Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(4,273)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.t (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: | \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 205.6 | ||
Root | \(0.560998i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.205 |
Dual form | 273.2.t.d.4.5 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.560998i | 0.396685i | 0.980133 | + | 0.198343i | \(0.0635559\pi\) | ||||
−0.980133 | + | 0.198343i | \(0.936444\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.68528 | 0.842641 | ||||||||
\(5\) | 0.449963 | + | 0.259786i | 0.201230 | + | 0.116180i | 0.597229 | − | 0.802071i | \(-0.296268\pi\) |
−0.395999 | + | 0.918251i | \(0.629602\pi\) | |||||||
\(6\) | 0.485838 | + | 0.280499i | 0.198343 | + | 0.114513i | ||||
\(7\) | 0.680125 | − | 2.55684i | 0.257063 | − | 0.966395i | ||||
\(8\) | 2.06743i | 0.730948i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.145740 | + | 0.252428i | −0.0460869 | + | 0.0798248i | ||||
\(11\) | −1.87712 | − | 1.08375i | −0.565972 | − | 0.326764i | 0.189567 | − | 0.981868i | \(-0.439292\pi\) |
−0.755539 | + | 0.655104i | \(0.772625\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | 2.21074 | 0.552684 | ||||||||
\(17\) | −4.96102 | −1.20322 | −0.601612 | − | 0.798789i | \(-0.705475\pi\) | ||||
−0.601612 | + | 0.798789i | \(0.705475\pi\) | |||||||
\(18\) | 0.485838 | − | 0.280499i | 0.114513 | − | 0.0661142i | ||||
\(19\) | −4.78119 | + | 2.76042i | −1.09688 | + | 0.633284i | −0.935400 | − | 0.353592i | \(-0.884960\pi\) |
−0.161481 | + | 0.986876i | \(0.551627\pi\) | |||||||
\(20\) | 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 | ||||
\(23\) | 6.79504 | 1.41686 | 0.708432 | − | 0.705779i | \(-0.249403\pi\) | ||||
0.708432 | + | 0.705779i | \(0.249403\pi\) | |||||||
\(24\) | 1.79045 | + | 1.03372i | 0.365474 | + | 0.211007i | ||||
\(25\) | −2.36502 | − | 4.09634i | −0.473004 | − | 0.819268i | ||||
\(26\) | −0.815910 | + | 1.85085i | −0.160013 | + | 0.362981i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.14620 | − | 4.30900i | 0.216612 | − | 0.814324i | ||||
\(29\) | 3.81357 | + | 6.60529i | 0.708161 | + | 1.22657i | 0.965538 | + | 0.260260i | \(0.0838084\pi\) |
−0.257377 | + | 0.966311i | \(0.582858\pi\) | |||||||
\(30\) | 0.145740 | + | 0.252428i | 0.0266083 | + | 0.0460869i | ||||
\(31\) | 5.15974 | − | 2.97898i | 0.926717 | − | 0.535040i | 0.0409451 | − | 0.999161i | \(-0.486963\pi\) |
0.885772 | + | 0.464121i | \(0.153630\pi\) | |||||||
\(32\) | 5.37509i | 0.950190i | ||||||||
\(33\) | −1.87712 | + | 1.08375i | −0.326764 | + | 0.188657i | ||||
\(34\) | − | 2.78312i | − | 0.477301i | ||||||
\(35\) | 0.970263 | − | 0.973797i | 0.164004 | − | 0.164602i | ||||
\(36\) | −0.842641 | − | 1.45950i | −0.140440 | − | 0.243249i | ||||
\(37\) | 5.84715i | 0.961266i | 0.876922 | + | 0.480633i | \(0.159593\pi\) | ||||
−0.876922 | + | 0.480633i | \(0.840407\pi\) | |||||||
\(38\) | −1.54859 | − | 2.68224i | −0.251215 | − | 0.435116i | ||||
\(39\) | 2.90914 | − | 2.13000i | 0.465835 | − | 0.341073i | ||||
\(40\) | −0.537091 | + | 0.930269i | −0.0849216 | + | 0.147089i | ||||
\(41\) | −9.23279 | + | 5.33055i | −1.44192 | + | 0.832492i | −0.997978 | − | 0.0635633i | \(-0.979754\pi\) |
−0.443941 | + | 0.896056i | \(0.646420\pi\) | |||||||
