Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(88,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.88");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + 27166 x^{4} + 6435 x^{2} + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.5 | ||
Root | \(0.560998i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.121 |
Dual form | 273.2.bl.d.88.5 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.485838 | + | 0.280499i | −0.343540 | + | 0.198343i | −0.661836 | − | 0.749649i | \(-0.730223\pi\) |
0.318297 | + | 0.947991i | \(0.396889\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.842641 | + | 1.45950i | −0.421320 | + | 0.729748i | ||||
\(5\) | −0.449963 | − | 0.259786i | −0.201230 | − | 0.116180i | 0.395999 | − | 0.918251i | \(-0.370398\pi\) |
−0.597229 | + | 0.802071i | \(0.703732\pi\) | |||||||
\(6\) | 0.485838 | − | 0.280499i | 0.198343 | − | 0.114513i | ||||
\(7\) | −1.87423 | − | 1.86743i | −0.708391 | − | 0.705820i | ||||
\(8\) | − | 2.06743i | − | 0.730948i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.291479 | 0.0921738 | ||||||||
\(11\) | − | 2.16751i | − | 0.653528i | −0.945106 | − | 0.326764i | \(-0.894042\pi\) | ||
0.945106 | − | 0.326764i | \(-0.105958\pi\) | |||||||
\(12\) | 0.842641 | − | 1.45950i | 0.243249 | − | 0.421320i | ||||
\(13\) | 3.29920 | − | 1.45439i | 0.915035 | − | 0.403375i | ||||
\(14\) | 1.43438 | + | 0.381548i | 0.383355 | + | 0.101973i | ||||
\(15\) | 0.449963 | + | 0.259786i | 0.116180 | + | 0.0670766i | ||||
\(16\) | −1.10537 | − | 1.91455i | −0.276342 | − | 0.478639i | ||||
\(17\) | 2.48051 | − | 4.29637i | 0.601612 | − | 1.04202i | −0.390965 | − | 0.920405i | \(-0.627859\pi\) |
0.992577 | − | 0.121617i | \(-0.0388079\pi\) | |||||||
\(18\) | −0.485838 | + | 0.280499i | −0.114513 | + | 0.0661142i | ||||
\(19\) | 5.52084i | 1.26657i | 0.773919 | + | 0.633284i | \(0.218294\pi\) | ||||
−0.773919 | + | 0.633284i | \(0.781706\pi\) | |||||||
\(20\) | 0.758315 | − | 0.437813i | 0.169564 | − | 0.0978980i | ||||
\(21\) | 1.87423 | + | 1.86743i | 0.408990 | + | 0.407506i | ||||
\(22\) | 0.607984 | + | 1.05306i | 0.129623 | + | 0.224513i | ||||
\(23\) | −3.39752 | − | 5.88468i | −0.708432 | − | 1.22704i | −0.965439 | − | 0.260631i | \(-0.916069\pi\) |
0.257006 | − | 0.966410i | \(-0.417264\pi\) | |||||||
\(24\) | 2.06743i | 0.422013i | ||||||||
\(25\) | −2.36502 | − | 4.09634i | −0.473004 | − | 0.819268i | ||||
\(26\) | −1.19492 | + | 1.63202i | −0.234344 | + | 0.320066i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.30480 | − | 1.16186i | 0.813531 | − | 0.219571i | ||||
\(29\) | 3.81357 | − | 6.60529i | 0.708161 | − | 1.22657i | −0.257377 | − | 0.966311i | \(-0.582858\pi\) |
0.965538 | − | 0.260260i | \(-0.0838084\pi\) | |||||||
\(30\) | −0.291479 | −0.0532166 | ||||||||
\(31\) | −5.15974 | + | 2.97898i | −0.926717 | + | 0.535040i | −0.885772 | − | 0.464121i | \(-0.846370\pi\) |
−0.0409451 | + | 0.999161i | \(0.513037\pi\) | |||||||
\(32\) | 4.65496 | + | 2.68754i | 0.822889 | + | 0.475095i | ||||
\(33\) | 2.16751i | 0.377315i | ||||||||
\(34\) | 2.78312i | 0.477301i | ||||||||
\(35\) | 0.358201 | + | 1.32717i | 0.0605471 | + | 0.224333i | ||||
\(36\) | −0.842641 | + | 1.45950i | −0.140440 | + | 0.243249i | ||||
\(37\) | −5.06378 | + | 2.92358i | −0.832481 | + | 0.480633i | −0.854701 | − | 0.519120i | \(-0.826260\pi\) |
0.0222205 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(38\) | −1.54859 | − | 2.68224i | −0.251215 | − | 0.435116i | ||||
\(39\) | −3.29920 | + | 1.45439i | −0.528295 | + | 0.232889i | ||||
\(40\) | −0.537091 | + | 0.930269i | −0.0849216 | + | 0.147089i | ||||
\(41\) | −9.23279 | − | 5.33055i | −1.44192 | − | 0.832492i | −0.443941 | − | 0.896056i | \(-0.646420\pi\) |
−0.997978 | + | 0.0635633i | \(0.979754\pi\) | |||||||
\(42\) | −1.43438 | − | 0.381548i | −0.221330 | − | 0.0588742i | ||||
\(43\) | −2.11946 | − | 3.67102i | −0.323215 | − | 0.559825i | 0.657934 | − | 0.753075i | \(-0.271430\pi\) |
−0.981150 | + | 0.193250i | \(0.938097\pi\) | |||||||
\(44\) | 3.16347 | + | 1.82643i | 0.476911 | + | 0.275345i | ||||
\(45\) | −0.449963 | − | 0.259786i | −0.0670766 | − | 0.0387267i | ||||
\(46\) | 3.30129 | + | 1.90600i | 0.486749 | + | 0.281025i | ||||
\(47\) | 9.69377 | + | 5.59670i | 1.41398 | + | 0.816363i | 0.995761 | − | 0.0919829i | \(-0.0293205\pi\) |
0.418221 | + | 0.908345i | \(0.362654\pi\) | |||||||
\(48\) | 1.10537 | + | 1.91455i | 0.159546 | + | 0.276342i | ||||
\(49\) | 0.0254470 | + | 6.99995i | 0.00363529 | + | 0.999993i | ||||
\(50\) | 2.29804 | + | 1.32677i | 0.324991 | + | 0.187634i | ||||
\(51\) | −2.48051 | + | 4.29637i | −0.347341 | + | 0.601612i | ||||
\(52\) | −0.657365 | + | 6.04071i | −0.0911602 | + | 0.837695i | ||||
\(53\) | 1.04639 | + | 1.81239i | 0.143732 | + | 0.248951i | 0.928899 | − | 0.370333i | \(-0.120756\pi\) |
−0.785167 | + | 0.619284i | \(0.787423\pi\) | |||||||
\(54\) | 0.485838 | − | 0.280499i | 0.0661142 | − | 0.0381711i | ||||
\(55\) | −0.563089 | + | 0.975299i | −0.0759269 | + | 0.131509i | ||||
\(56\) | −3.86078 | + | 3.87484i | −0.515918 | + | 0.517797i | ||||
\(57\) | − | 5.52084i | − | 0.731254i | ||||||
\(58\) | 4.27880i | 0.561834i | ||||||||
\(59\) | −2.63992 | − | 1.52416i | −0.343688 | − | 0.198428i | 0.318214 | − | 0.948019i | \(-0.396917\pi\) |
−0.661902 | + | 0.749591i | \(0.730250\pi\) | |||||||
\(60\) | −0.758315 | + | 0.437813i | −0.0978980 | + | 0.0565214i | ||||
\(61\) | 6.24908 | 0.800112 | 0.400056 | − | 0.916491i | \(-0.368991\pi\) | ||||
0.400056 | + | 0.916491i | \(0.368991\pi\) | |||||||
\(62\) | 1.67120 | − | 2.89460i | 0.212243 | − | 0.367615i | ||||
\(63\) | −1.87423 | − | 1.86743i | −0.236130 | − | 0.235273i | ||||
\(64\) | 1.40606 | 0.175758 | ||||||||
\(65\) | −1.86235 | − | 0.202666i | −0.230996 | − | 0.0251376i | ||||
\(66\) | −0.607984 | − | 1.05306i | −0.0748376 | − | 0.129623i | ||||
\(67\) | − | 1.98125i | − | 0.242049i | −0.992650 | − | 0.121024i | \(-0.961382\pi\) | ||
0.992650 | − | 0.121024i | \(-0.0386179\pi\) | |||||||
\(68\) | 4.18036 | + | 7.24059i | 0.506943 | + | 0.878050i | ||||
\(69\) | 3.39752 | + | 5.88468i | 0.409014 | + | 0.708432i | ||||
\(70\) | −0.546298 | − | 0.544315i | −0.0652951 | − | 0.0650581i | ||||
\(71\) | −8.61474 | + | 4.97372i | −1.02238 | + | 0.590272i | −0.914793 | − | 0.403923i | \(-0.867646\pi\) |
−0.107589 | + | 0.994195i | \(0.534313\pi\) | |||||||
\(72\) | − | 2.06743i | − | 0.243649i | ||||||
\(73\) | 2.47088 | − | 1.42656i | 0.289195 | − | 0.166967i | −0.348384 | − | 0.937352i | \(-0.613269\pi\) |
0.637579 | + | 0.770385i | \(0.279936\pi\) | |||||||
\(74\) | 1.64012 | − | 2.84077i | 0.190660 | − | 0.330233i | ||||
\(75\) | 2.36502 | + | 4.09634i | 0.273089 | + | 0.473004i | ||||
\(76\) | −8.05765 | − | 4.65209i | −0.924276 | − | 0.533631i | ||||
\(77\) | −4.04766 | + | 4.06240i | −0.461274 | + | 0.462953i | ||||
\(78\) | 1.19492 | − | 1.63202i | 0.135299 | − | 0.184790i | ||||
\(79\) | 2.48141 | − | 4.29793i | 0.279181 | − | 0.483555i | −0.692001 | − | 0.721897i | \(-0.743271\pi\) |
0.971181 | + | 0.238342i | \(0.0766039\pi\) | |||||||
\(80\) | 1.14864i | 0.128422i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.98086 | 0.660475 | ||||||||
\(83\) | − | 3.65923i | − | 0.401653i | −0.979627 | − | 0.200826i | \(-0.935637\pi\) | ||
0.979627 | − | 0.200826i | \(-0.0643627\pi\) | |||||||
\(84\) | −4.30480 | + | 1.16186i | −0.469692 | + | 0.126769i | ||||
\(85\) | −2.23228 | + | 1.28880i | −0.242124 | + | 0.139791i | ||||
\(86\) | 2.05943 | + | 1.18901i | 0.222074 | + | 0.128215i | ||||
\(87\) | −3.81357 | + | 6.60529i | −0.408857 | + | 0.708161i | ||||
\(88\) | −4.48118 | −0.477696 | ||||||||
\(89\) | −2.19138 | + | 1.26519i | −0.232285 | + | 0.134110i | −0.611626 | − | 0.791147i | \(-0.709484\pi\) |
0.379341 | + | 0.925257i | \(0.376151\pi\) | |||||||
\(90\) | 0.291479 | 0.0307246 | ||||||||
\(91\) | −8.89942 | − | 3.43516i | −0.932913 | − | 0.360103i | ||||
\(92\) | 11.4516 | 1.19391 | ||||||||
\(93\) | 5.15974 | − | 2.97898i | 0.535040 | − | 0.308906i | ||||
\(94\) | −6.27947 | −0.647678 | ||||||||
\(95\) | 1.43424 | − | 2.48418i | 0.147150 | − | 0.254871i | ||||
\(96\) | −4.65496 | − | 2.68754i | −0.475095 | − | 0.274296i | ||||
\(97\) | 8.01957 | − | 4.63010i | 0.814264 | − | 0.470116i | −0.0341702 | − | 0.999416i | \(-0.510879\pi\) |
0.848435 | + | 0.529300i | \(0.177545\pi\) | |||||||
\(98\) | −1.97584 | − | 3.39371i | −0.199590 | − | 0.342816i | ||||
\(99\) | − | 2.16751i | − | 0.217843i | ||||||
\(100\) | 7.97146 | 0.797146 | ||||||||
\(101\) | −9.04398 | −0.899909 | −0.449955 | − | 0.893051i | \(-0.648560\pi\) | ||||
−0.449955 | + | 0.893051i | \(0.648560\pi\) | |||||||
\(102\) | − | 2.78312i | − | 0.275570i | ||||||
\(103\) | −8.82890 | + | 15.2921i | −0.869937 | + | 1.50678i | −0.00787730 | + | 0.999969i | \(0.502507\pi\) |
−0.862060 | + | 0.506806i | \(0.830826\pi\) | |||||||
\(104\) | −3.00686 | − | 6.82089i | −0.294847 | − | 0.668843i | ||||
\(105\) | −0.358201 | − | 1.32717i | −0.0349569 | − | 0.129519i | ||||
\(106\) | −1.01675 | − | 0.587020i | −0.0987553 | − | 0.0570164i | ||||
\(107\) | −9.73005 | − | 16.8529i | −0.940639 | − | 1.62923i | −0.764256 | − | 0.644913i | \(-0.776894\pi\) |
−0.176383 | − | 0.984322i | \(-0.556440\pi\) | |||||||
\(108\) | 0.842641 | − | 1.45950i | 0.0810831 | − | 0.140440i | ||||
\(109\) | 14.1408 | − | 8.16420i | 1.35444 | − | 0.781989i | 0.365576 | − | 0.930782i | \(-0.380872\pi\) |
0.988868 | + | 0.148793i | \(0.0475388\pi\) | |||||||
\(110\) | − | 0.631783i | − | 0.0602382i | ||||||
\(111\) | 5.06378 | − | 2.92358i | 0.480633 | − | 0.277494i | ||||
\(112\) | −1.50358 | + | 5.65250i | −0.142075 | + | 0.534111i | ||||
\(113\) | 6.19998 | + | 10.7387i | 0.583245 | + | 1.01021i | 0.995092 | + | 0.0989565i | \(0.0315505\pi\) |
−0.411847 | + | 0.911253i | \(0.635116\pi\) | |||||||
\(114\) | 1.54859 | + | 2.68224i | 0.145039 | + | 0.251215i | ||||
