Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,2,Mod(91,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.n (of order \(5\), degree \(4\), 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: | \(3.95259490005\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(1.69513 - 1.23158i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.361 |
Dual form | 495.2.n.e.181.2 |
$q$-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 \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(397\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.647481 | − | 1.99274i | 0.457839 | − | 1.40908i | −0.409932 | − | 0.912116i | \(-0.634447\pi\) |
0.867770 | − | 0.496966i | \(-0.165553\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93376 | − | 1.40496i | −0.966879 | − | 0.702479i | ||||
\(5\) | 0.309017 | + | 0.951057i | 0.138197 | + | 0.425325i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.48141 | + | 1.80285i | 0.937883 | + | 0.681412i | 0.947910 | − | 0.318538i | \(-0.103192\pi\) |
−0.0100271 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(8\) | −0.661536 | + | 0.480634i | −0.233888 | + | 0.169930i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.09529 | 0.662590 | ||||||||
\(11\) | −1.86337 | − | 2.74369i | −0.561828 | − | 0.827254i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.942444 | − | 2.90055i | 0.261387 | − | 0.804467i | −0.731117 | − | 0.682252i | \(-0.761001\pi\) |
0.992504 | − | 0.122214i | \(-0.0389995\pi\) | |||||||
\(14\) | 5.19927 | − | 3.77749i | 1.38956 | − | 1.00958i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.947813 | − | 2.91707i | −0.236953 | − | 0.729267i | ||||
\(17\) | 0.143336 | + | 0.441143i | 0.0347641 | + | 0.106993i | 0.966933 | − | 0.255031i | \(-0.0820858\pi\) |
−0.932169 | + | 0.362024i | \(0.882086\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.38769 | − | 4.64093i | 1.46544 | − | 1.06470i | 0.483533 | − | 0.875326i | \(-0.339353\pi\) |
0.981904 | − | 0.189377i | \(-0.0606468\pi\) | |||||||
\(20\) | 0.738630 | − | 2.27327i | 0.165163 | − | 0.508318i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.67397 | + | 1.93673i | −1.42290 | + | 0.412912i | ||||
\(23\) | 1.39026 | 0.289889 | 0.144944 | − | 0.989440i | \(-0.453700\pi\) | ||||
0.144944 | + | 0.989440i | \(0.453700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | −5.16983 | − | 3.75610i | −1.01389 | − | 0.736632i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.26552 | − | 6.97254i | −0.428142 | − | 1.31769i | ||||
\(29\) | 3.01085 | + | 2.18751i | 0.559101 | + | 0.406211i | 0.831130 | − | 0.556078i | \(-0.187695\pi\) |
−0.272029 | + | 0.962289i | \(0.587695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.23741 | + | 9.96371i | −0.581456 | + | 1.78954i | 0.0316054 | + | 0.999500i | \(0.489938\pi\) |
−0.613061 | + | 0.790036i | \(0.710062\pi\) | |||||||
\(32\) | −8.06206 | −1.42518 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.971892 | 0.166678 | ||||||||
\(35\) | −0.947813 | + | 2.91707i | −0.160210 | + | 0.493074i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.49226 | − | 1.08419i | −0.245326 | − | 0.178240i | 0.458327 | − | 0.888784i | \(-0.348449\pi\) |
−0.703653 | + | 0.710544i | \(0.748449\pi\) | |||||||
\(38\) | −5.11227 | − | 15.7340i | −0.829320 | − | 2.55238i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.661536 | − | 0.480634i | −0.104598 | − | 0.0759949i | ||||
\(41\) | −3.56585 | + | 2.59074i | −0.556892 | + | 0.404605i | −0.830320 | − | 0.557287i | \(-0.811842\pi\) |
0.273428 | + | 0.961892i | \(0.411842\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.31478 | −0.200502 | −0.100251 | − | 0.994962i | \(-0.531965\pi\) | ||||
−0.100251 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(44\) | −0.251461 | + | 7.92360i | −0.0379092 | + | 1.19453i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.900166 | − | 2.77042i | 0.132722 | − | 0.408477i | ||||
\(47\) | −2.41102 | + | 1.75171i | −0.351683 | + | 0.255513i | −0.749575 | − | 0.661920i | \(-0.769742\pi\) |
0.397892 | + | 0.917432i | \(0.369742\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.743998 | + | 2.28979i | 0.106285 | + | 0.327113i | ||||
\(50\) | 0.647481 | + | 1.99274i | 0.0915677 | + | 0.281816i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.89760 | + | 4.28486i | −0.817850 | + | 0.594203i | ||||
\(53\) | −1.29421 | + | 3.98316i | −0.177773 | + | 0.547129i | −0.999749 | − | 0.0223927i | \(-0.992872\pi\) |
0.821976 | + | 0.569522i | \(0.192872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.03359 | − | 2.62002i | 0.274210 | − | 0.353283i | ||||
\(56\) | −2.50805 | −0.335152 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.30862 | − | 4.58348i | 0.828363 | − | 0.601841i | ||||
\(59\) | 2.27740 | + | 1.65463i | 0.296493 | + | 0.215414i | 0.726079 | − | 0.687611i | \(-0.241341\pi\) |
−0.429586 | + | 0.903026i | \(0.641341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.623402 | − | 1.91863i | −0.0798185 | − | 0.245656i | 0.903182 | − | 0.429257i | \(-0.141225\pi\) |
−0.983001 | + | 0.183601i | \(0.941225\pi\) | |||||||
\(62\) | 17.7590 | + | 12.9026i | 2.25539 | + | 1.63864i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.32441 | + | 10.2315i | −0.415551 | + | 1.27894i | ||||
\(65\) | 3.04981 | 0.378283 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.75753 | −0.825564 | −0.412782 | − | 0.910830i | \(-0.635443\pi\) | ||||
−0.412782 | + | 0.910830i | \(0.635443\pi\) | |||||||
\(68\) | 0.342610 | − | 1.05444i | 0.0415476 | − | 0.127870i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.19927 | + | 3.77749i | 0.621432 | + | 0.451497i | ||||
\(71\) | 2.01539 | + | 6.20274i | 0.239183 | + | 0.736130i | 0.996539 | + | 0.0831276i | \(0.0264909\pi\) |
−0.757356 | + | 0.653003i | \(0.773509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.98970 | + | 5.80485i | 0.935123 | + | 0.679407i | 0.947242 | − | 0.320520i | \(-0.103858\pi\) |
−0.0121186 | + | 0.999927i | \(0.503858\pi\) | |||||||
\(74\) | −3.12672 | + | 2.27169i | −0.363474 | + | 0.264079i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.8726 | −2.16483 | ||||||||
\(77\) | 0.322676 | − | 10.1676i | 0.0367723 | − | 1.15870i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.57158 | + | 10.9922i | −0.401834 | + | 1.23672i | 0.521677 | + | 0.853143i | \(0.325307\pi\) |
−0.923510 | + | 0.383573i | \(0.874693\pi\) | |||||||
\(80\) | 2.48141 | − | 1.80285i | 0.277430 | − | 0.201564i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.85386 | + | 8.78327i | 0.315156 | + | 0.969950i | ||||
\(83\) | −2.75600 | − | 8.48210i | −0.302510 | − | 0.931032i | −0.980594 | − | 0.196047i | \(-0.937189\pi\) |
0.678084 | − | 0.734984i | \(-0.262811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.375259 | + | 0.272641i | −0.0407025 | + | 0.0295721i | ||||
\(86\) | −0.851296 | + | 2.62002i | −0.0917976 | + | 0.282524i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.55140 | + | 0.919451i | 0.271980 | + | 0.0980138i | ||||
\(89\) | 6.76978 | 0.717595 | 0.358797 | − | 0.933415i | \(-0.383187\pi\) | ||||
0.358797 | + | 0.933415i | \(0.383187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.56782 | − | 5.49835i | 0.793324 | − | 0.576383i | ||||
\(92\) | −2.68842 | − | 1.95325i | −0.280287 | − | 0.203641i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.92961 | + | 5.93874i | 0.199024 | + | 0.612534i | ||||
\(95\) | 6.38769 | + | 4.64093i | 0.655364 | + | 0.476150i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.74475 | − | 14.6029i | 0.481757 | − | 1.48269i | −0.354867 | − | 0.934917i | \(-0.615474\pi\) |
0.836624 | − | 0.547778i | \(-0.184526\pi\) | |||||||
\(98\) | 5.04469 | 0.509591 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.39026 | 0.239026 | ||||||||
\(101\) | −3.62557 | + | 11.1584i | −0.360758 | + | 1.11030i | 0.591838 | + | 0.806057i | \(0.298403\pi\) |
−0.952595 | + | 0.304241i | \(0.901597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2357 | − | 8.16319i | −1.10708 | − | 0.804343i | −0.124882 | − | 0.992172i | \(-0.539855\pi\) |
−0.982202 | + | 0.187828i | \(0.939855\pi\) | |||||||
\(104\) | 0.770639 | + | 2.37178i | 0.0755674 | + | 0.232573i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.09944 | + | 5.15804i | 0.689559 | + | 0.500994i | ||||
\(107\) | −5.92282 | + | 4.30318i | −0.572580 | + | 0.416004i | −0.836042 | − | 0.548666i | \(-0.815136\pi\) |
0.263461 | + | 0.964670i | \(0.415136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.43306 | −0.711958 | −0.355979 | − | 0.934494i | \(-0.615853\pi\) | ||||
−0.355979 | + | 0.934494i | \(0.615853\pi\) | |||||||
\(110\) | −3.90431 | − | 5.74884i | −0.372261 | − | 0.548131i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.90712 | − | 8.94719i | 0.274697 | − | 0.845430i | ||||
\(113\) | −2.45650 | + | 1.78475i | −0.231088 | + | 0.167895i | −0.697304 | − | 0.716776i | \(-0.745617\pi\) |
