225137 | − | 0.129983i | ||||
\(995\) | −14.6603 | − | 8.46410i | −0.464761 | − | 0.268330i | ||||
\(996\) | 11.6603i | 0.369469i | ||||||||
\(997\) | 29.1147 | − | 50.4282i | 0.922073 | − | 1.59708i | 0.125871 | − | 0.992047i | \(-0.459828\pi\) |
0.796202 | − | 0.605031i | \(-0.206839\pi\) | |||||||
\(998\) | 19.4904 | + | 33.7583i | 0.616957 | + | 1.06860i | ||||
\(999\) | 4.09808 | − | 2.36603i | 0.129657 | − | 0.0748577i |
(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 | 546.2.s.d.127.2 | yes | 4 | |
3.2 | odd | 2 | 1638.2.bj.d.127.1 | 4 | |||
13.2 | odd | 12 | 7098.2.a.bs.1.1 | 2 | |||
13.4 | even | 6 | inner | 546.2.s.d.43.2 | ✓ | 4 | |
13.11 | odd | 12 | 7098.2.a.bj.1.2 | 2 | |||
39.17 | odd | 6 | 1638.2.bj.d.1135.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.d.43.2 | ✓ | 4 | 13.4 | even | 6 | inner | |
546.2.s.d.127.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.bj.d.127.1 | 4 | 3.2 | odd | 2 | |||
1638.2.bj.d.1135.1 | 4 | 39.17 | odd | 6 | |||
7098.2.a.bj.1.2 | 2 | 13.11 | odd | 12 | |||
7098.2.a.bs.1.1 | 2 | 13.2 | odd | 12 |