\(115\) | 3.53052i | 0.329223i | ||||||||
\(116\) | 6.42693 | + | 11.1318i | 0.596726 | + | 1.03356i | ||||
\(117\) | 3.29920 | − | 1.45439i | 0.305012 | − | 0.134458i | ||||
\(118\) | 1.71010 | 0.157427 | ||||||||
\(119\) | −12.6722 | + | 3.42020i | −1.16166 | + | 0.313529i | ||||
\(120\) | 0.537091 | − | 0.930269i | 0.0490295 | − | 0.0849216i | ||||
\(121\) | 6.30191 | 0.572901 | ||||||||
\(122\) | −3.03604 | + | 1.75286i | −0.274870 | + | 0.158696i | ||||
\(123\) | 9.23279 | + | 5.33055i | 0.832492 | + | 0.480640i | ||||
\(124\) | − | 10.0408i | − | 0.901693i | ||||||
\(125\) | 5.05547i | 0.452175i | ||||||||
\(126\) | 1.43438 | + | 0.381548i | 0.127785 | + | 0.0339910i | ||||
\(127\) | 10.1675 | − | 17.6107i | 0.902223 | − | 1.56270i | 0.0776210 | − | 0.996983i | \(-0.475268\pi\) |
0.824602 | − | 0.565713i | \(-0.191399\pi\) | |||||||
\(128\) | −9.99304 | + | 5.76949i | −0.883269 | + | 0.509955i | ||||
\(129\) | 2.11946 | + | 3.67102i | 0.186608 | + | 0.323215i | ||||
\(130\) | 0.961649 | − | 0.423925i | 0.0843422 | − | 0.0371806i | ||||
\(131\) | 6.88948 | − | 11.9329i | 0.601937 | − | 1.04258i | −0.390591 | − | 0.920564i | \(-0.627729\pi\) |
0.992528 | − | 0.122020i | \(-0.0389374\pi\) | |||||||
\(132\) | −3.16347 | − | 1.82643i | −0.275345 | − | 0.158970i | ||||
\(133\) | 10.3098 | − | 10.3473i | 0.893970 | − | 0.897226i | ||||
\(134\) | 0.555739 | + | 0.962568i | 0.0480085 | + | 0.0831532i | ||||
\(135\) | 0.449963 | + | 0.259786i | 0.0387267 | + | 0.0223589i | ||||
\(136\) | −8.88246 | − | 5.12829i | −0.761665 | − | 0.439747i | ||||
\(137\) | −1.40407 | − | 0.810643i | −0.119958 | − | 0.0692579i | 0.438820 | − | 0.898575i | \(-0.355396\pi\) |
−0.558778 | + | 0.829317i | \(0.688730\pi\) | |||||||
\(138\) | −3.30129 | − | 1.90600i | −0.281025 | − | 0.162250i | ||||
\(139\) | 3.66875 | + | 6.35446i | 0.311179 | + | 0.538979i | 0.978618 | − | 0.205686i | \(-0.0659426\pi\) |
−0.667439 | + | 0.744665i | \(0.732609\pi\) | |||||||
\(140\) | −2.23884 | − | 0.595535i | −0.189216 | − | 0.0503319i | ||||
\(141\) | −9.69377 | − | 5.59670i | −0.816363 | − | 0.471327i | ||||
\(142\) | 2.79025 | − | 4.83285i | 0.234152 | − | 0.405564i | ||||
\(143\) | −3.15240 | − | 7.15105i | −0.263617 | − | 0.598001i | ||||
\(144\) | −1.10537 | − | 1.91455i | −0.0921140 | − | 0.159546i | ||||
\(145\) | −3.43193 | + | 1.98142i | −0.285006 | + | 0.164548i | ||||
\(146\) | −0.800299 | + | 1.38616i | −0.0662332 | + | 0.114719i | ||||
\(147\) | −0.0254470 | − | 6.99995i | −0.00209884 | − | 0.577346i | ||||
\(148\) | − | 9.85410i | − | 0.810002i | ||||||
\(149\) | 1.07489i | 0.0880585i | 0.999030 | + | 0.0440293i | \(0.0140195\pi\) | ||||
−0.999030 | + | 0.0440293i | \(0.985981\pi\) | |||||||
\(150\) | −2.29804 | − | 1.32677i | −0.187634 | − | 0.108330i | ||||
\(151\) | −10.8708 | + | 6.27625i | −0.884652 | + | 0.510754i | −0.872189 | − | 0.489168i | \(-0.837300\pi\) |
−0.0124624 | + | 0.999922i | \(0.503967\pi\) | |||||||
\(152\) | 11.4140 | 0.925796 | ||||||||
\(153\) | 2.48051 | − | 4.29637i | 0.200537 | − | 0.347341i | ||||
\(154\) | 0.827009 | − | 3.10903i | 0.0666423 | − | 0.250533i | ||||
\(155\) | 3.09559 | 0.248644 | ||||||||
\(156\) | 0.657365 | − | 6.04071i | 0.0526313 | − | 0.483644i | ||||
\(157\) | 0.346108 | + | 0.599476i | 0.0276224 | + | 0.0478434i | 0.879506 | − | 0.475888i | \(-0.157873\pi\) |
−0.851884 | + | 0.523731i | \(0.824540\pi\) | |||||||
\(158\) | 2.78413i | 0.221494i | ||||||||
\(159\) | −1.04639 | − | 1.81239i | −0.0829838 | − | 0.143732i | ||||
\(160\) | −1.39637 | − | 2.41859i | −0.110393 | − | 0.191206i | ||||
\(161\) | −4.62148 | + | 17.3738i | −0.364223 | + | 1.36925i | ||||
\(162\) | −0.485838 | + | 0.280499i | −0.0381711 | + | 0.0220381i | ||||
\(163\) | − | 10.3974i | − | 0.814384i | −0.913343 | − | 0.407192i | \(-0.866508\pi\) | ||
0.913343 | − | 0.407192i | \(-0.133492\pi\) | |||||||
\(164\) | 15.5598 | − | 8.98348i | 1.21502 | − | 0.701492i | ||||
\(165\) | 0.563089 | − | 0.975299i | 0.0438364 | − | 0.0759269i | ||||
\(166\) | 1.02641 | + | 1.77779i | 0.0796648 | + | 0.137984i | ||||
\(167\) | 20.9105 | + | 12.0727i | 1.61810 | + | 0.934213i | 0.987410 | + | 0.158181i | \(0.0505629\pi\) |
0.630694 | + | 0.776032i | \(0.282770\pi\) | |||||||
\(168\) | 3.86078 | − | 3.87484i | 0.297866 | − | 0.298950i | ||||
\(169\) | 8.76949 | − | 9.59666i | 0.674577 | − | 0.738205i | ||||
\(170\) | 0.723017 | − | 1.25230i | 0.0554528 | − | 0.0960471i | ||||
\(171\) | 5.52084i | 0.422190i | ||||||||
\(172\) | 7.14379 | 0.544709 | ||||||||
\(173\) | 3.73858 | 0.284239 | 0.142119 | − | 0.989850i | \(-0.454608\pi\) | ||||
0.142119 | + | 0.989850i | \(0.454608\pi\) | |||||||
\(174\) | − | 4.27880i | − | 0.324375i | ||||||
\(175\) | −3.21702 | + | 12.0940i | −0.243184 | + | 0.914218i | ||||
\(176\) | −4.14981 | + | 2.39590i | −0.312804 | + | 0.180597i | ||||
\(177\) | 2.63992 | + | 1.52416i | 0.198428 | + | 0.114563i | ||||
\(178\) | 0.709770 | − | 1.22936i | 0.0531995 | − | 0.0921442i | ||||
\(179\) | −5.67810 | −0.424401 | −0.212200 | − | 0.977226i | \(-0.568063\pi\) | ||||
−0.212200 | + | 0.977226i | \(0.568063\pi\) | |||||||
\(180\) | 0.758315 | − | 0.437813i | 0.0565214 | − | 0.0326327i | ||||
\(181\) | −9.94903 | −0.739506 | −0.369753 | − | 0.929130i | \(-0.620558\pi\) | ||||
−0.369753 | + | 0.929130i | \(0.620558\pi\) | |||||||
\(182\) | 5.28724 | − | 0.827345i | 0.391916 | − | 0.0613269i | ||||
\(183\) | −6.24908 | −0.461945 | ||||||||
\(184\) | −12.1662 | + | 7.02415i | −0.896904 | + | 0.517827i | ||||
\(185\) | 3.03802 | 0.223360 | ||||||||
\(186\) | −1.67120 | + | 2.89460i | −0.122538 | + | 0.212243i | ||||
\(187\) | −9.31241 | − | 5.37652i | −0.680991 | − | 0.393170i | ||||
\(188\) | −16.3367 | + | 9.43201i | −1.19148 | + | 0.687900i | ||||
\(189\) | 1.87423 | + | 1.86743i | 0.136330 | + | 0.135835i | ||||
\(190\) | 1.60921i | 0.116744i | ||||||||
\(191\) | 9.50875 | 0.688029 | 0.344014 | − | 0.938964i | \(-0.388213\pi\) | ||||
0.344014 | + | 0.938964i | \(0.388213\pi\) | |||||||
\(192\) | −1.40606 | −0.101474 | ||||||||
\(193\) | − | 3.11196i | − | 0.224004i | −0.993708 | − | 0.112002i | \(-0.964274\pi\) | ||
0.993708 | − | 0.112002i | \(-0.0357263\pi\) | |||||||
\(194\) | −2.59748 | + | 4.49896i | −0.186488 | + | 0.323007i | ||||
\(195\) | 1.86235 | + | 0.202666i | 0.133366 | + | 0.0145132i | ||||
\(196\) | −10.2379 | − | 5.86131i | −0.731275 | − | 0.418665i | ||||
\(197\) | 4.41349 | + | 2.54813i | 0.314448 | + | 0.181547i | 0.648915 | − | 0.760861i | \(-0.275223\pi\) |
−0.334467 | + | 0.942407i | \(0.608556\pi\) | |||||||
\(198\) | 0.607984 | + | 1.05306i | 0.0432075 | + | 0.0748376i | ||||
\(199\) | −6.95536 | + | 12.0470i | −0.493053 | + | 0.853992i | −0.999968 | − | 0.00800358i | \(-0.997452\pi\) |
0.506915 | + | 0.861996i | \(0.330786\pi\) | |||||||
\(200\) | −8.46891 | + | 4.88953i | −0.598842 | + | 0.345742i | ||||
\(201\) | 1.98125i | 0.139747i | ||||||||
\(202\) | 4.39391 | − | 2.53683i | 0.309154 | − | 0.178490i | ||||
\(203\) | −19.4824 | + | 5.25826i | −1.36739 | + | 0.369057i | ||||
\(204\) | −4.18036 | − | 7.24059i | −0.292683 | − | 0.506943i | ||||
\(205\) | 2.76961 | + | 4.79711i | 0.193438 | + | 0.335044i | ||||
\(206\) | − | 9.90598i | − | 0.690183i | ||||||
\(207\) | −3.39752 | − | 5.88468i | −0.236144 | − | 0.409014i | ||||
\(208\) | −6.43135 | − | 4.70887i | −0.445934 | − | 0.326501i | ||||
\(209\) | 11.9665 | 0.827738 | ||||||||
\(210\) | 0.546298 | + | 0.544315i | 0.0376981 | + | 0.0375613i | ||||
\(211\) | −6.30791 | + | 10.9256i | −0.434255 | + | 0.752151i | −0.997234 | − | 0.0743195i | \(-0.976322\pi\) |
0.562980 | + | 0.826471i | \(0.309655\pi\) | |||||||
\(212\) | −3.52691 | −0.242229 | ||||||||
\(213\) | 8.61474 | − | 4.97372i | 0.590272 | − | 0.340794i | ||||
\(214\) | 9.45446 | + | 5.45853i | 0.646293 | + | 0.373138i | ||||
\(215\) | 2.20243i | 0.150205i | ||||||||
\(216\) | 2.06743i | 0.140671i | ||||||||
\(217\) | 15.2335 | + | 4.05215i | 1.03412 | + | 0.275078i | ||||
\(218\) | −4.58010 | + | 7.93296i | −0.310203 | + | 0.537288i | ||||
\(219\) | −2.47088 | + | 1.42656i | −0.166967 | + | 0.0963982i | ||||
\(220\) | −0.948964 | − | 1.64365i | −0.0639791 | − | 0.110815i | ||||
\(221\) | 1.93511 | − | 17.7822i | 0.130169 | − | 1.19616i | ||||
\(222\) | −1.64012 | + | 2.84077i | −0.110078 | + | 0.190660i | ||||
\(223\) | 0.659526 | + | 0.380777i | 0.0441651 | + | 0.0254987i | 0.521920 | − | 0.852994i | \(-0.325216\pi\) |
−0.477755 | + | 0.878493i | \(0.658549\pi\) | |||||||
\(224\) | −3.70567 | − | 13.7299i | −0.247595 | − | 0.917365i | ||||
\(225\) | −2.36502 | − | 4.09634i | −0.157668 | − | 0.273089i | ||||
\(226\) | −6.02437 | − | 3.47817i | −0.400735 | − | 0.231365i | ||||
\(227\) | 1.33416 | + | 0.770280i | 0.0885515 | + | 0.0511252i | 0.543622 | − | 0.839330i | \(-0.317053\pi\) |
−0.455070 | + | 0.890455i | \(0.650386\pi\) | |||||||
\(228\) | 8.05765 | + | 4.65209i | 0.533631 | + | 0.308092i | ||||
\(229\) | 4.86535 | + | 2.80901i | 0.321512 | + | 0.185625i | 0.652066 | − | 0.758162i | \(-0.273902\pi\) |
−0.330555 | + | 0.943787i | \(0.607236\pi\) | |||||||
\(230\) | −0.990307 | − | 1.71526i | −0.0652989 | − | 0.113101i | ||||
\(231\) | 4.04766 | − | 4.06240i | 0.266316 | − | 0.267286i | ||||
\(232\) | −13.6560 | − | 7.88430i | −0.896560 | − | 0.517629i | ||||
\(233\) | −8.57478 | + | 14.8520i | −0.561753 | + | 0.972984i | 0.435591 | + | 0.900145i | \(0.356539\pi\) |
−0.997344 | + | 0.0728395i | \(0.976794\pi\) | |||||||
\(234\) | −1.19492 | + | 1.63202i | −0.0781147 | + | 0.106689i | ||||
\(235\) | −2.90789 | − | 5.03662i | −0.189690 | − | 0.328553i | ||||
\(236\) | 4.44900 | − | 2.56863i | 0.289605 | − | 0.167204i | ||||
\(237\) | −2.48141 | + | 4.29793i | −0.161185 | + | 0.279181i | ||||
\(238\) | 5.19727 | − | 5.21620i | 0.336889 | − | 0.338116i | ||||
\(239\) | 25.6658i | 1.66018i | 0.557628 | + | 0.830091i | \(0.311711\pi\) | ||||