0.466216 | + | 0.884671i | \(0.345617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.429613 | + | 1.32221i | 0.0400616 | + | 0.123297i | ||||
\(116\) | −2.74890 | − | 8.46024i | −0.255229 | − | 0.785514i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.77183 | − | 3.46694i | 0.439282 | − | 0.319157i | ||||
\(119\) | −0.439638 | + | 1.35307i | −0.0403016 | + | 0.124035i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05569 | + | 10.2250i | −0.368699 | + | 0.929549i | ||||
\(122\) | −4.22699 | −0.382693 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20.2590 | − | 14.7190i | 1.81931 | − | 1.32181i | ||||
\(125\) | −0.809017 | − | 0.587785i | −0.0723607 | − | 0.0525731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.139551 | − | 0.429495i | −0.0123832 | − | 0.0381115i | 0.944674 | − | 0.328011i | \(-0.106378\pi\) |
−0.957057 | + | 0.289899i | \(0.906378\pi\) | |||||||
\(128\) | 5.19153 | + | 3.77187i | 0.458871 | + | 0.333389i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.97470 | − | 6.07750i | 0.173192 | − | 0.533032i | ||||
\(131\) | −0.629003 | −0.0549563 | −0.0274781 | − | 0.999622i | \(-0.508748\pi\) | ||||
−0.0274781 | + | 0.999622i | \(0.508748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.2173 | 2.09991 | ||||||||
\(134\) | −4.37538 | + | 13.4660i | −0.377975 | + | 1.16329i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.306850 | − | 0.222940i | −0.0263122 | − | 0.0191169i | ||||
\(137\) | −3.45586 | − | 10.6360i | −0.295254 | − | 0.908698i | −0.983136 | − | 0.182876i | \(-0.941459\pi\) |
0.687882 | − | 0.725823i | \(-0.258541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.92138 | + | 1.39596i | 0.162969 | + | 0.118404i | 0.666281 | − | 0.745701i | \(-0.267885\pi\) |
−0.503312 | + | 0.864105i | \(0.667885\pi\) | |||||||
\(140\) | 5.93120 | − | 4.30927i | 0.501278 | − | 0.364199i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.6654 | 1.14678 | ||||||||
\(143\) | −9.71433 | + | 2.81902i | −0.812353 | + | 0.235738i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.15004 | + | 3.53947i | −0.0955059 | + | 0.293937i | ||||
\(146\) | 16.7408 | − | 12.1629i | 1.38548 | − | 1.00661i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.36243 | + | 4.19312i | 0.111991 | + | 0.344672i | ||||
\(149\) | 2.69473 | + | 8.29354i | 0.220761 | + | 0.679433i | 0.998694 | + | 0.0510859i | \(0.0162682\pi\) |
−0.777933 | + | 0.628347i | \(0.783732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.65596 | + | 7.01547i | −0.785791 | + | 0.570911i | −0.906711 | − | 0.421752i | \(-0.861415\pi\) |
0.120920 | + | 0.992662i | \(0.461415\pi\) | |||||||
\(152\) | −1.99510 | + | 6.14028i | −0.161824 | + | 0.498043i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −20.0525 | − | 7.22633i | −1.61587 | − | 0.582315i | ||||
\(155\) | −10.4765 | −0.841490 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.13520 | + | 2.27786i | −0.250216 | + | 0.181793i | −0.705823 | − | 0.708389i | \(-0.749422\pi\) |
0.455606 | + | 0.890181i | \(0.349422\pi\) | |||||||
\(158\) | 19.5921 | + | 14.2345i | 1.55866 | + | 1.13243i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.49131 | − | 7.66748i | −0.196956 | − | 0.606167i | ||||
\(161\) | 3.44979 | + | 2.50642i | 0.271882 | + | 0.197534i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.07046 | + | 9.44990i | −0.240497 | + | 0.740173i | 0.755848 | + | 0.654748i | \(0.227225\pi\) |
−0.996345 | + | 0.0854258i | \(0.972775\pi\) | |||||||
\(164\) | 10.5354 | 0.822674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.6871 | −1.45040 | ||||||||
\(167\) | −4.30152 | + | 13.2387i | −0.332862 | + | 1.02444i | 0.634904 | + | 0.772591i | \(0.281040\pi\) |
−0.967766 | + | 0.251852i | \(0.918960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.99226 | + | 2.17400i | 0.230174 | + | 0.167231i | ||||
\(170\) | 0.300331 | + | 0.924324i | 0.0230343 | + | 0.0708924i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.54247 | + | 1.84721i | 0.193861 | + | 0.140848i | ||||
\(173\) | 8.76256 | − | 6.36637i | 0.666205 | − | 0.484026i | −0.202548 | − | 0.979272i | \(-0.564922\pi\) |
0.868753 | + | 0.495246i | \(0.164922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.06719 | −0.231857 | ||||||||
\(176\) | −6.23741 | + | 8.03609i | −0.470162 | + | 0.605743i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.38331 | − | 13.4904i | 0.328543 | − | 1.01115i | ||||
\(179\) | 18.3918 | − | 13.3624i | 1.37466 | − | 0.998752i | 0.377307 | − | 0.926088i | \(-0.376850\pi\) |
0.997356 | − | 0.0726638i | \(-0.0231500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.741120 | + | 2.28093i | 0.0550870 | + | 0.169540i | 0.974815 | − | 0.223017i | \(-0.0715905\pi\) |
−0.919728 | + | 0.392557i | \(0.871590\pi\) | |||||||
\(182\) | −6.05677 | − | 18.6408i | −0.448957 | − | 1.38175i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.919704 | + | 0.668204i | −0.0678015 | + | 0.0492607i | ||||
\(185\) | 0.569992 | − | 1.75425i | 0.0419066 | − | 0.128975i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.943272 | − | 1.21528i | 0.0689789 | − | 0.0888703i | ||||
\(188\) | 7.12340 | 0.519527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3841 | − | 9.72412i | 0.970985 | − | 0.705462i | ||||
\(191\) | 13.9525 | + | 10.1371i | 1.00957 | + | 0.733494i | 0.964118 | − | 0.265473i | \(-0.0855280\pi\) |
0.0454496 | + | 0.998967i | \(0.485528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.799036 | − | 2.45918i | −0.0575159 | − | 0.177016i | 0.918171 | − | 0.396184i | \(-0.129666\pi\) |
−0.975687 | + | 0.219168i | \(0.929666\pi\) | |||||||
\(194\) | −26.0276 | − | 18.9102i | −1.86867 | − | 1.35767i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.77835 | − | 5.47319i | 0.127025 | − | 0.390942i | ||||
\(197\) | −0.144731 | −0.0103116 | −0.00515582 | − | 0.999987i | \(-0.501641\pi\) | ||||
−0.00515582 | + | 0.999987i | \(0.501641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.54177 | −0.534622 | −0.267311 | − | 0.963610i | \(-0.586135\pi\) | ||||
−0.267311 | + | 0.963610i | \(0.586135\pi\) | |||||||
\(200\) | 0.252684 | − | 0.777682i | 0.0178675 | − | 0.0549904i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.8882 | + | 14.4497i | 1.39933 | + | 1.01667i | ||||
\(203\) | 3.52740 | + | 10.8562i | 0.247575 | + | 0.761957i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.56585 | − | 2.59074i | −0.249050 | − | 0.180945i | ||||
\(206\) | −23.5420 | + | 17.1043i | −1.64025 | + | 1.19171i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.35435 | −0.648607 | ||||||||
\(209\) | −24.6359 | − | 8.87809i | −1.70410 | − | 0.614110i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.701101 | + | 2.15777i | −0.0482658 | + | 0.148547i | −0.972285 | − | 0.233800i | \(-0.924884\pi\) |
0.924019 | + | 0.382347i | \(0.124884\pi\) | |||||||
\(212\) | 8.09886 | − | 5.88416i | 0.556232 | − | 0.404126i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.74021 | + | 14.5889i | 0.324034 | + | 0.997275i | ||||
\(215\) | −0.406289 | − | 1.25043i | −0.0277087 | − | 0.0852786i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.9964 | + | 18.8875i | −1.76475 | + | 1.28216i | ||||
\(218\) | −4.81277 | + | 14.8122i | −0.325962 | + | 1.00321i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.61349 | + | 2.20937i | −0.513302 | + | 0.148956i | ||||
\(221\) | 1.41464 | 0.0951591 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.94111 | + | 5.04301i | −0.464811 | + | 0.337705i | −0.795415 | − | 0.606065i | \(-0.792747\pi\) |
0.330605 | + | 0.943769i | \(0.392747\pi\) | |||||||
\(224\) | −20.0052 | − | 14.5347i | −1.33666 | − | 0.971138i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.96601 | + | 6.05076i | 0.130777 | + | 0.402491i | ||||
\(227\) | 5.01622 | + | 3.64450i | 0.332938 | + | 0.241894i | 0.741676 | − | 0.670758i | \(-0.234031\pi\) |
−0.408738 | + | 0.912652i | \(0.634031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.15865 | − | 22.0321i | 0.473057 | − | 1.45592i | −0.375503 | − | 0.926821i | \(-0.622530\pi\) |
0.848560 | − | 0.529099i | \(-0.177470\pi\) | |||||||
\(230\) | 2.91300 | 0.192077 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.04318 | −0.199794 | ||||||||
\(233\) | 8.61005 | − | 26.4990i | 0.564063 | − | 1.73601i | −0.106656 | − | 0.994296i | \(-0.534014\pi\) |
0.670719 | − | 0.741711i | \(-0.265986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.41102 | − | 1.75171i | −0.157278 | − | 0.114269i | ||||
\(236\) | −2.07926 | − | 6.39931i | −0.135348 | − | 0.416560i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.41166 | + | 1.75217i | 0.156325 | + | 0.113576i | ||||
\(239\) | −13.1758 | + | 9.57280i | −0.852274 | + | 0.619213i | −0.925772 | − | 0.378082i | \(-0.876584\pi\) |
0.0734982 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.39063 | 0.282826 | 0.141413 | − | 0.989951i | \(-0.454836\pi\) | ||||