\(42\) | 1.04762 | − | 1.05144i | 0.161651 | − | 0.162240i | ||||
\(43\) | −2.11946 | + | 3.67102i | −0.323215 | + | 0.559825i | −0.981150 | − | 0.193250i | \(-0.938097\pi\) |
0.657934 | + | 0.753075i | \(0.271430\pi\) | |||||||
\(44\) | −3.16347 | − | 1.82643i | −0.476911 | − | 0.275345i | ||||
\(45\) | − | 0.519573i | − | 0.0774533i | ||||||
\(46\) | 3.81200i | 0.562049i | ||||||||
\(47\) | −9.69377 | − | 5.59670i | −1.41398 | − | 0.816363i | −0.418221 | − | 0.908345i | \(-0.637346\pi\) |
−0.995761 | + | 0.0919829i | \(0.970679\pi\) | |||||||
\(48\) | 1.10537 | − | 1.91455i | 0.159546 | − | 0.276342i | ||||
\(49\) | −6.07486 | − | 3.47794i | −0.867837 | − | 0.496848i | ||||
\(50\) | 2.29804 | − | 1.32677i | 0.324991 | − | 0.187634i | ||||
\(51\) | −2.48051 | + | 4.29637i | −0.347341 | + | 0.601612i | ||||
\(52\) | 5.56009 | + | 2.45106i | 0.771045 | + | 0.339901i | ||||
\(53\) | 1.04639 | + | 1.81239i | 0.143732 | + | 0.248951i | 0.928899 | − | 0.370333i | \(-0.120756\pi\) |
−0.785167 | + | 0.619284i | \(0.787423\pi\) | |||||||
\(54\) | − | 0.560998i | − | 0.0763421i | ||||||
\(55\) | −0.563089 | − | 0.975299i | −0.0759269 | − | 0.131509i | ||||
\(56\) | 5.28610 | + | 1.40611i | 0.706385 | + | 0.187900i | ||||
\(57\) | 5.52084i | 0.731254i | ||||||||
\(58\) | −3.70555 | + | 2.13940i | −0.486563 | + | 0.280917i | ||||
\(59\) | − | 3.04831i | − | 0.396856i | −0.980115 | − | 0.198428i | \(-0.936416\pi\) | ||
0.980115 | − | 0.198428i | \(-0.0635837\pi\) | |||||||
\(60\) | 0.758315 | − | 0.437813i | 0.0978980 | − | 0.0565214i | ||||
\(61\) | −3.12454 | − | 5.41186i | −0.400056 | − | 0.692917i | 0.593676 | − | 0.804704i | \(-0.297676\pi\) |
−0.993732 | + | 0.111787i | \(0.964343\pi\) | |||||||
\(62\) | 1.67120 | + | 2.89460i | 0.212243 | + | 0.367615i | ||||
\(63\) | −2.55435 | + | 0.689415i | −0.321818 | + | 0.0868581i | ||||
\(64\) | 1.40606 | 0.175758 | ||||||||
\(65\) | 1.10669 | + | 1.51151i | 0.137268 | + | 0.187480i | ||||
\(66\) | −0.607984 | − | 1.05306i | −0.0748376 | − | 0.129623i | ||||
\(67\) | −1.71581 | − | 0.990626i | −0.209620 | − | 0.121024i | 0.391515 | − | 0.920172i | \(-0.371951\pi\) |
−0.601135 | + | 0.799148i | \(0.705285\pi\) | |||||||
\(68\) | −8.36071 | −1.01389 | ||||||||
\(69\) | 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 | −0.107589 | − | 0.994195i | \(-0.534313\pi\) |
−0.914793 | + | 0.403923i | \(0.867646\pi\) | |||||||
\(72\) | 1.79045 | − | 1.03372i | 0.211007 | − | 0.121825i | ||||
\(73\) | −2.47088 | + | 1.42656i | −0.289195 | + | 0.166967i | −0.637579 | − | 0.770385i | \(-0.720064\pi\) |
0.348384 | + | 0.937352i | \(0.386731\pi\) | |||||||
\(74\) | −3.28024 | −0.381320 | ||||||||
\(75\) | −4.73004 | −0.546178 | ||||||||
\(76\) | −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 | \(0.0766039\pi\) | |||||||
\(80\) | 0.994750 | + | 0.574319i | 0.111216 | + | 0.0642109i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.99043 | − | 5.17957i | −0.330238 | − | 0.571988i | ||||
\(83\) | 3.65923i | 0.401653i | 0.979627 | + | 0.200826i | \(0.0643627\pi\) | ||||
−0.979627 | + | 0.200826i | \(0.935637\pi\) | |||||||
\(84\) | −3.15860 | − | 3.14714i | −0.344631 | − | 0.343381i | ||||
\(85\) | −2.23228 | − | 1.28880i | −0.242124 | − | 0.139791i | ||||
\(86\) | −2.05943 | − | 1.18901i | −0.222074 | − | 0.128215i | ||||