−0.557628 | + | 0.830091i | \(0.688289\pi\) | |||||||
\(240\) | − | 1.14864i | − | 0.0741443i | ||||||
\(241\) | 4.08520 | + | 2.35859i | 0.263151 | + | 0.151930i | 0.625771 | − | 0.780007i | \(-0.284784\pi\) |
−0.362620 | + | 0.931937i | \(0.618118\pi\) | |||||||
\(242\) | −3.06171 | + | 1.76768i | −0.196814 | + | 0.113631i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.26573 | + | 9.12050i | −0.337104 | + | 0.583880i | ||||
\(245\) | 1.80704 | − | 3.15633i | 0.115448 | − | 0.201651i | ||||
\(246\) | −5.98086 | −0.381325 | ||||||||
\(247\) | 8.02947 | + | 18.2144i | 0.510903 | + | 1.15895i | ||||
\(248\) | 6.15884 | + | 10.6674i | 0.391087 | + | 0.677382i | ||||
\(249\) | 3.65923i | 0.231894i | ||||||||
\(250\) | −1.41805 | − | 2.45614i | −0.0896855 | − | 0.155340i | ||||
\(251\) | −0.0982527 | − | 0.170179i | −0.00620165 | − | 0.0107416i | 0.862908 | − | 0.505361i | \(-0.168641\pi\) |
−0.869110 | + | 0.494620i | \(0.835307\pi\) | |||||||
\(252\) | 4.30480 | − | 1.16186i | 0.271177 | − | 0.0731902i | ||||
\(253\) | −12.7551 | + | 7.36416i | −0.801906 | + | 0.462981i | ||||
\(254\) | 11.4079i | 0.715797i | ||||||||
\(255\) | 2.23228 | − | 1.28880i | 0.139791 | − | 0.0807081i | ||||
\(256\) | 1.83061 | − | 3.17070i | 0.114413 | − | 0.198169i | ||||
\(257\) | 0.753004 | + | 1.30424i | 0.0469711 | + | 0.0813563i | 0.888555 | − | 0.458770i | \(-0.151710\pi\) |
−0.841584 | + | 0.540126i | \(0.818376\pi\) | |||||||
\(258\) | −2.05943 | − | 1.18901i | −0.128215 | − | 0.0740248i | ||||
\(259\) | 14.9502 | + | 3.97679i | 0.928962 | + | 0.247106i | ||||
\(260\) | 1.86508 | − | 2.54732i | 0.115668 | − | 0.157978i | ||||
\(261\) | 3.81357 | − | 6.60529i | 0.236054 | − | 0.408857i | ||||
\(262\) | 7.72996i | 0.477559i | ||||||||
\(263\) | 6.88599 | 0.424608 | 0.212304 | − | 0.977204i | \(-0.431903\pi\) | ||||
0.212304 | + | 0.977204i | \(0.431903\pi\) | |||||||
\(264\) | 4.48118 | 0.275798 | ||||||||
\(265\) | − | 1.08735i | − | 0.0667952i | ||||||
\(266\) | −2.10647 | + | 7.91900i | −0.129156 | + | 0.485545i | ||||
\(267\) | 2.19138 | − | 1.26519i | 0.134110 | − | 0.0774285i | ||||
\(268\) | 2.89163 | + | 1.66948i | 0.176634 | + | 0.101980i | ||||
\(269\) | 5.93548 | − | 10.2806i | 0.361893 | − | 0.626816i | −0.626380 | − | 0.779518i | \(-0.715464\pi\) |
0.988272 | + | 0.152702i | \(0.0487974\pi\) | |||||||
\(270\) | −0.291479 | −0.0177389 | ||||||||
\(271\) | −11.9020 | + | 6.87163i | −0.722995 | + | 0.417422i | −0.815854 | − | 0.578258i | \(-0.803733\pi\) |
0.0928589 | + | 0.995679i | \(0.470399\pi\) | |||||||
\(272\) | −10.9675 | −0.665003 | ||||||||
\(273\) | 8.89942 | + | 3.43516i | 0.538617 | + | 0.207905i | ||||
\(274\) | 0.909537 | 0.0549472 | ||||||||
\(275\) | −8.87885 | + | 5.12620i | −0.535415 | + | 0.309122i | ||||
\(276\) | −11.4516 | −0.689303 | ||||||||
\(277\) | −5.60801 | + | 9.71335i | −0.336952 | + | 0.583619i | −0.983858 | − | 0.178951i | \(-0.942729\pi\) |
0.646905 | + | 0.762570i | \(0.276063\pi\) | |||||||
\(278\) | −3.56484 | − | 2.05816i | −0.213805 | − | 0.123440i | ||||
\(279\) | −5.15974 | + | 2.97898i | −0.308906 | + | 0.178347i | ||||
\(280\) | 2.74384 | − | 0.740558i | 0.163976 | − | 0.0442568i | ||||
\(281\) | − | 1.81616i | − | 0.108343i | −0.998532 | − | 0.0541714i | \(-0.982748\pi\) | ||
0.998532 | − | 0.0541714i | \(-0.0172517\pi\) | |||||||
\(282\) | 6.27947 | 0.373937 | ||||||||
\(283\) | 30.8377 | 1.83311 | 0.916556 | − | 0.399905i | \(-0.130957\pi\) | ||||
0.916556 | + | 0.399905i | \(0.130957\pi\) | |||||||
\(284\) | − | 16.7642i | − | 0.994775i | ||||||
\(285\) | −1.43424 | + | 2.48418i | −0.0849571 | + | 0.147150i | ||||
\(286\) | 3.53742 | + | 2.59001i | 0.209172 | + | 0.153150i | ||||
\(287\) | 7.34992 | + | 27.2322i | 0.433852 | + | 1.60747i | ||||
\(288\) | 4.65496 | + | 2.68754i | 0.274296 | + | 0.158365i | ||||
\(289\) | −3.80585 | − | 6.59193i | −0.223874 | − | 0.387760i | ||||
\(290\) | 1.11157 | − | 1.92530i | 0.0652739 | − | 0.113058i | ||||
\(291\) | −8.01957 | + | 4.63010i | −0.470116 | + | 0.271421i | ||||
\(292\) | 4.80832i | 0.281386i | ||||||||
\(293\) | −0.948761 | + | 0.547767i | −0.0554272 | + | 0.0320009i | −0.527458 | − | 0.849581i | \(-0.676855\pi\) |
0.472030 | + | 0.881582i | \(0.343521\pi\) | |||||||
\(294\) | 1.97584 | + | 3.39371i | 0.115233 | + | 0.197925i | ||||
\(295\) | 0.791910 | + | 1.37163i | 0.0461068 | + | 0.0798593i | ||||
\(296\) | 6.04430 | + | 10.4690i | 0.351318 | + | 0.608501i | ||||
\(297\) | 2.16751i | 0.125772i | ||||||||
\(298\) | −0.301506 | − | 0.522223i | −0.0174658 | − | 0.0302516i | ||||
\(299\) | −19.7677 | − | 14.4734i | −1.14320 | − | 0.837020i | ||||
\(300\) | −7.97146 | −0.460232 | ||||||||
\(301\) | −2.88300 | + | 10.8383i | −0.166173 | + | 0.624707i | ||||
\(302\) | 3.52096 | − | 6.09848i | 0.202609 | − | 0.350928i | ||||
\(303\) | 9.04398 | 0.519563 | ||||||||
\(304\) | 10.5700 | − | 6.10257i | 0.606229 | − | 0.350006i | ||||
\(305\) | −2.81185 | − | 1.62342i | −0.161006 | − | 0.0929570i | ||||
\(306\) | 2.78312i | 0.159100i | ||||||||
\(307\) | − | 4.90247i | − | 0.279799i | −0.990166 | − | 0.139899i | \(-0.955322\pi\) | ||
0.990166 | − | 0.139899i | \(-0.0446779\pi\) | |||||||
\(308\) | −2.51834 | − | 9.33069i | −0.143496 | − | 0.531665i | ||||
\(309\) | 8.82890 | − | 15.2921i | 0.502258 | − | 0.869937i | ||||
\(310\) | −1.50396 | + | 0.868310i | −0.0854190 | + | 0.0493167i | ||||
\(311\) | −5.78751 | − | 10.0243i | −0.328179 | − | 0.568423i | 0.653971 | − | 0.756519i | \(-0.273102\pi\) |
−0.982151 | + | 0.188096i | \(0.939768\pi\) | |||||||
\(312\) | 3.00686 | + | 6.82089i | 0.170230 | + | 0.386157i | ||||
\(313\) | 2.53480 | − | 4.39041i | 0.143275 | − | 0.248160i | −0.785453 | − | 0.618922i | \(-0.787570\pi\) |
0.928728 | + | 0.370761i | \(0.120903\pi\) | |||||||
\(314\) | −0.336305 | − | 0.194166i | −0.0189788 | − | 0.0109574i | ||||
\(315\) | 0.358201 | + | 1.32717i | 0.0201824 | + | 0.0747776i | ||||
\(316\) | 4.18188 | + | 7.24322i | 0.235249 | + | 0.407463i | ||||
\(317\) | −14.8929 | − | 8.59841i | −0.836468 | − | 0.482935i | 0.0195943 | − | 0.999808i | \(-0.493763\pi\) |
−0.856062 | + | 0.516873i | \(0.827096\pi\) | |||||||
\(318\) | 1.01675 | + | 0.587020i | 0.0570164 | + | 0.0329184i | ||||
\(319\) | −14.3170 | − | 8.26593i | −0.801599 | − | 0.462803i | ||||
\(320\) | −0.632676 | − | 0.365276i | −0.0353677 | − | 0.0204195i | ||||
\(321\) | 9.73005 | + | 16.8529i | 0.543078 | + | 0.940639i | ||||
\(322\) | −2.62805 | − | 9.73719i | −0.146456 | − | 0.542633i | ||||
\(323\) | 23.7196 | + | 13.6945i | 1.31979 | + | 0.761983i | ||||
\(324\) | −0.842641 | + | 1.45950i | −0.0468134 | + | 0.0810831i | ||||
\(325\) | −13.7604 | − | 10.0750i | −0.763288 | − | 0.558860i | ||||
\(326\) | 2.91645 | + | 5.05143i | 0.161527 | + | 0.279773i | ||||
\(327\) | −14.1408 | + | 8.16420i | −0.781989 | + | 0.451481i | ||||
\(328\) | −11.0206 | + | 19.0882i | −0.608509 | + | 1.05397i | ||||
\(329\) | −7.71690 | − | 28.5919i | −0.425446 | − | 1.57632i | ||||
\(330\) | 0.631783i | 0.0347785i | ||||||||
\(331\) | − | 20.4213i | − | 1.12246i | −0.827662 | − | 0.561228i | \(-0.810329\pi\) | ||
0.827662 | − | 0.561228i | \(-0.189671\pi\) | |||||||
\(332\) | 5.34063 | + | 3.08342i | 0.293105 | + | 0.169224i | ||||
\(333\) | −5.06378 | + | 2.92358i | −0.277494 | + | 0.160211i | ||||
\(334\) | −13.5455 | −0.741177 | ||||||||
\(335\) | −0.514702 | + | 0.891491i | −0.0281212 | + | 0.0487073i | ||||
\(336\) | 1.50358 | − | 5.65250i | 0.0820268 | − | 0.308369i | ||||
\(337\) | −13.1872 | −0.718353 | −0.359176 | − | 0.933270i | \(-0.616942\pi\) | ||||
−0.359176 | + | 0.933270i | \(0.616942\pi\) | |||||||
\(338\) | −1.56870 | + | 7.12226i | −0.0853262 | + | 0.387400i | ||||
\(339\) | −6.19998 | − | 10.7387i | −0.336736 | − | 0.583245i | ||||
\(340\) | − | 4.34400i | − | 0.235586i | ||||||
\(341\) | 6.45696 | + | 11.1838i | 0.349664 | + | 0.605636i | ||||
\(342\) | −1.54859 | − | 2.68224i | −0.0837382 | − | 0.145039i | ||||
\(343\) | 13.0242 | − | 13.1670i | 0.703240 | − | 0.710952i | ||||
\(344\) | −7.58959 | + | 4.38185i | −0.409203 | + | 0.236254i | ||||
\(345\) | − | 3.53052i | − | 0.190077i | ||||||
\(346\) | −1.81634 | + | 1.04867i | −0.0976473 | + | 0.0563767i | ||||
\(347\) | 4.34376 | − | 7.52361i | 0.233185 | − | 0.403889i | −0.725558 | − | 0.688161i | \(-0.758418\pi\) |
0.958744 | + | 0.284272i | \(0.0917518\pi\) | |||||||
\(348\) | −6.42693 | − | 11.1318i | −0.344520 | − | 0.596726i | ||||
\(349\) | 30.2239 | + | 17.4498i | 1.61785 | + | 0.934064i | 0.987476 | + | 0.157770i | \(0.0504303\pi\) |
0.630370 | + | 0.776294i | \(0.282903\pi\) | |||||||
\(350\) | −1.82939 | − | 6.77808i | −0.0977851 | − | 0.362304i | ||||
\(351\) | −3.29920 | + | 1.45439i | −0.176098 | + | 0.0776296i | ||||
\(352\) | 5.82527 | − | 10.0897i | 0.310488 | − | 0.537781i | ||||
\(353\) | − | 14.5143i | − | 0.772519i | −0.922390 | − | 0.386259i | \(-0.873767\pi\) | ||
0.922390 | − | 0.386259i | \(-0.126233\pi\) | |||||||
\(354\) | −1.71010 | −0.0908906 | ||||||||
\(355\) | 5.16842 | 0.274311 | ||||||||
\(356\) | − | 4.26441i | − | 0.226013i | ||||||
\(357\) | 12.6722 | − | 3.42020i | 0.670683 | − | 0.181016i | ||||
\(358\) | 2.75864 | − | 1.59270i | 0.145798 | − | 0.0841768i | ||||
\(359\) | −0.460772 | − | 0.266027i | −0.0243186 | − | 0.0140404i | 0.487791 | − | 0.872960i | \(-0.337803\pi\) |
−0.512110 | + | 0.858920i | \(0.671136\pi\) | |||||||
\(360\) | −0.537091 | + | 0.930269i | −0.0283072 | + | 0.0490295i | ||||
\(361\) | −11.4797 | −0.604196 | ||||||||
\(362\) | 4.83362 | − | 2.79069i | 0.254049 | − | 0.146675i | ||||
\(363\) | −6.30191 | −0.330764 | ||||||||
\(364\) | 12.5126 | − | 10.0941i | 0.655839 | − | 0.529073i | ||||
\(365\) | −1.48241 | −0.0775927 | ||||||||
\(366\) | 3.03604 | − | 1.75286i | 0.158696 | − | 0.0916234i | ||||
\(367\) | 5.85266 | 0.305506 | 0.152753 | − | 0.988264i | \(-0.451186\pi\) | ||||