0.141413 | + | 0.989951i | \(0.454836\pi\) | |||||||
\(242\) | 17.7499 | + | 14.7025i | 1.14101 | + | 0.945111i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.49009 | + | 4.58603i | −0.0953933 | + | 0.293590i | ||||
\(245\) | −1.94781 | + | 1.41517i | −0.124441 | + | 0.0904118i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.44119 | − | 22.9016i | −0.473471 | − | 1.45720i | ||||
\(248\) | −2.64724 | − | 8.14736i | −0.168100 | − | 0.517358i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.69513 | + | 1.23158i | −0.107209 | + | 0.0778921i | ||||
\(251\) | 0.824050 | − | 2.53616i | 0.0520136 | − | 0.160081i | −0.921676 | − | 0.387961i | \(-0.873179\pi\) |
0.973689 | + | 0.227880i | \(0.0731794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.59056 | − | 3.81444i | −0.162867 | − | 0.239812i | ||||
\(254\) | −0.946229 | −0.0593717 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.52905 | + | 4.74363i | −0.408066 | + | 0.296477i | ||||
\(257\) | −17.5012 | − | 12.7154i | −1.09169 | − | 0.793162i | −0.112010 | − | 0.993707i | \(-0.535729\pi\) |
−0.979685 | + | 0.200545i | \(0.935729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.74827 | − | 5.38063i | −0.108632 | − | 0.334336i | ||||
\(260\) | −5.89760 | − | 4.28486i | −0.365754 | − | 0.265736i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.407268 | + | 1.25344i | −0.0251611 | + | 0.0774379i | ||||
\(263\) | −22.1392 | −1.36516 | −0.682581 | − | 0.730810i | \(-0.739142\pi\) | ||||
−0.682581 | + | 0.730810i | \(0.739142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.18814 | −0.257276 | ||||||||
\(266\) | 15.6803 | − | 48.2590i | 0.961420 | − | 2.95895i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.0674 | + | 9.49404i | 0.798220 | + | 0.579941i | ||||
\(269\) | −6.40233 | − | 19.7044i | −0.390357 | − | 1.20140i | −0.932519 | − | 0.361121i | \(-0.882394\pi\) |
0.542162 | − | 0.840274i | \(-0.317606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.342305 | + | 0.248699i | 0.0207935 | + | 0.0151074i | 0.598133 | − | 0.801396i | \(-0.295909\pi\) |
−0.577340 | + | 0.816504i | \(0.695909\pi\) | |||||||
\(272\) | 1.15099 | − | 0.836242i | 0.0697889 | − | 0.0507046i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.4325 | −1.41561 | ||||||||
\(275\) | 3.12020 | + | 1.12443i | 0.188155 | + | 0.0678058i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.64906 | + | 8.15298i | −0.159167 | + | 0.489865i | −0.998559 | − | 0.0536607i | \(-0.982911\pi\) |
0.839392 | + | 0.543526i | \(0.182911\pi\) | |||||||
\(278\) | 4.02585 | − | 2.92495i | 0.241455 | − | 0.175427i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.775029 | − | 2.38529i | −0.0463168 | − | 0.142549i | ||||
\(281\) | 2.16654 | + | 6.66793i | 0.129245 | + | 0.397776i | 0.994651 | − | 0.103297i | \(-0.0329391\pi\) |
−0.865405 | + | 0.501072i | \(0.832939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.05229 | + | 5.85033i | −0.478659 | + | 0.347766i | −0.800806 | − | 0.598924i | \(-0.795595\pi\) |
0.322147 | + | 0.946690i | \(0.395595\pi\) | |||||||
\(284\) | 4.81731 | − | 14.8261i | 0.285855 | − | 0.879770i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.672272 | + | 21.1834i | −0.0397523 | + | 1.25260i | ||||
\(287\) | −13.5190 | −0.798002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5792 | − | 9.86589i | 0.798778 | − | 0.580346i | ||||
\(290\) | 6.30862 | + | 4.58348i | 0.370455 | + | 0.269151i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.29457 | − | 22.4504i | −0.426882 | − | 1.31381i | ||||
\(293\) | 17.6535 | + | 12.8260i | 1.03133 | + | 0.749302i | 0.968574 | − | 0.248727i | \(-0.0800122\pi\) |
0.0627522 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.869890 | + | 2.67725i | −0.0506470 | + | 0.155875i | ||||
\(296\) | 1.50828 | 0.0876670 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.2717 | 1.05845 | ||||||||
\(299\) | 1.31024 | − | 4.03250i | 0.0757731 | − | 0.233206i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.26250 | − | 2.37035i | −0.188048 | − | 0.136625i | ||||
\(302\) | 7.72797 | + | 23.7842i | 0.444694 | + | 1.36863i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −19.5922 | − | 14.2346i | −1.12369 | − | 0.816410i | ||||
\(305\) | 1.63209 | − | 1.18578i | 0.0934531 | − | 0.0678976i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.8674 | −1.76170 | −0.880849 | − | 0.473397i | \(-0.843028\pi\) | ||||
−0.880849 | + | 0.473397i | \(0.843028\pi\) | |||||||
\(308\) | −14.9090 | + | 19.2083i | −0.849519 | + | 1.09449i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.78332 | + | 20.8769i | −0.385267 | + | 1.18573i | ||||
\(311\) | −15.7071 | + | 11.4119i | −0.890667 | + | 0.647107i | −0.936052 | − | 0.351862i | \(-0.885549\pi\) |
0.0453850 | + | 0.998970i | \(0.485549\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.324922 | + | 1.00001i | 0.0183657 | + | 0.0565237i | 0.959819 | − | 0.280619i | \(-0.0905396\pi\) |
−0.941454 | + | 0.337142i | \(0.890540\pi\) | |||||||
\(314\) | 2.50920 | + | 7.72252i | 0.141602 | + | 0.435807i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.3501 | − | 16.2383i | 1.25729 | − | 0.913476i | ||||
\(317\) | 7.36432 | − | 22.6650i | 0.413621 | − | 1.27300i | −0.499857 | − | 0.866108i | \(-0.666614\pi\) |
0.913478 | − | 0.406887i | \(-0.133386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.391524 | − | 12.3370i | 0.0219211 | − | 0.690740i | ||||
\(320\) | −10.7580 | −0.601391 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.22833 | − | 5.25169i | 0.402819 | − | 0.292665i | ||||
\(323\) | 2.96290 | + | 2.15267i | 0.164860 | + | 0.119778i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.942444 | + | 2.90055i | 0.0522774 | + | 0.160893i | ||||
\(326\) | 16.8432 | + | 12.2373i | 0.932856 | + | 0.677760i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.11374 | − | 3.42773i | 0.0614959 | − | 0.189265i | ||||
\(329\) | −9.14077 | −0.503947 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.6693 | 1.41091 | 0.705457 | − | 0.708753i | \(-0.250742\pi\) | ||||
0.705457 | + | 0.708753i | \(0.250742\pi\) | |||||||
\(332\) | −6.58755 | + | 20.2744i | −0.361539 | + | 1.11270i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.5962 | + | 17.1436i | 1.29113 | + | 0.938059i | ||||
\(335\) | −2.08819 | − | 6.42679i | −0.114090 | − | 0.351133i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.3292 | + | 14.0435i | 1.05293 | + | 0.764996i | 0.972767 | − | 0.231786i | \(-0.0744570\pi\) |
0.0801597 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(338\) | 6.26966 | − | 4.55518i | 0.341025 | − | 0.247769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.10871 | 0.0601282 | ||||||||
\(341\) | 33.3699 | − | 9.68365i | 1.80708 | − | 0.524399i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.35271 | − | 13.3963i | 0.235024 | − | 0.723330i | ||||
\(344\) | 0.869774 | − | 0.631928i | 0.0468951 | − | 0.0340713i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.01295 | − | 21.5836i | −0.377018 | − | 1.16034i | ||||
\(347\) | 0.102641 | + | 0.315895i | 0.00551004 | + | 0.0169582i | 0.953774 | − | 0.300526i | \(-0.0971621\pi\) |
−0.948264 | + | 0.317484i | \(0.897162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.988203 | + | 0.717971i | −0.0528973 | + | 0.0384321i | −0.613920 | − | 0.789368i | \(-0.710408\pi\) |
0.561022 | + | 0.827801i | \(0.310408\pi\) | |||||||
\(350\) | −1.98595 | + | 6.11211i | −0.106153 | + | 0.326706i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0226 | + | 22.1198i | 0.800708 | + | 1.17899i | ||||
\(353\) | 25.7038 | 1.36808 | 0.684039 | − | 0.729446i | \(-0.260222\pi\) | ||||
0.684039 | + | 0.729446i | \(0.260222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.27637 | + | 3.83351i | −0.280041 | + | 0.203461i | ||||
\(356\) | −13.0911 | − | 9.51125i | −0.693828 | − | 0.504095i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.7195 | − | 45.3019i | −0.777949 | − | 2.39428i | ||||
\(359\) | −14.5069 | − | 10.5399i | −0.765643 | − | 0.556272i | 0.134993 | − | 0.990847i | \(-0.456899\pi\) |
−0.900636 | + | 0.434574i | \(0.856899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3931 | − | 41.2196i | 0.704899 | − | 2.16945i | ||||
\(362\) | 5.02517 | 0.264117 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.3593 | −1.17195 | ||||||||
\(365\) | −3.05179 | + | 9.39245i | −0.159738 | + | 0.491623i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.86929 | + | 4.99083i | 0.358574 | + | 0.260519i | 0.752457 | − | 0.658641i | \(-0.228869\pi\) |
−0.393883 | + | 0.919161i | \(0.628869\pi\) | |||||||
\(368\) | −1.31770 | − | 4.05547i | −0.0686900 | − | 0.211406i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.12672 | − | 2.27169i | −0.162550 | − | 0.118100i | ||||
\(371\) | −10.3925 | + | 7.55058i | −0.539551 | + | 0.392006i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.8450 | 1.85598 | 0.927991 | − | 0.372604i | \(-0.121535\pi\) | ||||