\(87\) | 7.62713 | 0.817714 | ||||||||
\(88\) | 2.24059 | − | 3.88082i | 0.238848 | − | 0.413696i | ||||
\(89\) | 2.53038i | 0.268220i | 0.990966 | + | 0.134110i | \(0.0428176\pi\) | ||||
−0.990966 | + | 0.134110i | \(0.957182\pi\) | |||||||
\(90\) | 0.291479 | 0.0307246 | ||||||||
\(91\) | 5.96251 | − | 7.44637i | 0.625041 | − | 0.780592i | ||||
\(92\) | 11.4516 | 1.19391 | ||||||||
\(93\) | − | 5.95796i | − | 0.617811i | ||||||
\(94\) | 3.13974 | − | 5.43818i | 0.323839 | − | 0.560906i | ||||
\(95\) | −2.86848 | −0.294300 | ||||||||
\(96\) | 4.65496 | + | 2.68754i | 0.475095 | + | 0.274296i | ||||
\(97\) | 8.01957 | + | 4.63010i | 0.814264 | + | 0.470116i | 0.848435 | − | 0.529300i | \(-0.177545\pi\) |
−0.0341702 | + | 0.999416i | \(0.510879\pi\) | |||||||
\(98\) | 1.95112 | − | 3.40798i | 0.197092 | − | 0.344258i | ||||
\(99\) | 2.16751i | 0.217843i | ||||||||
\(100\) | −3.98573 | − | 6.90348i | −0.398573 | − | 0.690348i | ||||
\(101\) | 4.52199 | − | 7.83231i | 0.449955 | − | 0.779344i | −0.548428 | − | 0.836198i | \(-0.684773\pi\) |
0.998383 | + | 0.0568535i | \(0.0181068\pi\) | |||||||
\(102\) | −2.41025 | − | 1.39156i | −0.238651 | − | 0.137785i | ||||
\(103\) | −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 | ||||
\(107\) | 19.4601 | 1.88128 | 0.940639 | − | 0.339408i | \(-0.110227\pi\) | ||||
0.940639 | + | 0.339408i | \(0.110227\pi\) | |||||||
\(108\) | −1.68528 | −0.162166 | ||||||||
\(109\) | −14.1408 | + | 8.16420i | −1.35444 | + | 0.781989i | −0.988868 | − | 0.148793i | \(-0.952461\pi\) |
−0.365576 | + | 0.930782i | \(0.619128\pi\) | |||||||
\(110\) | 0.547140 | − | 0.315892i | 0.0521678 | − | 0.0301191i | ||||
\(111\) | 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 | −0.411847 | − | 0.911253i | \(-0.635116\pi\) |
0.995092 | − | 0.0989565i | \(-0.0315505\pi\) | |||||||
\(114\) | −3.09718 | −0.290078 | ||||||||
\(115\) | 3.05752 | + | 1.76526i | 0.285115 | + | 0.164611i | ||||
\(116\) | 6.42693 | + | 11.1318i | 0.596726 | + | 1.03356i | ||||
\(117\) | −0.390063 | − | 3.58439i | −0.0360613 | − | 0.331377i | ||||
\(118\) | 1.71010 | 0.157427 | ||||||||
\(119\) | −3.37411 | + | 12.6845i | −0.309304 | + | 1.16279i | ||||
\(120\) | 0.537091 | + | 0.930269i | 0.0490295 | + | 0.0849216i | ||||
\(121\) | −3.15095 | − | 5.45761i | −0.286450 | − | 0.496147i | ||||
\(122\) | 3.03604 | − | 1.75286i | 0.274870 | − | 0.158696i | ||||
\(123\) | 10.6611i | 0.961280i | ||||||||
\(124\) | 8.69562 | − | 5.02042i | 0.780889 | − | 0.450847i | ||||
\(125\) | − | 5.05547i | − | 0.452175i | ||||||
\(126\) | −0.386760 | − | 1.43298i | −0.0344553 | − | 0.127660i | ||||
\(127\) | 10.1675 | + | 17.6107i | 0.902223 | + | 1.56270i | 0.824602 | + | 0.565713i | \(0.191399\pi\) |
0.0776210 | + | 0.996983i | \(0.475268\pi\) | |||||||
\(128\) | 11.5390i | 1.01991i | ||||||||
\(129\) | 2.11946 | + | 3.67102i | 0.186608 | + | 0.323215i | ||||
\(130\) | −0.847954 | + | 0.620850i | −0.0743705 | + | 0.0544522i | ||||
\(131\) | 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 | ||||
\(133\) | 3.80615 | + | 14.1022i | 0.330035 | + | 1.22281i | ||||
\(134\) | 0.555739 | − | 0.962568i | 0.0480085 | − | 0.0831532i | ||||
\(135\) | −0.449963 | − | 0.259786i | −0.0387267 | − | 0.0223589i | ||||
\(136\) | − | 10.2566i | − | 0.879494i | ||||||