0.152753 | + | 0.988264i | \(0.451186\pi\) | |||||||
\(368\) | −7.51103 | + | 13.0095i | −0.391539 | + | 0.678166i | ||||
\(369\) | −9.23279 | − | 5.33055i | −0.480640 | − | 0.277497i | ||||
\(370\) | −1.47599 | + | 0.852161i | −0.0767329 | + | 0.0443018i | ||||
\(371\) | 1.42334 | − | 5.35088i | 0.0738964 | − | 0.277804i | ||||
\(372\) | 10.0408i | 0.520593i | ||||||||
\(373\) | 24.2517 | 1.25571 | 0.627853 | − | 0.778332i | \(-0.283934\pi\) | ||||
0.627853 | + | 0.778332i | \(0.283934\pi\) | |||||||
\(374\) | 6.03243 | 0.311930 | ||||||||
\(375\) | − | 5.05547i | − | 0.261063i | ||||||
\(376\) | 11.5708 | − | 20.0412i | 0.596719 | − | 1.03355i | ||||
\(377\) | 2.97506 | − | 27.3386i | 0.153223 | − | 1.40801i | ||||
\(378\) | −1.43438 | − | 0.381548i | −0.0737766 | − | 0.0196247i | ||||
\(379\) | −1.19932 | − | 0.692428i | −0.0616050 | − | 0.0355677i | 0.468881 | − | 0.883261i | \(-0.344657\pi\) |
−0.530486 | + | 0.847694i | \(0.677991\pi\) | |||||||
\(380\) | 2.41710 | + | 4.18654i | 0.123995 | + | 0.214765i | ||||
\(381\) | −10.1675 | + | 17.6107i | −0.520899 | + | 0.902223i | ||||
\(382\) | −4.61971 | + | 2.66719i | −0.236365 | + | 0.136465i | ||||
\(383\) | − | 19.7383i | − | 1.00858i | −0.863534 | − | 0.504290i | \(-0.831754\pi\) | ||
0.863534 | − | 0.504290i | \(-0.168246\pi\) | |||||||
\(384\) | 9.99304 | − | 5.76949i | 0.509955 | − | 0.294423i | ||||
\(385\) | 2.87665 | − | 0.776404i | 0.146608 | − | 0.0395692i | ||||
\(386\) | 0.872902 | + | 1.51191i | 0.0444295 | + | 0.0769542i | ||||
\(387\) | −2.11946 | − | 3.67102i | −0.107738 | − | 0.186608i | ||||
\(388\) | 15.6061i | 0.792277i | ||||||||
\(389\) | 2.48623 | + | 4.30628i | 0.126057 | + | 0.218337i | 0.922146 | − | 0.386843i | \(-0.126434\pi\) |
−0.796089 | + | 0.605180i | \(0.793101\pi\) | |||||||
\(390\) | −0.961649 | + | 0.423925i | −0.0486950 | + | 0.0214663i | ||||
\(391\) | −33.7103 | −1.70480 | ||||||||
\(392\) | 14.4719 | − | 0.0526101i | 0.730944 | − | 0.00265721i | ||||
\(393\) | −6.88948 | + | 11.9329i | −0.347528 | + | 0.601937i | ||||
\(394\) | −2.85899 | −0.144034 | ||||||||
\(395\) | −2.23309 | + | 1.28927i | −0.112359 | + | 0.0648704i | ||||
\(396\) | 3.16347 | + | 1.82643i | 0.158970 | + | 0.0917816i | ||||
\(397\) | − | 9.82615i | − | 0.493161i | −0.969122 | − | 0.246580i | \(-0.920693\pi\) | ||
0.969122 | − | 0.246580i | \(-0.0793069\pi\) | |||||||
\(398\) | − | 7.80389i | − | 0.391173i | ||||||
\(399\) | −10.3098 | + | 10.3473i | −0.516134 | + | 0.518013i | ||||
\(400\) | −5.22844 | + | 9.05593i | −0.261422 | + | 0.452796i | ||||
\(401\) | −25.3395 | + | 14.6298i | −1.26540 | + | 0.730577i | −0.974113 | − | 0.226060i | \(-0.927416\pi\) |
−0.291283 | + | 0.956637i | \(0.594082\pi\) | |||||||
\(402\) | −0.555739 | − | 0.962568i | −0.0277177 | − | 0.0480085i | ||||
\(403\) | −12.6904 | + | 17.3325i | −0.632156 | + | 0.863395i | ||||
\(404\) | 7.62082 | − | 13.1997i | 0.379150 | − | 0.656707i | ||||
\(405\) | −0.449963 | − | 0.259786i | −0.0223589 | − | 0.0129089i | ||||
\(406\) | 7.99034 | − | 8.01944i | 0.396554 | − | 0.397998i | ||||
\(407\) | 6.33688 | + | 10.9758i | 0.314107 | + | 0.544050i | ||||
\(408\) | 8.88246 | + | 5.12829i | 0.439747 | + | 0.253888i | ||||
\(409\) | 11.1197 | + | 6.41994i | 0.549832 | + | 0.317446i | 0.749054 | − | 0.662509i | \(-0.230508\pi\) |
−0.199222 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(410\) | −2.69117 | − | 1.55374i | −0.132907 | − | 0.0767340i | ||||
\(411\) | 1.40407 | + | 0.810643i | 0.0692579 | + | 0.0399861i | ||||
\(412\) | −14.8792 | − | 25.7715i | −0.733045 | − | 1.26967i | ||||
\(413\) | 2.10155 | + | 7.78646i | 0.103411 | + | 0.383147i | ||||
\(414\) | 3.30129 | + | 1.90600i | 0.162250 | + | 0.0936749i | ||||
\(415\) | −0.950618 | + | 1.64652i | −0.0466640 | + | 0.0808244i | ||||
\(416\) | 19.2664 | + | 2.09662i | 0.944613 | + | 0.102795i | ||||
\(417\) | −3.66875 | − | 6.35446i | −0.179660 | − | 0.311179i | ||||
\(418\) | −5.81377 | + | 3.35658i | −0.284361 | + | 0.164176i | ||||
\(419\) | 13.1853 | − | 22.8376i | 0.644144 | − | 1.11569i | −0.340354 | − | 0.940297i | \(-0.610547\pi\) |
0.984498 | − | 0.175393i | \(-0.0561197\pi\) | |||||||
\(420\) | 2.23884 | + | 0.595535i | 0.109244 | + | 0.0290591i | ||||
\(421\) | − | 2.71377i | − | 0.132261i | −0.997811 | − | 0.0661306i | \(-0.978935\pi\) | ||
0.997811 | − | 0.0661306i | \(-0.0210654\pi\) | |||||||
\(422\) | − | 7.07745i | − | 0.344525i | ||||||
\(423\) | 9.69377 | + | 5.59670i | 0.471327 | + | 0.272121i | ||||
\(424\) | 3.74700 | − | 2.16333i | 0.181971 | − | 0.105061i | ||||
\(425\) | −23.4658 | −1.13826 | ||||||||
\(426\) | −2.79025 | + | 4.83285i | −0.135188 | + | 0.234152i | ||||
\(427\) | −11.7122 | − | 11.6697i | −0.566792 | − | 0.564735i | ||||
\(428\) | 32.7957 | 1.58524 | ||||||||
\(429\) | 3.15240 | + | 7.15105i | 0.152200 | + | 0.345256i | ||||
\(430\) | −0.617779 | − | 1.07003i | −0.0297920 | − | 0.0516012i | ||||
\(431\) | − | 37.0866i | − | 1.78640i | −0.449659 | − | 0.893200i | \(-0.648455\pi\) | ||
0.449659 | − | 0.893200i | \(-0.351545\pi\) | |||||||
\(432\) | 1.10537 | + | 1.91455i | 0.0531821 | + | 0.0921140i | ||||
\(433\) | 7.21536 | + | 12.4974i | 0.346748 | + | 0.600585i | 0.985670 | − | 0.168686i | \(-0.0539525\pi\) |
−0.638922 | + | 0.769272i | \(0.720619\pi\) | |||||||
\(434\) | −8.53766 | + | 2.30430i | −0.409821 | + | 0.110610i | ||||
\(435\) | 3.43193 | − | 1.98142i | 0.164548 | − | 0.0950020i | ||||
\(436\) | 27.5180i | 1.31787i | ||||||||
\(437\) | 32.4884 | − | 18.7572i | 1.55413 | − | 0.897278i | ||||
\(438\) | 0.800299 | − | 1.38616i | 0.0382398 | − | 0.0662332i | ||||
\(439\) | −7.31502 | − | 12.6700i | −0.349127 | − | 0.604706i | 0.636968 | − | 0.770891i | \(-0.280188\pi\) |
−0.986095 | + | 0.166185i | \(0.946855\pi\) | |||||||
\(440\) | 2.01637 | + | 1.16415i | 0.0961265 | + | 0.0554987i | ||||
\(441\) | 0.0254470 | + | 6.99995i | 0.00121176 | + | 0.333331i | ||||
\(442\) | 4.04774 | + | 9.18208i | 0.192532 | + | 0.436747i | ||||
\(443\) | 18.3045 | − | 31.7043i | 0.869672 | − | 1.50632i | 0.00733990 | − | 0.999973i | \(-0.497664\pi\) |
0.862332 | − | 0.506343i | \(-0.169003\pi\) | |||||||
\(444\) | 9.85410i | 0.467655i | ||||||||
\(445\) | 1.31472 | 0.0623236 | ||||||||
\(446\) | −0.427231 | −0.0202300 | ||||||||
\(447\) | − | 1.07489i | − | 0.0508406i | ||||||
\(448\) | −2.63528 | − | 2.62572i | −0.124505 | − | 0.124053i | ||||
\(449\) | −5.59341 | + | 3.22935i | −0.263969 | + | 0.152403i | −0.626144 | − | 0.779708i | \(-0.715368\pi\) |
0.362175 | + | 0.932110i | \(0.382034\pi\) | |||||||
\(450\) | 2.29804 | + | 1.32677i | 0.108330 | + | 0.0625446i | ||||
\(451\) | −11.5540 | + | 20.0121i | −0.544057 | + | 0.942335i | ||||
\(452\) | −20.8974 | −0.982932 | ||||||||
\(453\) | 10.8708 | − | 6.27625i | 0.510754 | − | 0.294884i | ||||
\(454\) | −0.864250 | −0.0405613 | ||||||||
\(455\) | 3.11200 | + | 3.85764i | 0.145893 | + | 0.180849i | ||||
\(456\) | −11.4140 | −0.534509 | ||||||||
\(457\) | 16.6225 | − | 9.59698i | 0.777565 | − | 0.448928i | −0.0580013 | − | 0.998317i | \(-0.518473\pi\) |
0.835567 | + | 0.549389i | \(0.185139\pi\) | |||||||
\(458\) | −3.15170 | −0.147269 | ||||||||
\(459\) | −2.48051 | + | 4.29637i | −0.115780 | + | 0.200537i | ||||
\(460\) | −5.15278 | − | 2.97496i | −0.240250 | − | 0.138708i | ||||
\(461\) | −5.50203 | + | 3.17660i | −0.256255 | + | 0.147949i | −0.622625 | − | 0.782520i | \(-0.713934\pi\) |
0.366370 | + | 0.930469i | \(0.380600\pi\) | |||||||
\(462\) | −0.827009 | + | 3.10903i | −0.0384759 | + | 0.144645i | ||||
\(463\) | 10.8299i | 0.503307i | 0.967817 | + | 0.251653i | \(0.0809743\pi\) | ||||
−0.967817 | + | 0.251653i | \(0.919026\pi\) | |||||||
\(464\) | −16.8616 | −0.782779 | ||||||||
\(465\) | −3.09559 | −0.143555 | ||||||||
\(466\) | − | 9.62087i | − | 0.445678i | ||||||
\(467\) | 5.84012 | − | 10.1154i | 0.270248 | − | 0.468084i | −0.698677 | − | 0.715437i | \(-0.746228\pi\) |
0.968925 | + | 0.247353i | \(0.0795609\pi\) | |||||||
\(468\) | −0.657365 | + | 6.04071i | −0.0303867 | + | 0.279232i | ||||
\(469\) | −3.69984 | + | 3.71331i | −0.170843 | + | 0.171465i | ||||
\(470\) | 2.82553 | + | 1.63132i | 0.130332 | + | 0.0752472i | ||||
\(471\) | −0.346108 | − | 0.599476i | −0.0159478 | − | 0.0276224i | ||||
\(472\) | −3.15109 | + | 5.45785i | −0.145041 | + | 0.251218i | ||||
\(473\) | −7.95696 | + | 4.59395i | −0.365862 | + | 0.211230i | ||||
\(474\) | − | 2.78413i | − | 0.127879i | ||||||
\(475\) | 22.6152 | − | 13.0569i | 1.03766 | − | 0.599093i | ||||
\(476\) | 5.68633 | − | 21.3770i | 0.260632 | − | 0.979813i | ||||
\(477\) | 1.04639 | + | 1.81239i | 0.0479107 | + | 0.0829838i | ||||
\(478\) | −7.19922 | − | 12.4694i | −0.329285 | − | 0.570338i | ||||
\(479\) | 24.0236i | 1.09767i | 0.835932 | + | 0.548833i | \(0.184928\pi\) | ||||
−0.835932 | + | 0.548833i | \(0.815072\pi\) | |||||||
\(480\) | 1.39637 | + | 2.41859i | 0.0637355 | + | 0.110393i | ||||
\(481\) | −12.4544 | + | 17.0102i | −0.567873 | + | 0.775598i | ||||
\(482\) | −2.64633 | −0.120537 | ||||||||
\(483\) | 4.62148 | − | 17.3738i | 0.210284 | − | 0.790537i | ||||
\(484\) | −5.31024 | + | 9.19761i | −0.241375 | + | 0.418073i | ||||
\(485\) | −4.81135 | −0.218472 | ||||||||
\(486\) | 0.485838 | − | 0.280499i | 0.0220381 | − | 0.0127237i | ||||
\(487\) | 5.23103 | + | 3.02014i | 0.237041 | + | 0.136856i | 0.613816 | − | 0.789449i | \(-0.289634\pi\) |
−0.376775 | + | 0.926305i | \(0.622967\pi\) | |||||||
\(488\) | − | 12.9196i | − | 0.584841i | ||||||
\(489\) | 10.3974i | 0.470185i | ||||||||
\(490\) | 0.00741728 | + | 2.04034i | 0.000335079 | + | 0.0921732i | ||||
\(491\) | −7.05626 | + | 12.2218i | −0.318444 | + | 0.551562i | −0.980164 | − | 0.198190i | \(-0.936494\pi\) |
0.661719 | + | 0.749752i | \(0.269827\pi\) | |||||||
\(492\) | −15.5598 | + | 8.98348i | −0.701492 | + | 0.405007i | ||||
\(493\) | −18.9192 | − | 32.7690i | −0.852076 | − | 1.47584i | ||||