0.927991 | + | 0.372604i | \(0.121535\pi\) | |||||||
\(374\) | −1.81100 | − | 2.66657i | −0.0936443 | − | 0.137885i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.753045 | − | 2.31763i | 0.0388353 | − | 0.119523i | ||||
\(377\) | 9.18254 | − | 6.67151i | 0.472925 | − | 0.343600i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.42373 | + | 16.6925i | 0.278598 | + | 0.857438i | 0.988245 | + | 0.152880i | \(0.0488547\pi\) |
−0.709646 | + | 0.704558i | \(0.751145\pi\) | |||||||
\(380\) | −5.83195 | − | 17.9489i | −0.299172 | − | 0.920758i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29.2346 | − | 21.2402i | 1.49577 | − | 1.08674i | ||||
\(383\) | 6.68251 | − | 20.5666i | 0.341460 | − | 1.05091i | −0.621991 | − | 0.783024i | \(-0.713676\pi\) |
0.963452 | − | 0.267882i | \(-0.0863238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.76966 | − | 2.83507i | 0.497908 | − | 0.144489i | ||||
\(386\) | −5.41788 | −0.275763 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −29.6916 | + | 21.5722i | −1.50736 | + | 1.09516i | ||||
\(389\) | 28.9156 | + | 21.0084i | 1.46608 | + | 1.06517i | 0.981727 | + | 0.190295i | \(0.0609444\pi\) |
0.484352 | + | 0.874873i | \(0.339056\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.199274 | + | 0.613302i | 0.0100777 | + | 0.0310160i | ||||
\(392\) | −1.59273 | − | 1.15719i | −0.0804451 | − | 0.0584468i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0937106 | + | 0.288411i | −0.00472107 | + | 0.0145300i | ||||
\(395\) | −11.5579 | −0.581539 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0447 | −1.00601 | −0.503007 | − | 0.864282i | \(-0.667773\pi\) | ||||
−0.503007 | + | 0.864282i | \(0.667773\pi\) | |||||||
\(398\) | −4.88315 | + | 15.0288i | −0.244770 | + | 0.753326i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.48141 | + | 1.80285i | 0.124070 | + | 0.0901423i | ||||
\(401\) | 6.45805 | + | 19.8758i | 0.322500 | + | 0.992551i | 0.972557 | + | 0.232666i | \(0.0747449\pi\) |
−0.650057 | + | 0.759885i | \(0.725255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.8491 | + | 18.7805i | 1.28764 | + | 0.935523i | ||||
\(404\) | 22.6880 | − | 16.4838i | 1.12877 | − | 0.820099i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.9176 | 1.18701 | ||||||||
\(407\) | −0.194050 | + | 6.11454i | −0.00961869 | + | 0.303087i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.26134 | − | 22.3481i | 0.359050 | − | 1.10504i | −0.594574 | − | 0.804041i | \(-0.702679\pi\) |
0.953624 | − | 0.301001i | \(-0.0973208\pi\) | |||||||
\(410\) | −7.47150 | + | 5.42836i | −0.368991 | + | 0.268088i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.2581 | + | 31.5713i | 0.505382 | + | 1.55541i | ||||
\(413\) | 2.66812 | + | 8.21161i | 0.131289 | + | 0.404067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.21531 | − | 5.24223i | 0.354185 | − | 0.257331i | ||||
\(416\) | −7.59804 | + | 23.3844i | −0.372525 | + | 1.14651i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −33.6431 | + | 43.3447i | −1.64554 | + | 2.12006i | ||||
\(419\) | 10.1128 | 0.494043 | 0.247022 | − | 0.969010i | \(-0.420548\pi\) | ||||
0.247022 | + | 0.969010i | \(0.420548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.21872 | + | 5.24471i | −0.351819 | + | 0.255611i | −0.749632 | − | 0.661855i | \(-0.769769\pi\) |
0.397813 | + | 0.917467i | \(0.369769\pi\) | |||||||
\(422\) | 3.84593 | + | 2.79423i | 0.187217 | + | 0.136021i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.05828 | − | 3.25704i | −0.0513945 | − | 0.158176i | ||||
\(425\) | −0.375259 | − | 0.272641i | −0.0182027 | − | 0.0132250i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.91209 | − | 5.88481i | 0.0925325 | − | 0.284786i | ||||
\(428\) | 17.4991 | 0.845850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.75485 | −0.132851 | ||||||||
\(431\) | 5.44248 | − | 16.7502i | 0.262155 | − | 0.806831i | −0.730180 | − | 0.683255i | \(-0.760564\pi\) |
0.992335 | − | 0.123576i | \(-0.0394362\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.39763 | − | 5.37469i | −0.355507 | − | 0.258291i | 0.395668 | − | 0.918393i | \(-0.370513\pi\) |
−0.751176 | + | 0.660102i | \(0.770513\pi\) | |||||||
\(434\) | 20.8057 | + | 64.0334i | 0.998706 | + | 3.07370i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.3737 | + | 10.4431i | 0.688377 | + | 0.500135i | ||||
\(437\) | 8.88054 | − | 6.45209i | 0.424814 | − | 0.308645i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.46946 | 0.308770 | 0.154385 | − | 0.988011i | \(-0.450660\pi\) | ||||
0.154385 | + | 0.988011i | \(0.450660\pi\) | |||||||
\(440\) | −0.0860245 | + | 2.71065i | −0.00410106 | + | 0.129225i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.915954 | − | 2.81902i | 0.0435675 | − | 0.134087i | ||||
\(443\) | −33.0760 | + | 24.0311i | −1.57149 | + | 1.14175i | −0.645774 | + | 0.763529i | \(0.723465\pi\) |
−0.925714 | + | 0.378224i | \(0.876535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.09198 | + | 6.43844i | 0.0991692 | + | 0.305211i | ||||
\(446\) | 5.55518 | + | 17.0971i | 0.263045 | + | 0.809571i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −26.6950 | + | 19.3951i | −1.26122 | + | 0.916330i | ||||
\(449\) | 3.75788 | − | 11.5656i | 0.177345 | − | 0.545813i | −0.822387 | − | 0.568928i | \(-0.807358\pi\) |
0.999733 | + | 0.0231150i | \(0.00735838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.7527 | + | 4.95608i | 0.647589 | + | 0.233373i | ||||
\(452\) | 7.25777 | 0.341377 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5105 | − | 7.63629i | 0.493280 | − | 0.358389i | ||||
\(455\) | 7.56782 | + | 5.49835i | 0.354785 | + | 0.257766i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.06001 | − | 9.41775i | −0.143141 | − | 0.440544i | 0.853626 | − | 0.520886i | \(-0.174398\pi\) |
−0.996767 | + | 0.0803428i | \(0.974398\pi\) | |||||||
\(458\) | −39.2691 | − | 28.5307i | −1.83493 | − | 1.33315i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.02689 | − | 3.16043i | 0.0478788 | − | 0.147356i | ||||
\(461\) | 3.12529 | 0.145559 | 0.0727796 | − | 0.997348i | \(-0.476813\pi\) | ||||
0.0727796 | + | 0.997348i | \(0.476813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3518 | −1.13173 | −0.565863 | − | 0.824499i | \(-0.691457\pi\) | ||||
−0.565863 | + | 0.824499i | \(0.691457\pi\) | |||||||
\(464\) | 3.52740 | − | 10.8562i | 0.163755 | − | 0.503987i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.2309 | − | 34.3152i | −2.18793 | − | 1.58962i | ||||
\(467\) | −10.2512 | − | 31.5501i | −0.474371 | − | 1.45996i | −0.846805 | − | 0.531904i | \(-0.821477\pi\) |
0.372434 | − | 0.928059i | \(-0.378523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.7682 | − | 12.1828i | −0.774282 | − | 0.562549i | ||||
\(470\) | −5.05179 | + | 3.67034i | −0.233022 | + | 0.169300i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.30185 | −0.105951 | ||||||||
\(473\) | 2.44992 | + | 3.60735i | 0.112648 | + | 0.165866i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.43988 | + | 7.50919i | −0.111949 | + | 0.344545i | ||||
\(476\) | 2.75116 | − | 1.99883i | 0.126099 | − | 0.0916163i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5450 | + | 32.4543i | 0.482318 | + | 1.48442i | ||||
\(479\) | 5.34529 | + | 16.4511i | 0.244232 | + | 0.751670i | 0.995762 | + | 0.0919705i | \(0.0293165\pi\) |
−0.751529 | + | 0.659700i | \(0.770683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.55111 | + | 3.30658i | −0.207513 | + | 0.150767i | ||||
\(482\) | 2.84285 | − | 8.74941i | 0.129488 | − | 0.398524i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.2085 | − | 14.0747i | 1.00948 | − | 0.639758i | ||||
\(485\) | 15.3543 | 0.697205 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.18138 | + | 4.49104i | −0.280105 | + | 0.203508i | −0.718963 | − | 0.695048i | \(-0.755383\pi\) |
0.438858 | + | 0.898556i | \(0.355383\pi\) | |||||||
\(488\) | 1.33456 | + | 0.969617i | 0.0604128 | + | 0.0438925i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.55889 | + | 4.79779i | 0.0704237 | + | 0.216742i | ||||
\(491\) | −24.8015 | − | 18.0193i | −1.11928 | − | 0.813201i | −0.135176 | − | 0.990822i | \(-0.543160\pi\) |
−0.984099 | + | 0.177620i | \(0.943160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.533442 | + | 1.64177i | −0.0240250 | + | 0.0739414i | ||||
\(494\) | −50.4551 | −2.27008 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.1333 | 1.44283 | ||||||||
\(497\) | −6.18159 | + | 19.0250i | −0.277282 | + | 0.853386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3206 | + | 22.0292i | 1.35734 | + | 0.986162i | 0.998609 | + | 0.0527188i | \(0.0167887\pi\) |
0.358726 | + | 0.933443i | \(0.383211\pi\) | |||||||
\(500\) | 0.738630 | + | 2.27327i | 0.0330325 | + | 0.101664i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.52037 | − | 3.28424i | −0.201754 | − | 0.146583i | ||||
\(503\) | 6.85800 | − | 4.98263i | 0.305783 | − | 0.222164i | −0.424302 | − | 0.905521i | \(-0.639480\pi\) |
0.730085 | + | 0.683356i | \(0.239480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.7326 | −0.522093 | ||||||||
\(506\) | −9.27854 | + | 2.69255i | −0.412481 | + | 0.119699i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.333563 | + | 1.02660i | −0.0147995 | + | 0.0455481i | ||||
\(509\) | −1.37309 | + | 0.997609i | −0.0608612 | + | 0.0442183i | −0.617800 | − | 0.786335i | \(-0.711976\pi\) |
0.556939 | + | 0.830554i | \(0.311976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.36041 | + | 28.8084i | 0.414080 | + | 1.27441i | ||||
\(512\) | 9.19138 | + | 28.2882i | 0.406206 | + | 1.25017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.6701 | + | 26.6424i | −1.61745 | + | 1.17515i | ||||
\(515\) | 4.29165 | − | 13.2083i | 0.189112 | − | 0.582028i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.29877 | + | 3.35101i | 0.408959 | + | 0.147377i | ||||
\(518\) | −11.8542 | −0.520843 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.01756 | + | 1.46584i | −0.0884759 | + | 0.0642815i | ||||
\(521\) | −30.0088 | − | 21.8027i | −1.31471 | − | 0.955192i | −0.999982 | − | 0.00601047i | \(-0.998087\pi\) |
−0.314728 | − | 0.949182i | \(-0.601913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.58759 | − | 17.1968i | −0.244328 | − | 0.751965i | −0.995746 | − | 0.0921382i | \(-0.970630\pi\) |
0.751418 | − | 0.659826i | \(-0.229370\pi\) | |||||||
\(524\) | 1.21634 | + | 0.883723i | 0.0531361 | + | 0.0386056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.3347 | + | 44.1177i | −0.625023 | + | 1.92362i | ||||
\(527\) | −4.85946 | −0.211681 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0672 | −0.915965 | ||||||||
\(530\) | −2.71174 | + | 8.34589i | −0.117791 | + | 0.362522i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −46.8305 | − | 34.0244i | −2.03036 | − | 1.47514i | ||||
\(533\) | 4.15394 | + | 12.7845i | 0.179927 | + | 0.553759i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.92282 | − | 4.30318i | −0.256066 | − | 0.186043i | ||||
\(536\) | 4.47035 | − | 3.24790i | 0.193090 | − | 0.140288i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −43.4111 | −1.87159 | ||||||||
\(539\) | 4.89614 | − | 6.30803i | 0.210892 | − | 0.271706i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.63169 | − | 11.1772i | 0.156139 | − | 0.480545i | −0.842136 | − | 0.539265i | \(-0.818702\pi\) |
0.998274 | + | 0.0587201i | \(0.0187019\pi\) | |||||||
\(542\) | 0.717229 | − | 0.521098i | 0.0308076 | − | 0.0223831i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.15558 | − | 3.55652i | −0.0495452 | − | 0.152485i | ||||
\(545\) | −2.29694 | − | 7.06926i | −0.0983902 | − | 0.302814i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6017 | − | 12.7884i | 0.752593 | − | 0.546791i | −0.144037 | − | 0.989572i | \(-0.546008\pi\) |
0.896629 | + | 0.442782i | \(0.146008\pi\) | |||||||
\(548\) | −8.26039 | + | 25.4229i | −0.352866 | + | 1.08601i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.26097 | − | 5.48971i | 0.181689 | − | 0.234082i | ||||
\(551\) | 29.3845 | 1.25182 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.6797 | + | 20.8370i | −1.21959 | + | 0.886081i | ||||
\(554\) | 14.5316 | + | 10.5578i | 0.617388 | + | 0.448558i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.75421 | − | 5.39891i | −0.0743952 | − | 0.228965i | ||||
\(557\) | 3.91104 | + | 2.84154i | 0.165716 | + | 0.120400i | 0.667552 | − | 0.744563i | \(-0.267342\pi\) |
−0.501836 | + | 0.864963i | \(0.667342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.23911 | + | 3.81358i | −0.0524086 | + | 0.161297i | ||||
\(560\) | 9.40763 | 0.397545 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.6903 | 0.619672 | ||||||||
\(563\) | −1.47463 | + | 4.53843i | −0.0621481 | + | 0.191272i | −0.977310 | − | 0.211815i | \(-0.932063\pi\) |
0.915162 | + | 0.403087i | \(0.132063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.45650 | − | 1.78475i | −0.103346 | − | 0.0750850i | ||||
\(566\) | 6.44449 | + | 19.8341i | 0.270882 | + | 0.833690i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.31450 | − | 3.13467i | −0.181032 | − | 0.131528i | ||||
\(569\) | 28.8971 | − | 20.9949i | 1.21143 | − | 0.880154i | 0.216068 | − | 0.976378i | \(-0.430677\pi\) |
0.995360 | + | 0.0962246i | \(0.0306767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9838 | −1.42218 | −0.711090 | − | 0.703101i | \(-0.751798\pi\) | ||||
−0.711090 | + | 0.703101i | \(0.751798\pi\) | |||||||
\(572\) | 22.7458 | + | 8.19692i | 0.951048 | + | 0.342731i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.75331 | + | 26.9399i | −0.365356 | + | 1.12445i | ||||
\(575\) | −1.12474 | + | 0.817172i | −0.0469050 | + | 0.0340784i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.38364 | − | 19.6468i | −0.265755 | − | 0.817909i | −0.991519 | − | 0.129965i | \(-0.958514\pi\) |
0.725764 | − | 0.687944i | \(-0.241486\pi\) | |||||||
\(578\) | −10.8679 | − | 33.4479i | −0.452044 | − | 1.39125i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.19671 | − | 5.22872i | 0.298827 | − | 0.217111i | ||||
\(581\) | 8.45317 | − | 26.0162i | 0.350697 | − | 1.07933i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3402 | − | 3.87120i | 0.552493 | − | 0.160329i | ||||
\(584\) | −8.07548 | −0.334166 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.9892 | − | 26.8742i | 1.52801 | − | 1.11016i | ||||
\(587\) | 10.8085 | + | 7.85284i | 0.446115 | + | 0.324121i | 0.788060 | − | 0.615599i | \(-0.211086\pi\) |
−0.341945 | + | 0.939720i | \(0.611086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.5614 | + | 78.6698i | 1.05324 | + | 3.24153i | ||||
\(590\) | 4.77183 | + | 3.46694i | 0.196453 | + | 0.142731i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.74827 | + | 5.38063i | −0.0718535 | + | 0.221142i | ||||
\(593\) | −20.8062 | −0.854410 | −0.427205 | − | 0.904155i | \(-0.640502\pi\) | ||||
−0.427205 | + | 0.904155i | \(0.640502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.42270 | −0.0583250 | ||||||||
\(596\) | 6.44111 | − | 19.8237i | 0.263838 | − | 0.812010i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.18739 | − | 5.22194i | −0.293914 | − | 0.213541i | ||||
\(599\) | 4.40214 | + | 13.5484i | 0.179867 | + | 0.553573i | 0.999822 | − | 0.0188544i | \(-0.00600189\pi\) |
−0.819956 | + | 0.572427i | \(0.806002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7840 | + | 12.1943i | 0.684634 | + | 0.497416i | 0.874892 | − | 0.484318i | \(-0.160932\pi\) |
−0.190257 | + | 0.981734i | \(0.560932\pi\) | |||||||
\(602\) | −6.83590 | + | 4.96657i | −0.278611 | + | 0.202422i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.5287 | 1.16082 | ||||||||
\(605\) | −10.9779 | − | 0.697484i | −0.446314 | − | 0.0283568i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.53818 | − | 17.0448i | 0.224788 | − | 0.691825i | −0.773525 | − | 0.633765i | \(-0.781508\pi\) |
0.998313 | − | 0.0580601i | \(-0.0184915\pi\) | |||||||
\(608\) | −51.4980 | + | 37.4155i | −2.08852 | + | 1.51740i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.30621 | − | 4.02010i | −0.0528869 | − | 0.162769i | ||||
\(611\) | 2.80866 | + | 8.64416i | 0.113626 | + | 0.349705i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.8158 | − | 16.5766i | 0.921521 | − | 0.669524i | −0.0223811 | − | 0.999750i | \(-0.507125\pi\) |
0.943902 | + | 0.330225i | \(0.107125\pi\) | |||||||
\(614\) | −19.9861 | + | 61.5109i | −0.806573 | + | 2.48238i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.67342 | + | 6.88131i | 0.188298 | + | 0.277256i | ||||
\(617\) | 4.72930 | 0.190394 | 0.0951972 | − | 0.995458i | \(-0.469652\pi\) | ||||
0.0951972 | + | 0.995458i | \(0.469652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.3170 | − | 17.6673i | 0.977383 | − | 0.710110i | 0.0202609 | − | 0.999795i | \(-0.493550\pi\) |
0.957122 | + | 0.289684i | \(0.0935503\pi\) | |||||||
\(620\) | 20.2590 | + | 14.7190i | 0.813619 | + | 0.591129i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.5709 | + | 38.6891i | 0.504046 | + | 1.55129i | ||||
\(623\) | 16.7986 | + | 12.2049i | 0.673020 | + | 0.488978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | 2.20314 | 0.0880551 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.26301 | 0.369634 | ||||||||
\(629\) | 0.264388 | − | 0.813702i | 0.0105418 | − | 0.0324444i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6487 | + | 18.6349i | 1.02106 | + | 0.741843i | 0.966500 | − | 0.256667i | \(-0.0826244\pi\) |
0.0545601 | + | 0.998510i | \(0.482624\pi\) | |||||||
\(632\) | −2.92049 | − | 8.98834i | −0.116171 | − | 0.357537i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −40.3973 | − | 29.3504i | −1.60438 | − | 1.16565i | ||||