\(494\) | −9.01014 | − | 6.59699i | −0.405385 | − | 0.296813i | ||||
\(495\) | −0.563089 | + | 0.975299i | −0.0253090 | + | 0.0438364i | ||||
\(496\) | 11.4068 | + | 6.58574i | 0.512182 | + | 0.295708i | ||||
\(497\) | 25.4340 | + | 6.76550i | 1.14087 | + | 0.303474i | ||||
\(498\) | −1.02641 | − | 1.77779i | −0.0459945 | − | 0.0796648i | ||||
\(499\) | 28.4481 | + | 16.4245i | 1.27351 | + | 0.735263i | 0.975647 | − | 0.219345i | \(-0.0703922\pi\) |
0.297865 | + | 0.954608i | \(0.403726\pi\) | |||||||
\(500\) | −7.37844 | − | 4.25994i | −0.329974 | − | 0.190510i | ||||
\(501\) | −20.9105 | − | 12.0727i | −0.934213 | − | 0.539368i | ||||
\(502\) | 0.0954698 | + | 0.0551195i | 0.00426103 | + | 0.00246010i | ||||
\(503\) | −19.5590 | − | 33.8772i | −0.872093 | − | 1.51051i | −0.859828 | − | 0.510584i | \(-0.829429\pi\) |
−0.0122649 | − | 0.999925i | \(-0.503904\pi\) | |||||||
\(504\) | −3.86078 | + | 3.87484i | −0.171973 | + | 0.172599i | ||||
\(505\) | 4.06946 | + | 2.34950i | 0.181088 | + | 0.104551i | ||||
\(506\) | 4.13127 | − | 7.15558i | 0.183658 | − | 0.318104i | ||||
\(507\) | −8.76949 | + | 9.59666i | −0.389467 | + | 0.426203i | ||||
\(508\) | 17.1352 | + | 29.6790i | 0.760250 | + | 1.31679i | ||||
\(509\) | 0.959846 | − | 0.554167i | 0.0425444 | − | 0.0245630i | −0.478577 | − | 0.878046i | \(-0.658847\pi\) |
0.521121 | + | 0.853483i | \(0.325514\pi\) | |||||||
\(510\) | −0.723017 | + | 1.25230i | −0.0320157 | + | 0.0554528i | ||||
\(511\) | −7.29499 | − | 1.94048i | −0.322711 | − | 0.0858418i | ||||
\(512\) | − | 21.0240i | − | 0.929139i | ||||||
\(513\) | − | 5.52084i | − | 0.243751i | ||||||
\(514\) | −0.731676 | − | 0.422433i | −0.0322728 | − | 0.0186327i | ||||
\(515\) | 7.94536 | − | 4.58726i | 0.350114 | − | 0.202139i | ||||
\(516\) | −7.14379 | −0.314488 | ||||||||
\(517\) | 12.1309 | − | 21.0113i | 0.533516 | − | 0.924077i | ||||
\(518\) | −8.37888 | + | 2.26145i | −0.368147 | + | 0.0993622i | ||||
\(519\) | −3.73858 | −0.164105 | ||||||||
\(520\) | −0.418998 | + | 3.85029i | −0.0183743 | + | 0.168846i | ||||
\(521\) | 6.87363 | + | 11.9055i | 0.301139 | + | 0.521589i | 0.976394 | − | 0.215996i | \(-0.0692997\pi\) |
−0.675255 | + | 0.737584i | \(0.735966\pi\) | |||||||
\(522\) | 4.27880i | 0.187278i | ||||||||
\(523\) | 1.20677 | + | 2.09020i | 0.0527686 | + | 0.0913979i | 0.891203 | − | 0.453604i | \(-0.149862\pi\) |
−0.838435 | + | 0.545002i | \(0.816529\pi\) | |||||||
\(524\) | 11.6107 | + | 20.1103i | 0.507216 | + | 0.878524i | ||||
\(525\) | 3.21702 | − | 12.0940i | 0.140402 | − | 0.527824i | ||||
\(526\) | −3.34548 | + | 1.93151i | −0.145870 | + | 0.0842179i | ||||
\(527\) | 29.5575i | 1.28755i | ||||||||
\(528\) | 4.14981 | − | 2.39590i | 0.180597 | − | 0.104268i | ||||
\(529\) | −11.5863 | + | 20.0681i | −0.503753 | + | 0.872525i | ||||
\(530\) | 0.305000 | + | 0.528275i | 0.0132483 | + | 0.0229468i | ||||
\(531\) | −2.63992 | − | 1.52416i | −0.114563 | − | 0.0661427i | ||||
\(532\) | 6.41444 | + | 23.7661i | 0.278101 | + | 1.03039i | ||||
\(533\) | −38.2136 | − | 4.15850i | −1.65521 | − | 0.180125i | ||||
\(534\) | −0.709770 | + | 1.22936i | −0.0307147 | + | 0.0531995i | ||||
\(535\) | 10.1109i | 0.437134i | ||||||||
\(536\) | −4.09611 | −0.176925 | ||||||||
\(537\) | 5.67810 | 0.245028 | ||||||||
\(538\) | 6.65958i | 0.287115i | ||||||||
\(539\) | 15.1725 | − | 0.0551567i | 0.653524 | − | 0.00237577i | ||||
\(540\) | −0.758315 | + | 0.437813i | −0.0326327 | + | 0.0188405i | ||||
\(541\) | −7.81869 | − | 4.51412i | −0.336152 | − | 0.194077i | 0.322417 | − | 0.946598i | \(-0.395505\pi\) |
−0.658569 | + | 0.752520i | \(0.728838\pi\) | |||||||
\(542\) | 3.85497 | − | 6.67700i | 0.165585 | − | 0.286802i | ||||
\(543\) | 9.94903 | 0.426954 | ||||||||
\(544\) | 23.0934 | − | 13.3330i | 0.990119 | − | 0.571646i | ||||
\(545\) | −8.48379 | −0.363406 | ||||||||
\(546\) | −5.28724 | + | 0.827345i | −0.226273 | + | 0.0354071i | ||||
\(547\) | −24.3206 | −1.03987 | −0.519936 | − | 0.854205i | \(-0.674044\pi\) | ||||
−0.519936 | + | 0.854205i | \(0.674044\pi\) | |||||||
\(548\) | 2.36626 | − | 1.36616i | 0.101082 | − | 0.0583595i | ||||
\(549\) | 6.24908 | 0.266704 | ||||||||
\(550\) | 2.87579 | − | 4.98101i | 0.122624 | − | 0.212391i | ||||
\(551\) | 36.4668 | + | 21.0541i | 1.55354 | + | 0.896935i | ||||
\(552\) | 12.1662 | − | 7.02415i | 0.517827 | − | 0.298968i | ||||
\(553\) | −12.6768 | + | 3.42144i | −0.539072 | + | 0.145495i | ||||
\(554\) | − | 6.29216i | − | 0.267328i | ||||||
\(555\) | −3.03802 | −0.128957 | ||||||||
\(556\) | −12.3658 | −0.524425 | ||||||||
\(557\) | 27.5933i | 1.16916i | 0.811335 | + | 0.584582i | \(0.198742\pi\) | ||||
−0.811335 | + | 0.584582i | \(0.801258\pi\) | |||||||
\(558\) | 1.67120 | − | 2.89460i | 0.0707475 | − | 0.122538i | ||||
\(559\) | −12.3316 | − | 9.02891i | −0.521573 | − | 0.381882i | ||||
\(560\) | 2.14500 | − | 2.15281i | 0.0906427 | − | 0.0909728i | ||||
\(561\) | 9.31241 | + | 5.37652i | 0.393170 | + | 0.226997i | ||||
\(562\) | 0.509430 | + | 0.882358i | 0.0214890 | + | 0.0372200i | ||||
\(563\) | 3.85215 | − | 6.67211i | 0.162349 | − | 0.281196i | −0.773362 | − | 0.633965i | \(-0.781426\pi\) |
0.935711 | + | 0.352769i | \(0.114760\pi\) | |||||||
\(564\) | 16.3367 | − | 9.43201i | 0.687900 | − | 0.397159i | ||||
\(565\) | − | 6.44268i | − | 0.271045i | ||||||
\(566\) | −14.9822 | + | 8.64995i | −0.629747 | + | 0.363584i | ||||
\(567\) | −1.87423 | − | 1.86743i | −0.0787101 | − | 0.0784245i | ||||
\(568\) | 10.2828 | + | 17.8104i | 0.431459 | + | 0.747308i | ||||
\(569\) | 11.6240 | + | 20.1333i | 0.487302 | + | 0.844033i | 0.999893 | − | 0.0146003i | \(-0.00464758\pi\) |
−0.512591 | + | 0.858633i | \(0.671314\pi\) | |||||||
\(570\) | − | 1.60921i | − | 0.0674024i | ||||||
\(571\) | −2.06269 | − | 3.57268i | −0.0863209 | − | 0.149512i | 0.819632 | − | 0.572890i | \(-0.194178\pi\) |
−0.905953 | + | 0.423378i | \(0.860844\pi\) | |||||||
\(572\) | 13.0933 | + | 1.42484i | 0.547458 | + | 0.0595757i | ||||
\(573\) | −9.50875 | −0.397234 | ||||||||
\(574\) | −11.2095 | − | 11.1688i | −0.467874 | − | 0.466177i | ||||
\(575\) | −16.0704 | + | 27.8348i | −0.670183 | + | 1.16079i | ||||
\(576\) | 1.40606 | 0.0585859 | ||||||||
\(577\) | 6.14307 | − | 3.54670i | 0.255739 | − | 0.147651i | −0.366650 | − | 0.930359i | \(-0.619495\pi\) |
0.622389 | + | 0.782708i | \(0.286162\pi\) | |||||||
\(578\) | 3.69806 | + | 2.13507i | 0.153819 | + | 0.0888074i | ||||
\(579\) | 3.11196i | 0.129329i | ||||||||
\(580\) | − | 6.67852i | − | 0.277310i | ||||||
\(581\) | −6.83334 | + | 6.85822i | −0.283495 | + | 0.284527i | ||||
\(582\) | 2.59748 | − | 4.49896i | 0.107669 | − | 0.186488i | ||||
\(583\) | 3.92838 | − | 2.26805i | 0.162697 | − | 0.0939330i | ||||
\(584\) | −2.94933 | − | 5.10838i | −0.122044 | − | 0.211386i | ||||
\(585\) | −1.86235 | − | 0.202666i | −0.0769988 | − | 0.00837920i | ||||
\(586\) | 0.307296 | − | 0.532253i | 0.0126943 | − | 0.0219871i | ||||
\(587\) | −1.42269 | − | 0.821391i | −0.0587208 | − | 0.0339025i | 0.470352 | − | 0.882479i | \(-0.344127\pi\) |
−0.529073 | + | 0.848576i | \(0.677460\pi\) | |||||||
\(588\) | 10.2379 | + | 5.86131i | 0.422202 | + | 0.241716i | ||||
\(589\) | −16.4465 | − | 28.4861i | −0.677665 | − | 1.17375i | ||||
\(590\) | −0.769480 | − | 0.444260i | −0.0316790 | − | 0.0182899i | ||||
\(591\) | −4.41349 | − | 2.54813i | −0.181547 | − | 0.104816i | ||||
\(592\) | 11.1947 | + | 6.46326i | 0.460099 | + | 0.265638i | ||||
\(593\) | −37.1597 | − | 21.4542i | −1.52597 | − | 0.881016i | −0.999525 | − | 0.0308039i | \(-0.990193\pi\) |
−0.526440 | − | 0.850212i | \(-0.676473\pi\) | |||||||
\(594\) | −0.607984 | − | 1.05306i | −0.0249459 | − | 0.0432075i | ||||
\(595\) | 6.59054 | + | 1.75310i | 0.270186 | + | 0.0718699i | ||||
\(596\) | −1.56880 | − | 0.905747i | −0.0642606 | − | 0.0371009i | ||||
\(597\) | 6.95536 | − | 12.0470i | 0.284664 | − | 0.493053i | ||||
\(598\) | 13.6637 | + | 1.48692i | 0.558751 | + | 0.0608047i | ||||
\(599\) | 15.5990 | + | 27.0183i | 0.637358 | + | 1.10394i | 0.986010 | + | 0.166684i | \(0.0533060\pi\) |
−0.348653 | + | 0.937252i | \(0.613361\pi\) | |||||||
\(600\) | 8.46891 | − | 4.88953i | 0.345742 | − | 0.199614i | ||||
\(601\) | −17.5568 | + | 30.4093i | −0.716157 | + | 1.24042i | 0.246354 | + | 0.969180i | \(0.420767\pi\) |
−0.962511 | + | 0.271241i | \(0.912566\pi\) | |||||||
\(602\) | −1.63945 | − | 6.07432i | −0.0668189 | − | 0.247571i | ||||
\(603\) | − | 1.98125i | − | 0.0806828i | ||||||
\(604\) | − | 21.1545i | − | 0.860764i | ||||||
\(605\) | −2.83563 | − | 1.63715i | −0.115285 | − | 0.0665596i | ||||
\(606\) | −4.39391 | + | 2.53683i | −0.178490 | + | 0.103051i | ||||
\(607\) | −2.31771 | −0.0940730 | −0.0470365 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470365 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(608\) | −14.8375 | + | 25.6993i | −0.601741 | + | 1.04225i | ||||
\(609\) | 19.4824 | − | 5.25826i | 0.789465 | − | 0.213075i | ||||
\(610\) | 1.82148 | 0.0737494 | ||||||||
\(611\) | 40.1215 | + | 4.36613i | 1.62314 | + | 0.176635i | ||||
\(612\) | 4.18036 | + | 7.24059i | 0.168981 | + | 0.292683i | ||||
\(613\) | − | 17.0601i | − | 0.689050i | −0.938777 | − | 0.344525i | \(-0.888040\pi\) | ||
0.938777 | − | 0.344525i | \(-0.111960\pi\) | |||||||
\(614\) | 1.37514 | + | 2.38181i | 0.0554960 | + | 0.0961219i | ||||
\(615\) | −2.76961 | − | 4.79711i | −0.111681 | − | 0.193438i | ||||
\(616\) | 8.39875 | + | 8.36827i | 0.338395 | + | 0.337167i | ||||
\(617\) | −20.5147 | + | 11.8442i | −0.825890 | + | 0.476828i | −0.852443 | − | 0.522820i | \(-0.824880\pi\) |
0.0265537 | + | 0.999647i | \(0.491547\pi\) | |||||||
\(618\) | 9.90598i | 0.398477i | ||||||||
\(619\) | 13.5416 | − | 7.81825i | 0.544283 | − | 0.314242i | −0.202530 | − | 0.979276i | \(-0.564916\pi\) |
0.746813 | + | 0.665034i | \(0.231583\pi\) | |||||||