\(635\) | 0.365350 | − | 0.265442i | 0.0144985 | − | 0.0105338i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.34282 | 0.290933 | ||||||||
\(638\) | −24.3310 | − | 8.76819i | −0.963272 | − | 0.347136i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.98299 | + | 6.10301i | −0.0783845 | + | 0.241243i | ||||
\(641\) | −15.3368 | + | 11.1428i | −0.605768 | + | 0.440116i | −0.847921 | − | 0.530122i | \(-0.822146\pi\) |
0.242154 | + | 0.970238i | \(0.422146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.2015 | − | 34.4747i | −0.441745 | − | 1.35955i | −0.886015 | − | 0.463657i | \(-0.846537\pi\) |
0.444270 | − | 0.895893i | \(-0.353463\pi\) | |||||||
\(644\) | −3.14965 | − | 9.69362i | −0.124114 | − | 0.381982i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.20815 | − | 4.51048i | 0.244256 | − | 0.177463i | ||||
\(647\) | 10.8007 | − | 33.2412i | 0.424620 | − | 1.30685i | −0.478737 | − | 0.877958i | \(-0.658905\pi\) |
0.903357 | − | 0.428889i | \(-0.141095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.296148 | − | 9.33168i | 0.0116248 | − | 0.366301i | ||||
\(650\) | 6.39026 | 0.250646 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.2142 | − | 13.9600i | 0.752488 | − | 0.546714i | ||||
\(653\) | −24.1000 | − | 17.5097i | −0.943106 | − | 0.685207i | 0.00605995 | − | 0.999982i | \(-0.498071\pi\) |
−0.949166 | + | 0.314775i | \(0.898071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.194373 | − | 0.598218i | −0.00759477 | − | 0.0233743i | ||||
\(656\) | 10.9371 | + | 7.94628i | 0.427023 | + | 0.310250i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.91848 | + | 18.2152i | −0.230726 | + | 0.710103i | ||||
\(659\) | 7.30532 | 0.284575 | 0.142287 | − | 0.989825i | \(-0.454554\pi\) | ||||
0.142287 | + | 0.989825i | \(0.454554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.7352 | −0.884296 | −0.442148 | − | 0.896942i | \(-0.645783\pi\) | ||||
−0.442148 | + | 0.896942i | \(0.645783\pi\) | |||||||
\(662\) | 16.6204 | − | 51.1524i | 0.645971 | − | 1.98809i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.89998 | + | 4.28658i | 0.228964 | + | 0.166352i | ||||
\(665\) | 7.48357 | + | 23.0321i | 0.290200 | + | 0.893145i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.18586 | + | 3.04120i | 0.162077 | + | 0.117756i | ||||
\(668\) | 26.9179 | − | 19.5570i | 1.04149 | − | 0.756684i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.1590 | −0.547010 | ||||||||
\(671\) | −4.10251 | + | 5.28555i | −0.158376 | + | 0.204046i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.48354 | + | 16.8766i | −0.211375 | + | 0.650546i | 0.788016 | + | 0.615655i | \(0.211108\pi\) |
−0.999391 | + | 0.0348910i | \(0.988892\pi\) | |||||||
\(674\) | 40.5003 | − | 29.4252i | 1.56001 | − | 1.13342i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.73192 | − | 8.40799i | −0.105074 | − | 0.323384i | ||||
\(677\) | −2.52224 | − | 7.76267i | −0.0969377 | − | 0.298344i | 0.890816 | − | 0.454364i | \(-0.150133\pi\) |
−0.987754 | + | 0.156020i | \(0.950133\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.1004 | − | 27.6815i | 1.46216 | − | 1.06232i | ||||
\(680\) | 0.117206 | − | 0.360724i | 0.00449466 | − | 0.0138331i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.30933 | − | 72.7675i | 0.0884289 | − | 2.78641i | ||||
\(683\) | 6.19100 | 0.236892 | 0.118446 | − | 0.992960i | \(-0.462209\pi\) | ||||
0.118446 | + | 0.992960i | \(0.462209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.04756 | − | 6.57343i | 0.345689 | − | 0.251158i | ||||
\(686\) | −23.8770 | − | 17.3477i | −0.911628 | − | 0.662336i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.24617 | + | 3.83530i | 0.0475096 | + | 0.146220i | ||||
\(689\) | 10.3336 | + | 7.50781i | 0.393680 | + | 0.286025i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.29438 | − | 22.4498i | 0.277491 | − | 0.854030i | −0.711058 | − | 0.703133i | \(-0.751784\pi\) |
0.988549 | − | 0.150897i | \(-0.0482162\pi\) | |||||||
\(692\) | −25.8892 | −0.984158 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.695956 | 0.0264181 | ||||||||
\(695\) | −0.733901 | + | 2.25872i | −0.0278385 | + | 0.0856779i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.65400 | − | 1.20170i | −0.0626497 | − | 0.0455177i | ||||
\(698\) | 0.790889 | + | 2.43411i | 0.0299356 | + | 0.0921323i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.93120 | + | 4.30927i | 0.224178 | + | 0.162875i | ||||
\(701\) | 30.1184 | − | 21.8823i | 1.13756 | − | 0.826483i | 0.150779 | − | 0.988567i | \(-0.451822\pi\) |
0.986777 | + | 0.162084i | \(0.0518217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.5637 | −0.549282 | ||||||||
\(704\) | 34.2667 | − | 9.94389i | 1.29147 | − | 0.374775i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.6428 | − | 51.2211i | 0.626358 | − | 1.92773i | ||||
\(707\) | −29.1133 | + | 21.1521i | −1.09492 | + | 0.795505i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.64072 | + | 17.3603i | 0.211842 | + | 0.651981i | 0.999363 | + | 0.0356939i | \(0.0113641\pi\) |
−0.787521 | + | 0.616288i | \(0.788636\pi\) | |||||||
\(710\) | 4.22284 | + | 12.9966i | 0.158480 | + | 0.487753i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.47845 | + | 3.25378i | −0.167837 | + | 0.121941i | ||||
\(713\) | −4.50083 | + | 13.8521i | −0.168557 | + | 0.518766i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.68294 | − | 8.36775i | −0.212530 | − | 0.312936i | ||||
\(716\) | −54.3388 | −2.03074 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.3961 | + | 22.0841i | −1.13437 | + | 0.824171i | ||||
\(719\) | 7.74544 | + | 5.62739i | 0.288856 | + | 0.209866i | 0.722771 | − | 0.691088i | \(-0.242868\pi\) |
−0.433915 | + | 0.900954i | \(0.642868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.1633 | − | 40.5124i | −0.490226 | − | 1.50876i | ||||
\(722\) | −73.4684 | − | 53.3779i | −2.73421 | − | 1.98652i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.77147 | − | 5.45202i | 0.0658361 | − | 0.202623i | ||||
\(725\) | −3.72162 | −0.138217 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0175 | −0.519882 | −0.259941 | − | 0.965625i | \(-0.583703\pi\) | ||||
−0.259941 | + | 0.965625i | \(0.583703\pi\) | |||||||
\(728\) | −2.36369 | + | 7.27470i | −0.0876043 | + | 0.269618i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.7408 | + | 12.1629i | 0.619603 | + | 0.450168i | ||||
\(731\) | −0.188455 | − | 0.580006i | −0.00697027 | − | 0.0214523i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.51392 | − | 5.45918i | −0.277533 | − | 0.201640i | 0.440308 | − | 0.897847i | \(-0.354869\pi\) |
−0.717841 | + | 0.696207i | \(0.754869\pi\) | |||||||
\(734\) | 14.3932 | − | 10.4573i | 0.531262 | − | 0.385984i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.2083 | −0.413145 | ||||||||
\(737\) | 12.5918 | + | 18.5406i | 0.463824 | + | 0.682951i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.0389 | + | 37.0519i | −0.442857 | + | 1.36298i | 0.441959 | + | 0.897035i | \(0.354284\pi\) |
−0.884816 | + | 0.465940i | \(0.845716\pi\) | |||||||
\(740\) | −3.56688 | + | 2.59149i | −0.131121 | + | 0.0952651i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.31742 | + | 25.5984i | 0.305342 | + | 0.939747i | ||||
\(743\) | −14.1930 | − | 43.6817i | −0.520692 | − | 1.60252i | −0.772681 | − | 0.634795i | \(-0.781085\pi\) |
0.251989 | − | 0.967730i | \(-0.418915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.05490 | + | 5.12569i | −0.258472 | + | 0.187791i | ||||
\(746\) | 23.2089 | − | 71.4298i | 0.849740 | − | 2.61523i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.53148 | + | 1.02481i | −0.129124 | + | 0.0374706i | ||||
\(749\) | −22.4549 | −0.820483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.7634 | + | 13.6324i | −0.684686 | + | 0.497453i | −0.874909 | − | 0.484288i | \(-0.839079\pi\) |
0.190223 | + | 0.981741i | \(0.439079\pi\) | |||||||
\(752\) | 7.39504 | + | 5.37281i | 0.269669 | + | 0.195926i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.34907 | − | 22.6181i | −0.267637 | − | 0.823703i | ||||
\(755\) | −9.65596 | − | 7.01547i | −0.351416 | − | 0.255319i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.01541 | + | 6.20281i | −0.0732515 | + | 0.225445i | −0.980979 | − | 0.194116i | \(-0.937816\pi\) |
0.907727 | + | 0.419561i | \(0.137816\pi\) | |||||||
\(758\) | 36.7757 | 1.33575 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.45628 | −0.234194 | ||||||||
\(761\) | 2.02926 | − | 6.24542i | 0.0735606 | − | 0.226396i | −0.907516 | − | 0.420018i | \(-0.862024\pi\) |
0.981076 | + | 0.193622i | \(0.0620236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.4444 | − | 13.4007i | −0.667733 | − | 0.485137i | ||||
\(764\) | −12.7386 | − | 39.2054i | −0.460866 | − | 1.41840i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.6572 | − | 26.6330i | −1.32448 | − | 0.962291i | ||||