\(620\) | −2.60847 | + | 4.51801i | −0.104759 | + | 0.181447i | ||||
\(621\) | 3.39752 | + | 5.88468i | 0.136338 | + | 0.236144i | ||||
\(622\) | 5.62359 | + | 3.24678i | 0.225485 | + | 0.130184i | ||||
\(623\) | 6.46979 | + | 1.72098i | 0.259206 | + | 0.0689494i | ||||
\(624\) | 6.43135 | + | 4.70887i | 0.257460 | + | 0.188506i | ||||
\(625\) | −10.5118 | + | 18.2069i | −0.420471 | + | 0.728277i | ||||
\(626\) | 2.84404i | 0.113671i | ||||||||
\(627\) | −11.9665 | −0.477895 | ||||||||
\(628\) | −1.16658 | −0.0465515 | ||||||||
\(629\) | 29.0078i | 1.15662i | ||||||||
\(630\) | −0.546298 | − | 0.544315i | −0.0217650 | − | 0.0216860i | ||||
\(631\) | −19.8241 | + | 11.4455i | −0.789186 | + | 0.455637i | −0.839676 | − | 0.543088i | \(-0.817255\pi\) |
0.0504898 | + | 0.998725i | \(0.483922\pi\) | |||||||
\(632\) | −8.88569 | − | 5.13015i | −0.353454 | − | 0.204067i | ||||
\(633\) | 6.30791 | − | 10.9256i | 0.250717 | − | 0.434255i | ||||
\(634\) | 9.64738 | 0.383146 | ||||||||
\(635\) | −9.15004 | + | 5.28278i | −0.363108 | + | 0.209641i | ||||
\(636\) | 3.52691 | 0.139851 | ||||||||
\(637\) | 10.2646 | + | 23.0573i | 0.406699 | + | 0.913562i | ||||
\(638\) | 9.27434 | 0.367175 | ||||||||
\(639\) | −8.61474 | + | 4.97372i | −0.340794 | + | 0.196757i | ||||
\(640\) | 5.99534 | 0.236986 | ||||||||
\(641\) | 23.1024 | − | 40.0145i | 0.912490 | − | 1.58048i | 0.101954 | − | 0.994789i | \(-0.467491\pi\) |
0.810536 | − | 0.585689i | \(-0.199176\pi\) | |||||||
\(642\) | −9.45446 | − | 5.45853i | −0.373138 | − | 0.215431i | ||||
\(643\) | 8.19662 | − | 4.73232i | 0.323243 | − | 0.186625i | −0.329594 | − | 0.944123i | \(-0.606912\pi\) |
0.652837 | + | 0.757498i | \(0.273579\pi\) | |||||||
\(644\) | −21.4628 | − | 21.3849i | −0.845753 | − | 0.842684i | ||||
\(645\) | − | 2.20243i | − | 0.0867206i | ||||||
\(646\) | −15.3652 | −0.604535 | ||||||||
\(647\) | 5.70593 | 0.224323 | 0.112162 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112162 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(648\) | − | 2.06743i | − | 0.0812165i | ||||||
\(649\) | −3.30362 | + | 5.72204i | −0.129678 | + | 0.224610i | ||||
\(650\) | 9.51134 | + | 1.03505i | 0.373065 | + | 0.0405979i | ||||
\(651\) | −15.2335 | − | 4.05215i | −0.597049 | − | 0.158816i | ||||
\(652\) | 15.1749 | + | 8.76124i | 0.594295 | + | 0.343117i | ||||
\(653\) | −16.5067 | − | 28.5904i | −0.645956 | − | 1.11883i | −0.984080 | − | 0.177727i | \(-0.943126\pi\) |
0.338124 | − | 0.941101i | \(-0.390208\pi\) | |||||||
\(654\) | 4.58010 | − | 7.93296i | 0.179096 | − | 0.310203i | ||||
\(655\) | −6.20002 | + | 3.57959i | −0.242255 | + | 0.139866i | ||||
\(656\) | 23.5689i | 0.920211i | ||||||||
\(657\) | 2.47088 | − | 1.42656i | 0.0963982 | − | 0.0556555i | ||||
\(658\) | 11.7691 | + | 11.7264i | 0.458809 | + | 0.457144i | ||||
\(659\) | −11.4177 | − | 19.7760i | −0.444770 | − | 0.770363i | 0.553267 | − | 0.833004i | \(-0.313381\pi\) |
−0.998036 | + | 0.0626408i | \(0.980048\pi\) | |||||||
\(660\) | 0.948964 | + | 1.64365i | 0.0369384 | + | 0.0639791i | ||||
\(661\) | − | 1.83380i | − | 0.0713266i | −0.999364 | − | 0.0356633i | \(-0.988646\pi\) | ||
0.999364 | − | 0.0356633i | \(-0.0113544\pi\) | |||||||
\(662\) | 5.72815 | + | 9.92144i | 0.222631 | + | 0.385608i | ||||
\(663\) | −1.93511 | + | 17.7822i | −0.0751534 | + | 0.690604i | ||||
\(664\) | −7.56522 | −0.293587 | ||||||||
\(665\) | −7.32710 | + | 1.97757i | −0.284133 | + | 0.0766870i | ||||
\(666\) | 1.64012 | − | 2.84077i | 0.0635533 | − | 0.110078i | ||||
\(667\) | −51.8267 | −2.00674 | ||||||||
\(668\) | −35.2401 | + | 20.3459i | −1.36348 | + | 0.787206i | ||||
\(669\) | −0.659526 | − | 0.380777i | −0.0254987 | − | 0.0147217i | ||||
\(670\) | − | 0.577494i | − | 0.0223105i | ||||||
\(671\) | − | 13.5449i | − | 0.522896i | ||||||
\(672\) | 3.70567 | + | 13.7299i | 0.142949 | + | 0.529641i | ||||
\(673\) | 14.8231 | − | 25.6743i | 0.571387 | − | 0.989672i | −0.425037 | − | 0.905176i | \(-0.639739\pi\) |
0.996424 | − | 0.0844955i | \(-0.0269278\pi\) | |||||||
\(674\) | 6.40685 | − | 3.69900i | 0.246783 | − | 0.142480i | ||||
\(675\) | 2.36502 | + | 4.09634i | 0.0910297 | + | 0.157668i | ||||
\(676\) | 6.61677 | + | 20.8856i | 0.254491 | + | 0.803292i | ||||
\(677\) | −21.1048 | + | 36.5546i | −0.811124 | + | 1.40491i | 0.100954 | + | 0.994891i | \(0.467811\pi\) |
−0.912078 | + | 0.410017i | \(0.865523\pi\) | |||||||
\(678\) | 6.02437 | + | 3.47817i | 0.231365 | + | 0.133578i | ||||
\(679\) | −23.6769 | − | 6.29809i | −0.908635 | − | 0.241699i | ||||
\(680\) | 2.66452 | + | 4.61508i | 0.102180 | + | 0.176980i | ||||
\(681\) | −1.33416 | − | 0.770280i | −0.0511252 | − | 0.0295172i | ||||
\(682\) | −6.27407 | − | 3.62234i | −0.240247 | − | 0.138707i | ||||
\(683\) | 21.5544 | + | 12.4444i | 0.824757 | + | 0.476173i | 0.852054 | − | 0.523454i | \(-0.175357\pi\) |
−0.0272974 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(684\) | −8.05765 | − | 4.65209i | −0.308092 | − | 0.177877i | ||||
\(685\) | 0.421188 | + | 0.729519i | 0.0160928 | + | 0.0278735i | ||||
\(686\) | −2.63432 | + | 10.0503i | −0.100579 | + | 0.383723i | ||||
\(687\) | −4.86535 | − | 2.80901i | −0.185625 | − | 0.107171i | ||||
\(688\) | −4.68558 | + | 8.11566i | −0.178636 | + | 0.309407i | ||||
\(689\) | 6.08817 | + | 4.45760i | 0.231941 | + | 0.169821i | ||||
\(690\) | 0.990307 | + | 1.71526i | 0.0377003 | + | 0.0652989i | ||||
\(691\) | 32.5266 | − | 18.7792i | 1.23737 | − | 0.714396i | 0.268815 | − | 0.963192i | \(-0.413368\pi\) |
0.968556 | + | 0.248796i | \(0.0800347\pi\) | |||||||
\(692\) | −3.15028 | + | 5.45644i | −0.119756 | + | 0.207423i | ||||
\(693\) | −4.04766 | + | 4.06240i | −0.153758 | + | 0.154318i | ||||
\(694\) | 4.87368i | 0.185002i | ||||||||
\(695\) | − | 3.81237i | − | 0.144611i | ||||||
\(696\) | 13.6560 | + | 7.88430i | 0.517629 | + | 0.298853i | ||||
\(697\) | −45.8040 | + | 26.4450i | −1.73495 | + | 1.00167i | ||||
\(698\) | −19.5785 | −0.741059 | ||||||||
\(699\) | 8.57478 | − | 14.8520i | 0.324328 | − | 0.561753i | ||||
\(700\) | −14.9403 | − | 14.8861i | −0.564691 | − | 0.562642i | ||||
\(701\) | 36.1312 | 1.36466 | 0.682328 | − | 0.731046i | \(-0.260968\pi\) | ||||
0.682328 | + | 0.731046i | \(0.260968\pi\) | |||||||
\(702\) | 1.19492 | − | 1.63202i | 0.0450995 | − | 0.0615967i | ||||
\(703\) | −16.1406 | − | 27.9564i | −0.608755 | − | 1.05439i | ||||
\(704\) | − | 3.04765i | − | 0.114863i | ||||||
\(705\) | 2.90789 | + | 5.03662i | 0.109518 | + | 0.189690i | ||||
\(706\) | 4.07125 | + | 7.05161i | 0.153223 | + | 0.265391i | ||||
\(707\) | 16.9505 | + | 16.8890i | 0.637488 | + | 0.635174i | ||||
\(708\) | −4.44900 | + | 2.56863i | −0.167204 | + | 0.0965351i | ||||
\(709\) | 25.0157i | 0.939486i | 0.882803 | + | 0.469743i | \(0.155653\pi\) | ||||
−0.882803 | + | 0.469743i | \(0.844347\pi\) | |||||||
\(710\) | −2.51102 | + | 1.44974i | −0.0942368 | + | 0.0544076i | ||||
\(711\) | 2.48141 | − | 4.29793i | 0.0930602 | − | 0.161185i | ||||
\(712\) | 2.61570 | + | 4.53053i | 0.0980275 | + | 0.169789i | ||||
\(713\) | 35.0607 | + | 20.2423i | 1.31303 | + | 0.758079i | ||||
\(714\) | −5.19727 | + | 5.21620i | −0.194503 | + | 0.195211i | ||||
\(715\) | −0.439280 | + | 4.03666i | −0.0164281 | + | 0.150963i | ||||
\(716\) | 4.78460 | − | 8.28716i | 0.178809 | − | 0.309706i | ||||
\(717\) | − | 25.6658i | − | 0.958506i | ||||||
\(718\) | 0.298481 | 0.0111392 | ||||||||
\(719\) | −6.63648 | −0.247499 | −0.123749 | − | 0.992314i | \(-0.539492\pi\) | ||||
−0.123749 | + | 0.992314i | \(0.539492\pi\) | |||||||
\(720\) | 1.14864i | 0.0428072i | ||||||||
\(721\) | 45.1042 | − | 12.1735i | 1.67977 | − | 0.453367i | ||||
\(722\) | 5.57729 | − | 3.22005i | 0.207565 | − | 0.119838i | ||||
\(723\) | −4.08520 | − | 2.35859i | −0.151930 | − | 0.0877170i | ||||
\(724\) | 8.38346 | − | 14.5206i | 0.311569 | − | 0.539653i | ||||
\(725\) | −36.0767 | −1.33985 | ||||||||
\(726\) | 3.06171 | − | 1.76768i | 0.113631 | − | 0.0656047i | ||||
\(727\) | 18.2640 | 0.677375 | 0.338688 | − | 0.940899i | \(-0.390017\pi\) | ||||
0.338688 | + | 0.940899i | \(0.390017\pi\) | |||||||
\(728\) | −7.10197 | + | 18.3990i | −0.263216 | + | 0.681911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.720210 | − | 0.415813i | 0.0266562 | − | 0.0153899i | ||||
\(731\) | −21.0294 | −0.777800 | ||||||||
\(732\) | 5.26573 | − | 9.12050i | 0.194627 | − | 0.337104i | ||||
\(733\) | −26.5047 | − | 15.3025i | −0.978972 | − | 0.565210i | −0.0770123 | − | 0.997030i | \(-0.524538\pi\) |
−0.901960 | + | 0.431820i | \(0.857871\pi\) | |||||||
\(734\) | −2.84345 | + | 1.64166i | −0.104953 | + | 0.0605949i | ||||
\(735\) | −1.80704 | + | 3.15633i | −0.0666538 | + | 0.116423i | ||||
\(736\) | − | 36.5240i | − | 1.34629i | ||||||
\(737\) | −4.29438 | −0.158186 | ||||||||
\(738\) | 5.98086 | 0.220158 | ||||||||
\(739\) | − | 34.9923i | − | 1.28721i | −0.765356 | − | 0.643607i | \(-0.777437\pi\) | ||
0.765356 | − | 0.643607i | \(-0.222563\pi\) | |||||||
\(740\) | −2.55996 | + | 4.43398i | −0.0941060 | + | 0.162996i | ||||
\(741\) | −8.02947 | − | 18.2144i | −0.294970 | − | 0.669122i | ||||
\(742\) | 0.809400 | + | 2.99891i | 0.0297140 | + | 0.110093i | ||||
\(743\) | 6.87469 | + | 3.96910i | 0.252208 | + | 0.145612i | 0.620775 | − | 0.783989i | \(-0.286818\pi\) |
−0.368567 | + | 0.929601i | \(0.620151\pi\) | |||||||
\(744\) | −6.15884 | − | 10.6674i | −0.225794 | − | 0.391087i | ||||
\(745\) | 0.279242 | − | 0.483662i | 0.0102306 | − | 0.0177200i | ||||
\(746\) | −11.7824 | + | 6.80258i | −0.431385 | + | 0.249060i | ||||
\(747\) | − | 3.65923i | − | 0.133884i | ||||||
\(748\) | 15.6940 | − | 9.06096i | 0.573831 | − | 0.331301i | ||||
\(749\) | −13.2353 | + | 49.7563i | −0.483607 | + | 1.81806i | ||||
\(750\) | 1.41805 | + | 2.45614i | 0.0517800 | + | 0.0896855i | ||||
\(751\) | 15.4194 | + | 26.7072i | 0.562662 | + | 0.974559i | 0.997263 | + | 0.0739360i | \(0.0235560\pi\) |
−0.434601 | + | 0.900623i | \(0.643111\pi\) | |||||||
\(752\) | − | 24.7457i | − | 0.902381i | ||||||
\(753\) | 0.0982527 | + | 0.170179i | 0.00358053 | + | 0.00620165i | ||||
\(754\) | 6.22305 | + | 14.1166i | 0.226630 | + | 0.514098i | ||||
\(755\) | 6.52194 | 0.237358 | ||||||||
\(756\) | −4.30480 | + | 1.16186i | −0.156564 | + | 0.0422564i | ||||
\(757\) | 3.83594 | − | 6.64405i | 0.139420 | − | 0.241482i | −0.787857 | − | 0.615858i | \(-0.788810\pi\) |
0.927277 | + | 0.374376i | \(0.122143\pi\) | |||||||
\(758\) | 0.776901 | 0.0282183 | ||||||||
\(759\) | 12.7551 | − | 7.36416i | 0.462981 | − | 0.267302i | ||||
\(760\) | −5.13587 | − | 2.96520i | −0.186298 | − | 0.107559i | ||||
\(761\) | − | 28.3330i | − | 1.02707i | −0.858068 | − | 0.513535i | \(-0.828335\pi\) | ||
0.858068 | − | 0.513535i | \(-0.171665\pi\) | |||||||
\(762\) | − | 11.4079i | − | 0.413266i | ||||||
\(763\) | −41.7491 | − | 11.1053i | −1.51142 | − | 0.402041i | ||||
\(764\) | −8.01246 | + | 13.8780i | −0.289881 | + | 0.502088i | ||||
\(765\) | −2.23228 | + | 1.28880i | −0.0807081 | + | 0.0465968i | ||||
\(766\) | 5.53657 | + | 9.58962i | 0.200044 | + | 0.346487i | ||||
\(767\) | −10.9263 | − | 1.18903i | −0.394527 | − | 0.0429335i | ||||
\(768\) | −1.83061 | + | 3.17070i | −0.0660563 | + | 0.114413i | ||||
\(769\) | 8.61926 | + | 4.97633i | 0.310819 | + | 0.179451i | 0.647293 | − | 0.762242i | \(-0.275901\pi\) |
−0.336474 | + | 0.941693i | \(0.609234\pi\) | |||||||
\(770\) | −1.17981 | + | 1.18410i | −0.0425173 | + | 0.0426722i | ||||
\(771\) | −0.753004 | − | 1.30424i | −0.0271188 | − | 0.0469711i | ||||
\(772\) | 4.54190 | + | 2.62227i | 0.163466 | + | 0.0943774i | ||||
\(773\) | −31.8718 | − | 18.4012i | −1.14635 | − | 0.661844i | −0.198353 | − | 0.980131i | \(-0.563559\pi\) |
−0.947995 | + | 0.318286i | \(0.896893\pi\) | |||||||
\(774\) | 2.05943 | + | 1.18901i | 0.0740248 | + | 0.0427382i | ||||
\(775\) | 24.4058 | + | 14.0907i | 0.876682 | + | 0.506153i | ||||
\(776\) | −9.57244 | − | 16.5799i | −0.343630 | − | 0.595185i | ||||
\(777\) | −14.9502 | − | 3.97679i | −0.536337 | − | 0.142667i | ||||
\(778\) | −2.41581 | − | 1.39477i | −0.0866111 | − | 0.0500050i | ||||
\(779\) | 29.4292 | − | 50.9728i | 1.05441 | − | 1.82629i | ||||
\(780\) | −1.86508 | + | 2.54732i | −0.0667807 | + | 0.0912087i | ||||
\(781\) | 10.7806 | + | 18.6725i | 0.385760 | + | 0.668155i | ||||
\(782\) | 16.3778 | − | 9.45571i | 0.585668 | − | 0.338136i | ||||
\(783\) | −3.81357 | + | 6.60529i | −0.136286 | + | 0.236054i | ||||
\(784\) | 13.3737 | − | 7.78625i | 0.477631 | − | 0.278080i | ||||
\(785\) | − | 0.359656i | − | 0.0128367i | ||||||
\(786\) | − | 7.72996i | − | 0.275719i | ||||||
\(787\) | −12.4610 | − | 7.19437i | −0.444187 | − | 0.256451i | 0.261185 | − | 0.965289i | \(-0.415887\pi\) |
−0.705372 | + | 0.708837i | \(0.749220\pi\) | |||||||
\(788\) | −7.43798 | + | 4.29432i | −0.264967 | + | 0.152979i | ||||
\(789\) | −6.88599 | −0.245148 | ||||||||
\(790\) | 0.723279 | − | 1.25276i | 0.0257331 | − | 0.0445711i | ||||
\(791\) | 8.43351 | − | 31.7047i | 0.299861 | − | 1.12729i | ||||
\(792\) | −4.48118 | −0.159232 | ||||||||
\(793\) | 20.6170 | − | 9.08860i | 0.732130 | − | 0.322746i | ||||
\(794\) | 2.75623 | + | 4.77392i | 0.0978148 | + | 0.169420i | ||||
\(795\) | 1.08735i | 0.0385642i | ||||||||
\(796\) | −11.7217 | − | 20.3027i | −0.415466 | − | 0.719609i | ||||
\(797\) | 15.6589 | + | 27.1221i | 0.554668 | + | 0.960712i | 0.997929 | + | 0.0643202i | \(0.0204879\pi\) |
−0.443262 | + | 0.896392i | \(0.646179\pi\) | |||||||
\(798\) | 2.10647 | − | 7.91900i | 0.0745682 | − | 0.280329i | ||||
\(799\) | 48.0910 | − | 27.7653i | 1.70134 | − | 0.982267i | ||||
\(800\) | − | 25.4244i | − | 0.898888i | ||||||
\(801\) | −2.19138 | + | 1.26519i | −0.0774285 | + | 0.0447034i | ||||
\(802\) | 8.20728 | − | 14.2154i | 0.289809 | − | 0.501964i | ||||
\(803\) | −3.09209 | − | 5.35565i | −0.109117 | − | 0.188997i | ||||
\(804\) | −2.89163 | − | 1.66948i | −0.101980 | − | 0.0588782i | ||||
\(805\) | 6.59298 | − | 6.61699i | 0.232372 | − | 0.233218i | ||||
\(806\) | 1.30374 | − | 11.9805i | 0.0459225 | − | 0.421994i | ||||
\(807\) | −5.93548 | + | 10.2806i | −0.208939 | + | 0.361893i | ||||
\(808\) | 18.6978i | 0.657787i | ||||||||
\(809\) | 55.4621 | 1.94995 | 0.974973 | − | 0.222325i | \(-0.0713647\pi\) | ||||
0.974973 | + | 0.222325i | \(0.0713647\pi\) | |||||||
\(810\) | 0.291479 | 0.0102415 | ||||||||
\(811\) | − | 8.46874i | − | 0.297378i | −0.988884 | − | 0.148689i | \(-0.952495\pi\) | ||
0.988884 | − | 0.148689i | \(-0.0475053\pi\) | |||||||
\(812\) | 8.74223 | − | 32.8653i | 0.306792 | − | 1.15334i | ||||
\(813\) | 11.9020 | − | 6.87163i | 0.417422 | − | 0.240998i | ||||
\(814\) | −6.15739 | − | 3.55497i | −0.215817 | − | 0.124602i | ||||
\(815\) | −2.70109 | + | 4.67843i | −0.0946151 | + | 0.163878i | ||||
\(816\) | 10.9675 | 0.383940 | ||||||||
\(817\) | 20.2671 | − | 11.7012i | 0.709057 | − | 0.409374i | ||||
\(818\) | −7.20315 | −0.251852 | ||||||||
\(819\) | −8.89942 | − | 3.43516i | −0.310971 | − | 0.120034i | ||||
\(820\) | −9.33515 | −0.325997 | ||||||||
\(821\) | −23.0243 | + | 13.2931i | −0.803552 | + | 0.463931i | −0.844712 | − | 0.535222i | \(-0.820228\pi\) |
0.0411597 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(822\) | −0.909537 | −0.0317238 | ||||||||
\(823\) | 24.4813 | − | 42.4029i | 0.853366 | − | 1.47807i | −0.0247866 | − | 0.999693i | \(-0.507891\pi\) |
0.878153 | − | 0.478381i | \(-0.158776\pi\) | |||||||
\(824\) | 31.6154 | + | 18.2532i | 1.10138 | + | 0.635879i | ||||
\(825\) | 8.87885 | − | 5.12620i | 0.309122 | − | 0.178472i | ||||
\(826\) | −3.20511 | − | 3.19348i | −0.111520 | − | 0.111115i | ||||
\(827\) | − | 16.8817i | − | 0.587034i | −0.955954 | − | 0.293517i | \(-0.905174\pi\) | ||
0.955954 | − | 0.293517i | \(-0.0948257\pi\) | |||||||
\(828\) | 11.4516 | 0.397969 | ||||||||
\(829\) | 9.44160 | 0.327920 | 0.163960 | − | 0.986467i | \(-0.447573\pi\) | ||||
0.163960 | + | 0.986467i | \(0.447573\pi\) | |||||||
\(830\) | − | 1.06659i | − | 0.0370218i | ||||||
\(831\) | 5.60801 | − | 9.71335i | 0.194540 | − | 0.336952i | ||||
\(832\) | 4.63889 | − | 2.04496i | 0.160824 | − | 0.0708964i | ||||
\(833\) | 30.1375 | + | 17.2541i | 1.04420 | + | 0.597820i | ||||
\(834\) | 3.56484 | + | 2.05816i | 0.123440 | + | 0.0712683i | ||||
\(835\) | −6.27264 | − | 10.8645i | −0.217074 | − | 0.375983i | ||||
\(836\) | −10.0834 | + | 17.4650i | −0.348743 | + | 0.604041i | ||||
\(837\) | 5.15974 | − | 2.97898i | 0.178347 | − | 0.102969i | ||||
\(838\) | 14.7939i | 0.511045i | ||||||||
\(839\) | −32.5016 | + | 18.7648i | −1.12208 | + | 0.647833i | −0.941931 | − | 0.335806i | \(-0.890991\pi\) |
−0.180149 | + | 0.983639i | \(0.557658\pi\) | |||||||
\(840\) | −2.74384 | + | 0.740558i | −0.0946714 | + | 0.0255517i | ||||
\(841\) | −14.5866 | − | 25.2647i | −0.502985 | − | 0.871195i | ||||
\(842\) | 0.761211 | + | 1.31846i | 0.0262330 | + | 0.0454370i | ||||
\(843\) | 1.81616i | 0.0625517i | ||||||||
\(844\) | −10.6306 | − | 18.4128i | −0.365921 | − | 0.633793i | ||||
\(845\) | −6.43903 | + | 2.03995i | −0.221509 | + | 0.0701764i | ||||
\(846\) | −6.27947 | −0.215893 | ||||||||
\(847\) | −11.8112 | − | 11.7683i | −0.405838 | − | 0.404365i | ||||
\(848\) | 2.31328 | − | 4.00672i | 0.0794385 | − | 0.137591i | ||||
\(849\) | −30.8377 | −1.05835 | ||||||||
\(850\) | 11.4006 | − | 6.58214i | 0.391037 | − | 0.225766i | ||||
\(851\) | 34.4086 | + | 19.8658i | 1.17951 | + | 0.680992i | ||||
\(852\) | 16.7642i | 0.574334i | ||||||||
\(853\) | − | 35.3664i | − | 1.21092i | −0.795875 | − | 0.605461i | \(-0.792989\pi\) | ||
0.795875 | − | 0.605461i | \(-0.207011\pi\) | |||||||
\(854\) | 8.96356 | + | 2.38432i | 0.306727 | + | 0.0815899i | ||||
\(855\) | 1.43424 | − | 2.48418i | 0.0490500 | − | 0.0849571i | ||||
\(856\) | −34.8423 | + | 20.1162i | −1.19089 | + | 0.687559i | ||||
\(857\) | −2.53098 | − | 4.38379i | −0.0864568 | − | 0.149748i | 0.819554 | − | 0.573002i | \(-0.194221\pi\) |
−0.906011 | + | 0.423254i | \(0.860888\pi\) | |||||||
\(858\) | −3.53742 | − | 2.59001i | −0.120766 | − | 0.0884214i | ||||
\(859\) | 2.61058 | − | 4.52166i | 0.0890719 | − | 0.154277i | −0.818047 | − | 0.575151i | \(-0.804943\pi\) |
0.907119 | + | 0.420874i | \(0.138277\pi\) | |||||||
\(860\) | −3.21444 | − | 1.85586i | −0.109612 | − | 0.0632842i | ||||
\(861\) | −7.34992 | − | 27.2322i | −0.250485 | − | 0.928071i | ||||
\(862\) | 10.4028 | + | 18.0181i | 0.354319 | + | 0.613699i | ||||
\(863\) | 1.53116 | + | 0.884017i | 0.0521214 | + | 0.0300923i | 0.525834 | − | 0.850587i | \(-0.323753\pi\) |
−0.473713 | + | 0.880679i | \(0.657087\pi\) | |||||||
\(864\) | −4.65496 | − | 2.68754i | −0.158365 | − | 0.0914321i | ||||
\(865\) | −1.68222 | − | 0.971232i | −0.0571973 | − | 0.0330229i | ||||
\(866\) | −7.01100 | − | 4.04780i | −0.238243 | − | 0.137550i | ||||
\(867\) | 3.80585 | + | 6.59193i | 0.129253 | + | 0.223874i | ||||
\(868\) | −18.7505 | + | 18.8188i | −0.636434 | + | 0.638751i | ||||
\(869\) | −9.31580 | − | 5.37848i | −0.316017 | − | 0.182452i | ||||
\(870\) | −1.11157 | + | 1.92530i | −0.0376859 | + | 0.0652739i | ||||
\(871\) | −2.88152 | − | 6.53656i | −0.0976364 | − | 0.221483i | ||||
\(872\) | −16.8790 | − | 29.2352i | −0.571593 | − | 0.990029i | ||||
\(873\) | 8.01957 | − | 4.63010i | 0.271421 | − | 0.156705i | ||||
\(874\) | −10.5227 | + | 18.2259i | −0.355937 | + | 0.616501i | ||||
\(875\) | 9.44070 | − | 9.47509i | 0.319154 | − | 0.320316i | ||||
\(876\) | − | 4.80832i | − | 0.162458i | ||||||
\(877\) | − | 56.8326i | − | 1.91910i | −0.281537 | − | 0.959550i | \(-0.590844\pi\) | ||
0.281537 | − | 0.959550i | \(-0.409156\pi\) | |||||||
\(878\) | 7.10784 | + | 4.10371i | 0.239878 | + | 0.138494i | ||||
\(879\) | 0.948761 | − | 0.547767i | 0.0320009 | − | 0.0184757i | ||||
\(880\) | 2.48968 | 0.0839272 | ||||||||