\(767\) | 6.94565 | − | 5.04631i | 0.250793 | − | 0.182212i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.5950 | 0.454188 | 0.227094 | − | 0.973873i | \(-0.427078\pi\) | ||||
0.227094 | + | 0.973873i | \(0.427078\pi\) | |||||||
\(770\) | 0.676101 | − | 21.3041i | 0.0243650 | − | 0.767746i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.90990 | + | 5.87807i | −0.0687389 | + | 0.211557i | ||||
\(773\) | 17.7537 | − | 12.8988i | 0.638557 | − | 0.463939i | −0.220797 | − | 0.975320i | \(-0.570866\pi\) |
0.859354 | + | 0.511381i | \(0.170866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.23741 | − | 9.96371i | −0.116291 | − | 0.357907i | ||||
\(776\) | 3.87980 | + | 11.9408i | 0.139277 | + | 0.428650i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 60.5867 | − | 44.0188i | 2.17214 | − | 1.57815i | ||||
\(779\) | −10.7541 | + | 33.0977i | −0.385305 | + | 1.18585i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.2630 | − | 17.0876i | 0.474587 | − | 0.611444i | ||||
\(782\) | 1.35118 | 0.0483181 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.97430 | − | 4.34059i | 0.213368 | − | 0.155021i | ||||
\(785\) | −3.13520 | − | 2.27786i | −0.111900 | − | 0.0813002i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.16981 | + | 15.9110i | 0.184284 | + | 0.567167i | 0.999935 | − | 0.0113766i | \(-0.00362136\pi\) |
−0.815652 | + | 0.578543i | \(0.803621\pi\) | |||||||
\(788\) | 0.279875 | + | 0.203341i | 0.00997012 | + | 0.00724372i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.48350 | + | 23.0318i | −0.266251 | + | 0.819436i | ||||
\(791\) | −9.31320 | −0.331139 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.15261 | −0.218486 | ||||||||
\(794\) | −12.9786 | + | 39.9439i | −0.460592 | + | 1.41756i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.5840 | + | 10.5959i | 0.516915 | + | 0.375560i | ||||
\(797\) | 3.63735 | + | 11.1946i | 0.128842 | + | 0.396533i | 0.994581 | − | 0.103961i | \(-0.0331516\pi\) |
−0.865740 | + | 0.500494i | \(0.833152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.11834 | − | 0.812521i | −0.0395640 | − | 0.0287449i | ||||
\(800\) | 6.52234 | − | 4.73876i | 0.230600 | − | 0.167541i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 43.7889 | 1.54624 | ||||||||
\(803\) | 1.03896 | − | 32.7379i | 0.0366641 | − | 1.15529i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.31770 | + | 4.05547i | −0.0464429 | + | 0.142937i | ||||
\(806\) | 54.1615 | − | 39.3507i | 1.90776 | − | 1.38607i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.96464 | − | 9.12422i | −0.104296 | − | 0.320989i | ||||
\(809\) | −0.369567 | − | 1.13741i | −0.0129933 | − | 0.0399893i | 0.944350 | − | 0.328943i | \(-0.106693\pi\) |
−0.957343 | + | 0.288954i | \(0.906693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.9833 | + | 21.0576i | −1.01774 | + | 0.739431i | −0.965818 | − | 0.259220i | \(-0.916535\pi\) |
−0.0519216 | + | 0.998651i | \(0.516535\pi\) | |||||||
\(812\) | 8.43138 | − | 25.9491i | 0.295884 | − | 0.910636i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0591 | + | 4.34575i | 0.422670 | + | 0.152318i | ||||
\(815\) | −9.93621 | −0.348050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.39841 | + | 6.10181i | −0.293823 | + | 0.213475i | ||||
\(818\) | −39.8324 | − | 28.9400i | −1.39271 | − | 1.01186i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.25561 | + | 10.0197i | 0.113691 | + | 0.349904i | ||||
\(821\) | 4.44312 | + | 3.22811i | 0.155066 | + | 0.112662i | 0.662613 | − | 0.748962i | \(-0.269448\pi\) |
−0.507547 | + | 0.861624i | \(0.669448\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.2028 | − | 40.6341i | 0.460222 | − | 1.41642i | −0.404672 | − | 0.914462i | \(-0.632614\pi\) |
0.864894 | − | 0.501955i | \(-0.167386\pi\) | |||||||
\(824\) | 11.3563 | 0.395616 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0912 | 0.629473 | ||||||||
\(827\) | −10.0186 | + | 30.8340i | −0.348380 | + | 1.07220i | 0.611369 | + | 0.791345i | \(0.290619\pi\) |
−0.959749 | + | 0.280858i | \(0.909381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.35544 | + | 1.71133i | 0.0818079 | + | 0.0594369i | 0.627937 | − | 0.778264i | \(-0.283899\pi\) |
−0.546130 | + | 0.837701i | \(0.683899\pi\) | |||||||
\(830\) | −5.77463 | − | 17.7725i | −0.200440 | − | 0.616892i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26.5438 | + | 19.2852i | 0.920241 | + | 0.668594i | ||||
\(833\) | −0.903483 | + | 0.656419i | −0.0313038 | + | 0.0227436i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9200 | −0.481722 | ||||||||
\(836\) | 35.1666 | + | 51.7805i | 1.21626 | + | 1.79087i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.54786 | − | 20.1522i | 0.226192 | − | 0.696147i | ||||
\(839\) | −16.8652 | + | 12.2533i | −0.582250 | + | 0.423030i | −0.839535 | − | 0.543306i | \(-0.817172\pi\) |
0.257284 | + | 0.966336i | \(0.417172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.68147 | − | 14.4081i | −0.161430 | − | 0.496830i | ||||
\(842\) | 5.77737 | + | 17.7809i | 0.199101 | + | 0.612771i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.38733 | − | 3.18758i | 0.151018 | − | 0.109721i | ||||
\(845\) | −1.14294 | + | 3.51761i | −0.0393184 | + | 0.121009i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.4980 | + | 18.0607i | −0.979203 | + | 0.620572i | ||||
\(848\) | 12.8458 | 0.441127 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.786277 | + | 0.571264i | −0.0269691 | + | 0.0195942i | ||||
\(851\) | −2.07462 | − | 1.50730i | −0.0711171 | − | 0.0516696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6768 | + | 32.8599i | 0.365567 | + | 1.12510i | 0.949625 | + | 0.313388i | \(0.101464\pi\) |
−0.584058 | + | 0.811712i | \(0.698536\pi\) | |||||||
\(854\) | −10.4889 | − | 7.62061i | −0.358922 | − | 0.260772i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.84990 | − | 5.69341i | 0.0632283 | − | 0.194597i | ||||
\(857\) | −33.2969 | −1.13740 | −0.568699 | − | 0.822545i | \(-0.692553\pi\) | ||||
−0.568699 | + | 0.822545i | \(0.692553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7665 | −0.572067 | −0.286034 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286034 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(860\) | −0.971136 | + | 2.98885i | −0.0331155 | + | 0.101919i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.8550 | − | 21.6909i | −1.01687 | − | 0.738796i | ||||
\(863\) | 0.458628 | + | 1.41151i | 0.0156119 | + | 0.0480484i | 0.958559 | − | 0.284894i | \(-0.0919585\pi\) |
−0.942947 | + | 0.332943i | \(0.891958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.76256 | + | 6.36637i | 0.297936 | + | 0.216463i | ||||
\(866\) | −15.5002 | + | 11.2616i | −0.526719 | + | 0.382683i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 76.8068 | 2.60699 | ||||||||
\(869\) | 36.8143 | − | 10.6832i | 1.24884 | − | 0.362403i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.36860 | + | 19.6005i | −0.215792 | + | 0.664138i | ||||
\(872\) | 4.91723 | − | 3.57258i | 0.166518 | − | 0.120983i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.10737 | − | 21.8742i | −0.240410 | − | 0.739907i | ||||
\(875\) | −0.947813 | − | 2.91707i | −0.0320419 | − | 0.0986149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.1134 | − | 14.6132i | 0.679180 | − | 0.493453i | −0.193905 | − | 0.981020i | \(-0.562115\pi\) |
0.873086 | + | 0.487567i | \(0.162115\pi\) | |||||||
\(878\) | 4.18885 | − | 12.8920i | 0.141367 | − | 0.435083i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.57024 | − | 3.44884i | −0.322613 | − | 0.116260i | ||||
\(881\) | −32.6968 | −1.10158 | −0.550792 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550792 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.5268 | + | 27.9914i | −1.29653 | + | 0.941985i | −0.999915 | − | 0.0130124i | \(-0.995858\pi\) |
−0.296615 | + | 0.954997i | \(0.595858\pi\) | |||||||
\(884\) | −2.73557 | − | 1.98751i | −0.0920073 | − | 0.0668472i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.4717 | + | 81.4717i | 0.889336 | + | 2.73709i | ||||
\(887\) | 47.8097 | + | 34.7358i | 1.60529 | + | 1.16631i | 0.876267 | + | 0.481826i | \(0.160026\pi\) |
0.729025 | + | 0.684487i | \(0.239974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.428030 | − | 1.31734i | 0.0143557 | − | 0.0441822i | ||||
\(890\) | 14.1847 | 0.475471 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.5076 | 0.686646 | ||||||||
\(893\) | −7.27130 | + | 22.3787i | −0.243325 | + | 0.748876i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.3918 | + | 13.3624i | 0.614768 | + | 0.446655i | ||||
\(896\) | 6.08220 | + | 18.7191i | 0.203192 | + | 0.625360i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.6140 | − | 14.9770i | −0.687900 | − | 0.499788i | ||||
\(899\) | −31.5431 | + | 22.9174i | −1.05202 | + | 0.764338i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.94265 | −0.0647190 | ||||||||