\(881\) | 20.9164 | − | 36.2283i | 0.704693 | − | 1.22056i | −0.262110 | − | 0.965038i | \(-0.584418\pi\) |
0.966802 | − | 0.255525i | \(-0.0822484\pi\) | |||||||
\(882\) | −1.97584 | − | 3.39371i | −0.0665301 | − | 0.114272i | ||||
\(883\) | −8.23784 | −0.277225 | −0.138613 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138613 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(884\) | 24.3225 | + | 17.8083i | 0.818054 | + | 0.598958i | ||||
\(885\) | −0.791910 | − | 1.37163i | −0.0266198 | − | 0.0461068i | ||||
\(886\) | 20.5375i | 0.689972i | ||||||||
\(887\) | 27.3772 | + | 47.4187i | 0.919236 | + | 1.59216i | 0.800578 | + | 0.599229i | \(0.204526\pi\) |
0.118659 | + | 0.992935i | \(0.462141\pi\) | |||||||
\(888\) | −6.04430 | − | 10.4690i | −0.202834 | − | 0.351318i | ||||
\(889\) | −51.9429 | + | 14.0193i | −1.74211 | + | 0.470192i | ||||
\(890\) | −0.638741 | + | 0.368777i | −0.0214106 | + | 0.0123614i | ||||
\(891\) | − | 2.16751i | − | 0.0726143i | ||||||
\(892\) | −1.11149 | + | 0.641717i | −0.0372153 | + | 0.0214863i | ||||
\(893\) | −30.8985 | + | 53.5178i | −1.03398 | + | 1.79090i | ||||
\(894\) | 0.301506 | + | 0.522223i | 0.0100839 | + | 0.0174658i | ||||
\(895\) | 2.55493 | + | 1.47509i | 0.0854020 | + | 0.0493069i | ||||
\(896\) | 29.5033 | + | 7.84794i | 0.985636 | + | 0.262181i | ||||
\(897\) | 19.7677 | + | 14.4734i | 0.660026 | + | 0.483254i | ||||
\(898\) | 1.81166 | − | 3.13789i | 0.0604559 | − | 0.104713i | ||||
\(899\) | 45.4421i | 1.51558i | ||||||||
\(900\) | 7.97146 | 0.265715 | ||||||||
\(901\) | 10.3823 | 0.345884 | ||||||||
\(902\) | − | 12.9636i | − | 0.431639i | ||||||
\(903\) | 2.88300 | − | 10.8383i | 0.0959402 | − | 0.360675i | ||||
\(904\) | 22.2015 | − | 12.8180i | 0.738411 | − | 0.426322i | ||||
\(905\) | 4.47670 | + | 2.58462i | 0.148810 | + | 0.0859158i | ||||
\(906\) | −3.52096 | + | 6.09848i | −0.116976 | + | 0.202609i | ||||
\(907\) | 11.5571 | 0.383748 | 0.191874 | − | 0.981420i | \(-0.438543\pi\) | ||||
0.191874 | + | 0.981420i | \(0.438543\pi\) | |||||||
\(908\) | −2.24844 | + | 1.29814i | −0.0746171 | + | 0.0430802i | ||||
\(909\) | −9.04398 | −0.299970 | ||||||||
\(910\) | −2.59400 | − | 1.00128i | −0.0859901 | − | 0.0331920i | ||||
\(911\) | 23.9338 | 0.792961 | 0.396481 | − | 0.918043i | \(-0.370231\pi\) | ||||
0.396481 | + | 0.918043i | \(0.370231\pi\) | |||||||
\(912\) | −10.5700 | + | 6.10257i | −0.350006 | + | 0.202076i | ||||
\(913\) | −7.93141 | −0.262491 | ||||||||
\(914\) | −5.38388 | + | 9.32516i | −0.178083 | + | 0.308449i | ||||
\(915\) | 2.81185 | + | 1.62342i | 0.0929570 | + | 0.0536688i | ||||
\(916\) | −8.19949 | + | 4.73398i | −0.270919 | + | 0.156415i | ||||
\(917\) | −35.1963 | + | 9.49942i | −1.16228 | + | 0.313698i | ||||
\(918\) | − | 2.78312i | − | 0.0918566i | ||||||
\(919\) | 3.13809 | 0.103516 | 0.0517580 | − | 0.998660i | \(-0.483518\pi\) | ||||
0.0517580 | + | 0.998660i | \(0.483518\pi\) | |||||||
\(920\) | 7.29912 | 0.240645 | ||||||||
\(921\) | 4.90247i | 0.161542i | ||||||||
\(922\) | 1.78206 | − | 3.08662i | 0.0586891 | − | 0.101653i | ||||
\(923\) | −21.1880 | + | 28.9385i | −0.697413 | + | 0.952523i | ||||
\(924\) | 2.51834 | + | 9.33069i | 0.0828472 | + | 0.306957i | ||||
\(925\) | 23.9519 | + | 13.8286i | 0.787534 | + | 0.454683i | ||||
\(926\) | −3.03777 | − | 5.26157i | −0.0998272 | − | 0.172906i | ||||
\(927\) | −8.82890 | + | 15.2921i | −0.289979 | + | 0.502258i | ||||
\(928\) | 35.5040 | − | 20.4982i | 1.16548 | − | 0.672888i | ||||
\(929\) | − | 21.1971i | − | 0.695455i | −0.937596 | − | 0.347728i | \(-0.886953\pi\) | ||
0.937596 | − | 0.347728i | \(-0.113047\pi\) | |||||||
\(930\) | 1.50396 | − | 0.868310i | 0.0493167 | − | 0.0284730i | ||||
\(931\) | −38.6457 | + | 0.140489i | −1.26656 | + | 0.00460435i | ||||
\(932\) | −14.4509 | − | 25.0297i | −0.473356 | − | 0.819876i | ||||
\(933\) | 5.78751 | + | 10.0243i | 0.189474 | + | 0.328179i | ||||
\(934\) | 6.55258i | 0.214407i | ||||||||
\(935\) | 2.79350 | + | 4.83848i | 0.0913571 | + | 0.158235i | ||||
\(936\) | −3.00686 | − | 6.82089i | −0.0982822 | − | 0.222948i | ||||
\(937\) | −26.0293 | −0.850339 | −0.425169 | − | 0.905114i | \(-0.639786\pi\) | ||||
−0.425169 | + | 0.905114i | \(0.639786\pi\) | |||||||
\(938\) | 0.755943 | − | 2.84187i | 0.0246824 | − | 0.0927904i | ||||
\(939\) | −2.53480 | + | 4.39041i | −0.0827201 | + | 0.143275i | ||||
\(940\) | 9.80124 | 0.319681 | ||||||||
\(941\) | −14.2589 | + | 8.23240i | −0.464828 | + | 0.268369i | −0.714072 | − | 0.700072i | \(-0.753151\pi\) |
0.249244 | + | 0.968441i | \(0.419818\pi\) | |||||||
\(942\) | 0.336305 | + | 0.194166i | 0.0109574 | + | 0.00632625i | ||||
\(943\) | 72.4427i | 2.35906i | ||||||||
\(944\) | 6.73902i | 0.219336i | ||||||||
\(945\) | −0.358201 | − | 1.32717i | −0.0116523 | − | 0.0431729i | ||||
\(946\) | 2.57720 | − | 4.46384i | 0.0837919 | − | 0.145132i | ||||
\(947\) | 12.3262 | − | 7.11651i | 0.400546 | − | 0.231255i | −0.286173 | − | 0.958178i | \(-0.592383\pi\) |
0.686720 | + | 0.726922i | \(0.259050\pi\) | |||||||
\(948\) | −4.18188 | − | 7.24322i | −0.135821 | − | 0.235249i | ||||
\(949\) | 6.07716 | − | 8.30015i | 0.197273 | − | 0.269434i | ||||
\(950\) | −7.32490 | + | 12.6871i | −0.237651 | + | 0.411624i | ||||
\(951\) | 14.8929 | + | 8.59841i | 0.482935 | + | 0.278823i | ||||
\(952\) | 7.07104 | + | 26.1989i | 0.229174 | + | 0.849111i | ||||
\(953\) | −22.2750 | − | 38.5815i | −0.721559 | − | 1.24978i | −0.960375 | − | 0.278712i | \(-0.910092\pi\) |
0.238815 | − | 0.971065i | \(-0.423241\pi\) | |||||||
\(954\) | −1.01675 | − | 0.587020i | −0.0329184 | − | 0.0190055i | ||||
\(955\) | −4.27859 | − | 2.47024i | −0.138452 | − | 0.0799352i | ||||
\(956\) | −37.4591 | − | 21.6270i | −1.21151 | − | 0.699468i | ||||
\(957\) | 14.3170 | + | 8.26593i | 0.462803 | + | 0.267200i | ||||
\(958\) | −6.73859 | − | 11.6716i | −0.217714 | − | 0.377092i | ||||
\(959\) | 1.11774 | + | 4.14133i | 0.0360937 | + | 0.133731i | ||||
\(960\) | 0.632676 | + | 0.365276i | 0.0204195 | + | 0.0117892i | ||||
\(961\) | 2.24861 | − | 3.89472i | 0.0725360 | − | 0.125636i | ||||
\(962\) | 1.27950 | − | 11.7577i | 0.0412527 | − | 0.379082i | ||||
\(963\) | −9.73005 | − | 16.8529i | −0.313546 | − | 0.543078i | ||||
\(964\) | −6.88471 | + | 3.97489i | −0.221742 | + | 0.128023i | ||||
\(965\) | −0.808445 | + | 1.40027i | −0.0260248 | + | 0.0450762i | ||||
\(966\) | 2.62805 | + | 9.73719i | 0.0845562 | + | 0.313289i | ||||
\(967\) | 17.7030i | 0.569289i | 0.958633 | + | 0.284645i | \(0.0918756\pi\) | ||||
−0.958633 | + | 0.284645i | \(0.908124\pi\) | |||||||
\(968\) | − | 13.0288i | − | 0.418761i | ||||||
\(969\) | −23.7196 | − | 13.6945i | −0.761983 | − | 0.439931i | ||||
\(970\) | 2.33754 | − | 1.34958i | 0.0750538 | − | 0.0433324i | ||||
\(971\) | 6.32688 | 0.203039 | 0.101520 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101520 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(972\) | 0.842641 | − | 1.45950i | 0.0270277 | − | 0.0468134i | ||||
\(973\) | 4.99042 | − | 18.7608i | 0.159985 | − | 0.601444i | ||||
\(974\) | −3.38858 | −0.108577 | ||||||||
\(975\) | 13.7604 | + | 10.0750i | 0.440684 | + | 0.322658i | ||||
\(976\) | −6.90753 | − | 11.9642i | −0.221105 | − | 0.382965i | ||||
\(977\) | − | 9.17489i | − | 0.293531i | −0.989171 | − | 0.146765i | \(-0.953114\pi\) | ||
0.989171 | − | 0.146765i | \(-0.0468862\pi\) | |||||||
\(978\) | −2.91645 | − | 5.05143i | −0.0932577 | − | 0.161527i | ||||
\(979\) | 2.74231 | + | 4.74983i | 0.0876447 | + | 0.151805i | ||||
\(980\) | 3.08397 | + | 5.29703i | 0.0985138 | + | 0.169207i | ||||
\(981\) | 14.1408 | − | 8.16420i | 0.451481 | − | 0.260663i | ||||
\(982\) | − | 7.91709i | − | 0.252644i | ||||||
\(983\) | −42.7704 | + | 24.6935i | −1.36416 | + | 0.787601i | −0.990175 | − | 0.139832i | \(-0.955344\pi\) |
−0.373990 | + | 0.927433i | \(0.622010\pi\) | |||||||
\(984\) | 11.0206 | − | 19.0882i | 0.351323 | − | 0.608509i | ||||
\(985\) | −1.32394 | − | 2.29313i | −0.0421842 | − | 0.0730652i | ||||
\(986\) | 18.3833 | + | 10.6136i | 0.585444 | + | 0.338006i | ||||
\(987\) | 7.71690 | + | 28.5919i | 0.245632 | + | 0.910089i | ||||
\(988\) | −33.3498 | − | 3.62921i | −1.06100 | − | 0.115461i | ||||
\(989\) | −14.4018 | + | 24.9447i | −0.457952 | + | 0.793196i | ||||
\(990\) | − | 0.631783i | − | 0.0200794i | ||||||
\(991\) | 35.8929 | 1.14018 | 0.570088 | − | 0.821584i | \(-0.306909\pi\) | ||||
0.570088 | + | 0.821584i | \(0.306909\pi\) | |||||||
\(992\) | −32.0245 | −1.01678 | ||||||||
\(993\) | 20.4213i | 0.648050i | ||||||||
\(994\) | −14.2545 | + | 3.84728i | −0.452126 | + | 0.122028i | ||||
\(995\) | 6.25932 | − | 3.61382i | 0.198434 | − | 0.114566i | ||||
\(996\) | −5.34063 | − | 3.08342i | −0.169224 | − | 0.0977018i | ||||
\(997\) | −21.1225 | + | 36.5853i | −0.668957 | + | 1.15867i | 0.309239 | + | 0.950984i | \(0.399926\pi\) |
−0.978196 | + | 0.207684i | \(0.933408\pi\) | |||||||
\(998\) | −18.4282 | −0.583336 | ||||||||
\(999\) | 5.06378 | − | 2.92358i | 0.160211 | − | 0.0924979i |
(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 | 273.2.bl.d.121.5 | yes | 20 | |
3.2 | odd | 2 | 819.2.do.g.667.6 | 20 | |||
7.4 | even | 3 | 273.2.t.d.4.5 | ✓ | 20 | ||
13.10 | even | 6 | 273.2.t.d.205.6 | yes | 20 | ||
21.11 | odd | 6 | 819.2.bm.g.550.6 | 20 | |||
39.23 | odd | 6 | 819.2.bm.g.478.5 | 20 | |||
91.88 | even | 6 | inner | 273.2.bl.d.88.5 | yes | 20 | |
273.179 | odd | 6 | 819.2.do.g.361.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.d.4.5 | ✓ | 20 | 7.4 | even | 3 | ||
273.2.t.d.205.6 | yes | 20 | 13.10 | even | 6 | ||
273.2.bl.d.88.5 | yes | 20 | 91.88 | even | 6 | inner | |
273.2.bl.d.121.5 | yes | 20 | 1.1 | even | 1 | trivial | |
819.2.bm.g.478.5 | 20 | 39.23 | odd | 6 | |||
819.2.bm.g.550.6 | 20 | 21.11 | odd | 6 | |||
819.2.do.g.361.6 | 20 | 273.179 | odd | 6 | |||
819.2.do.g.667.6 | 20 | 3.2 | odd | 2 |