\(902\) | 18.7808 | − | 24.1966i | 0.625332 | − | 0.805659i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.767250 | − | 2.36135i | 0.0255183 | − | 0.0785374i | ||||
\(905\) | −1.94028 | + | 1.40969i | −0.0644970 | + | 0.0468598i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7098 | + | 32.9613i | 0.355612 | + | 1.09446i | 0.955654 | + | 0.294493i | \(0.0951508\pi\) |
−0.600041 | + | 0.799969i | \(0.704849\pi\) | |||||||
\(908\) | −4.57979 | − | 14.0952i | −0.151986 | − | 0.467764i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.8568 | − | 11.5207i | 0.525648 | − | 0.381906i | ||||
\(911\) | 3.14834 | − | 9.68961i | 0.104309 | − | 0.321031i | −0.885258 | − | 0.465099i | \(-0.846019\pi\) |
0.989568 | + | 0.144069i | \(0.0460186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.1368 | + | 23.3669i | −0.600241 | + | 0.773332i | ||||
\(914\) | −20.7484 | −0.686298 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44.7972 | + | 32.5471i | −1.48014 | + | 1.07539i | ||||
\(917\) | −1.56081 | − | 1.13400i | −0.0515426 | − | 0.0374479i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1644 | − | 34.3606i | −0.368281 | − | 1.13345i | −0.947901 | − | 0.318565i | \(-0.896799\pi\) |
0.579620 | − | 0.814887i | \(-0.303201\pi\) | |||||||
\(920\) | −0.919704 | − | 0.668204i | −0.0303218 | − | 0.0220300i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.02357 | − | 6.22790i | 0.0666427 | − | 0.205105i | ||||
\(923\) | 19.8907 | 0.654711 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.84453 | 0.0606479 | ||||||||
\(926\) | −15.7674 | + | 48.5269i | −0.518148 | + | 1.59469i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24.2737 | − | 17.6359i | −0.796823 | − | 0.578926i | ||||
\(929\) | −8.69078 | − | 26.7475i | −0.285135 | − | 0.877556i | −0.986358 | − | 0.164614i | \(-0.947362\pi\) |
0.701223 | − | 0.712942i | \(-0.252638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.3792 | + | 11.1736i | 0.504033 | + | 0.366201i | ||||
\(932\) | −53.8797 | + | 39.1459i | −1.76489 | + | 1.28227i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −69.5087 | −2.27439 | ||||||||
\(935\) | 1.44729 | + | 0.521562i | 0.0473314 | + | 0.0170569i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0263183 | − | 0.0809993i | 0.000859781 | − | 0.00264613i | −0.950626 | − | 0.310340i | \(-0.899557\pi\) |
0.951485 | + | 0.307694i | \(0.0995572\pi\) | |||||||
\(938\) | −35.1342 | + | 25.5265i | −1.14717 | + | 0.833471i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.20125 | + | 6.77476i | 0.0717969 | + | 0.220968i | ||||
\(941\) | 12.9217 | + | 39.7688i | 0.421234 | + | 1.29643i | 0.906554 | + | 0.422089i | \(0.138703\pi\) |
−0.485320 | + | 0.874337i | \(0.661297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.95744 | + | 3.60179i | −0.161437 | + | 0.117291i | ||||
\(944\) | 2.66812 | − | 8.21161i | 0.0868398 | − | 0.267265i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.77481 | − | 2.54638i | 0.285294 | − | 0.0827898i | ||||
\(947\) | −8.92463 | −0.290012 | −0.145006 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145006 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.3671 | − | 17.7037i | 0.790989 | − | 0.574687i | ||||
\(950\) | 13.3841 | + | 9.72412i | 0.434237 | + | 0.315492i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.359493 | − | 1.10641i | −0.0116512 | − | 0.0358589i | ||||
\(953\) | 4.25853 | + | 3.09400i | 0.137947 | + | 0.100225i | 0.654619 | − | 0.755959i | \(-0.272829\pi\) |
−0.516672 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.32938 | + | 16.4022i | −0.172455 | + | 0.530761i | ||||
\(956\) | 38.9283 | 1.25903 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.2438 | 1.17098 | ||||||||
\(959\) | 10.5998 | − | 32.6227i | 0.342284 | − | 1.05344i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −63.7153 | − | 46.2919i | −2.05533 | − | 1.49329i | ||||
\(962\) | 3.64240 | + | 11.2101i | 0.117436 | + | 0.361429i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.49043 | − | 6.16866i | −0.273458 | − | 0.198679i | ||||
\(965\) | 2.09190 | − | 1.51986i | 0.0673408 | − | 0.0489259i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.5421 | −0.596275 | −0.298138 | − | 0.954523i | \(-0.596365\pi\) | ||||
−0.298138 | + | 0.954523i | \(0.596365\pi\) | |||||||
\(968\) | −2.23151 | − | 8.71353i | −0.0717235 | − | 0.280063i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.94165 | − | 30.5973i | 0.319207 | − | 0.982419i | ||||
\(971\) | −19.5968 | + | 14.2379i | −0.628893 | + | 0.456917i | −0.856016 | − | 0.516949i | \(-0.827068\pi\) |
0.227124 | + | 0.973866i | \(0.427068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.25101 | + | 6.92790i | 0.0721641 | + | 0.222098i | ||||
\(974\) | 4.94715 | + | 15.2258i | 0.158517 | + | 0.487865i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00592 | + | 3.63701i | −0.160236 | + | 0.116418i | ||||
\(977\) | −15.1609 | + | 46.6606i | −0.485041 | + | 1.49280i | 0.346880 | + | 0.937910i | \(0.387241\pi\) |
−0.831921 | + | 0.554894i | \(0.812759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.6146 | − | 18.5742i | −0.403165 | − | 0.593634i | ||||
\(980\) | 5.75485 | 0.183832 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −51.9664 | + | 37.7558i | −1.65831 | + | 1.20484i | ||||
\(983\) | 39.7546 | + | 28.8834i | 1.26798 | + | 0.921239i | 0.999120 | − | 0.0419415i | \(-0.0133543\pi\) |
0.268856 | + | 0.963180i | \(0.413354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0447243 | − | 0.137647i | −0.00142503 | − | 0.00438581i | ||||
\(986\) | 2.92622 | + | 2.12603i | 0.0931899 | + | 0.0677064i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.7863 | + | 54.7408i | −0.565859 | + | 1.74154i | ||||
\(989\) | −1.82788 | −0.0581233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.9620 | 0.983541 | 0.491771 | − | 0.870725i | \(-0.336350\pi\) | ||||
0.491771 | + | 0.870725i | \(0.336350\pi\) | |||||||
\(992\) | 26.1002 | − | 80.3281i | 0.828681 | − | 2.55042i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.9094 | + | 24.6366i | 1.07554 | + | 0.781426i | ||||
\(995\) | −2.33053 | − | 7.17265i | −0.0738829 | − | 0.227388i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5216 | − | 13.4567i | −0.586584 | − | 0.426178i | 0.254507 | − | 0.967071i | \(-0.418087\pi\) |
−0.841092 | + | 0.540892i | \(0.818087\pi\) | |||||||
\(998\) | 63.5305 | − | 46.1576i | 2.01102 | − | 1.46109i | ||||
\(999\) | 0 | 0 |
(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 | 495.2.n.e.361.2 | 8 | ||
3.2 | odd | 2 | 55.2.g.b.31.1 | yes | 8 | ||
11.4 | even | 5 | 5445.2.a.bp.1.4 | 4 | |||
11.5 | even | 5 | inner | 495.2.n.e.181.2 | 8 | ||
11.7 | odd | 10 | 5445.2.a.bi.1.1 | 4 | |||
12.11 | even | 2 | 880.2.bo.h.801.2 | 8 | |||
15.2 | even | 4 | 275.2.z.a.174.1 | 16 | |||
15.8 | even | 4 | 275.2.z.a.174.4 | 16 | |||
15.14 | odd | 2 | 275.2.h.a.251.2 | 8 | |||
33.2 | even | 10 | 605.2.g.e.366.1 | 8 | |||
33.5 | odd | 10 | 55.2.g.b.16.1 | ✓ | 8 | ||
33.8 | even | 10 | 605.2.g.e.81.1 | 8 | |||
33.14 | odd | 10 | 605.2.g.m.81.2 | 8 | |||
33.17 | even | 10 | 605.2.g.k.511.2 | 8 | |||
33.20 | odd | 10 | 605.2.g.m.366.2 | 8 | |||
33.26 | odd | 10 | 605.2.a.j.1.1 | 4 | |||
33.29 | even | 10 | 605.2.a.k.1.4 | 4 | |||
33.32 | even | 2 | 605.2.g.k.251.2 | 8 | |||
132.59 | even | 10 | 9680.2.a.cn.1.1 | 4 | |||
132.71 | even | 10 | 880.2.bo.h.401.2 | 8 | |||
132.95 | odd | 10 | 9680.2.a.cm.1.1 | 4 | |||
165.29 | even | 10 | 3025.2.a.w.1.1 | 4 | |||
165.38 | even | 20 | 275.2.z.a.49.1 | 16 | |||
165.59 | odd | 10 | 3025.2.a.bd.1.4 | 4 | |||
165.104 | odd | 10 | 275.2.h.a.126.2 | 8 | |||
165.137 | even | 20 | 275.2.z.a.49.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.16.1 | ✓ | 8 | 33.5 | odd | 10 | ||
55.2.g.b.31.1 | yes | 8 | 3.2 | odd | 2 | ||
275.2.h.a.126.2 | 8 | 165.104 | odd | 10 | |||
275.2.h.a.251.2 | 8 | 15.14 | odd | 2 | |||
275.2.z.a.49.1 | 16 | 165.38 | even | 20 | |||
275.2.z.a.49.4 | 16 | 165.137 | even | 20 | |||
275.2.z.a.174.1 | 16 | 15.2 | even | 4 | |||
275.2.z.a.174.4 | 16 | 15.8 | even | 4 | |||
495.2.n.e.181.2 | 8 | 11.5 | even | 5 | inner | ||
495.2.n.e.361.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.a.j.1.1 | 4 | 33.26 | odd | 10 | |||
605.2.a.k.1.4 | 4 | 33.29 | even | 10 | |||
605.2.g.e.81.1 | 8 | 33.8 | even | 10 | |||
605.2.g.e.366.1 | 8 | 33.2 | even | 10 | |||
605.2.g.k.251.2 | 8 | 33.32 | even | 2 | |||
605.2.g.k.511.2 | 8 | 33.17 | even | 10 | |||
605.2.g.m.81.2 | 8 | 33.14 | odd | 10 | |||
605.2.g.m.366.2 | 8 | 33.20 | odd | 10 | |||
880.2.bo.h.401.2 | 8 | 132.71 | even | 10 | |||
880.2.bo.h.801.2 | 8 | 12.11 | even | 2 | |||
3025.2.a.w.1.1 | 4 | 165.29 | even | 10 | |||
3025.2.a.bd.1.4 | 4 | 165.59 | odd | 10 | |||
5445.2.a.bi.1.1 | 4 | 11.7 | odd | 10 | |||
5445.2.a.bp.1.4 | 4 | 11.4 | even | 5 | |||
9680.2.a.cm.1.1 | 4 | 132.95 | odd | 10 | |||
9680.2.a.cn.1.1 | 4 | 132.59 | even | 10 |