\(137\) | − | 1.62129i | − | 0.138516i | −0.997599 | − | 0.0692579i | \(-0.977937\pi\) | ||
0.997599 | − | 0.0692579i | \(-0.0220631\pi\) | |||||||
\(138\) | 3.30129 | + | 1.90600i | 0.281025 | + | 0.162250i | ||||
\(139\) | 3.66875 | − | 6.35446i | 0.311179 | − | 0.538979i | −0.667439 | − | 0.744665i | \(-0.732609\pi\) |
0.978618 | + | 0.205686i | \(0.0659426\pi\) | |||||||
\(140\) | 1.63517 | − | 1.64112i | 0.138197 | − | 0.138700i | ||||
\(141\) | −9.69377 | + | 5.59670i | −0.816363 | + | 0.471327i | ||||
\(142\) | 2.79025 | − | 4.83285i | 0.234152 | − | 0.405564i | ||||
\(143\) | −4.61679 | − | 6.30559i | −0.386075 | − | 0.527300i | ||||
\(144\) | −1.10537 | − | 1.91455i | −0.0921140 | − | 0.159546i | ||||
\(145\) | 3.96285i | 0.329097i | ||||||||
\(146\) | −0.800299 | − | 1.38616i | −0.0662332 | − | 0.114719i | ||||
\(147\) | −6.04941 | + | 3.52201i | −0.498947 | + | 0.290491i | ||||
\(148\) | 9.85410i | 0.810002i | ||||||||
\(149\) | −0.930883 | + | 0.537446i | −0.0762609 | + | 0.0440293i | −0.537646 | − | 0.843171i | \(-0.680686\pi\) |
0.461385 | + | 0.887200i | \(0.347353\pi\) | |||||||
\(150\) | − | 2.65354i | − | 0.216661i | ||||||
\(151\) | 10.8708 | − | 6.27625i | 0.884652 | − | 0.510754i | 0.0124624 | − | 0.999922i | \(-0.496033\pi\) |
0.872189 | + | 0.489168i | \(0.162700\pi\) | |||||||
\(152\) | −5.70699 | − | 9.88480i | −0.462898 | − | 0.801763i | ||||
\(153\) | 2.48051 | + | 4.29637i | 0.200537 | + | 0.347341i | ||||
\(154\) | −2.27900 | − | 2.27073i | −0.183647 | − | 0.182980i | ||||
\(155\) | 3.09559 | 0.248644 | ||||||||
\(156\) | 4.90272 | − | 3.58965i | 0.392532 | − | 0.287402i | ||||
\(157\) | 0.346108 | + | 0.599476i | 0.0276224 | + | 0.0478434i | 0.879506 | − | 0.475888i | \(-0.157873\pi\) |
−0.851884 | + | 0.523731i | \(0.824540\pi\) | |||||||
\(158\) | 2.41113 | + | 1.39207i | 0.191819 | + | 0.110747i | ||||
\(159\) | 2.09277 | 0.165968 | ||||||||
\(160\) | −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 | ||||
\(163\) | 9.00438 | − | 5.19868i | 0.705277 | − | 0.407192i | −0.104033 | − | 0.994574i | \(-0.533175\pi\) |
0.809310 | + | 0.587382i | \(0.199841\pi\) | |||||||
\(164\) | −15.5598 | + | 8.98348i | −1.21502 | + | 0.701492i | ||||
\(165\) | −1.12618 | −0.0876729 | ||||||||
\(166\) | −2.05282 | −0.159330 | ||||||||
\(167\) | 20.9105 | − | 12.0727i | 1.61810 | − | 0.934213i | 0.630694 | − | 0.776032i | \(-0.282770\pi\) |
0.987410 | − | 0.158181i | \(-0.0505629\pi\) | |||||||
\(168\) | 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 | ||||
\(171\) | 4.78119 | + | 2.76042i | 0.365627 | + | 0.211095i | ||||
\(172\) | −3.57189 | + | 6.18670i | −0.272354 | + | 0.471731i | ||||
\(173\) | −1.86929 | − | 3.23770i | −0.142119 | − | 0.246158i | 0.786175 | − | 0.618004i | \(-0.212058\pi\) |
−0.928295 | + | 0.371846i | \(0.878725\pi\) | |||||||
\(174\) | 4.27880i | 0.324375i | ||||||||
\(175\) | −12.0822 | + | 3.26096i | −0.913328 | + | 0.246506i | ||||
\(176\) | −4.14981 | − | 2.39590i | −0.312804 | − | 0.180597i | ||||
\(177\) | −2.63992 | − | 1.52416i | −0.198428 | − | 0.114563i | ||||
\(178\) | −1.41954 | −0.106399 | ||||||||
\(179\) | 2.83905 | − | 4.91738i | 0.212200 | − | 0.367542i | −0.740202 | − | 0.672384i | \(-0.765270\pi\) |
0.952403 | + | 0.304842i | \(0.0986037\pi\) | |||||||
\(180\) | − | 0.875626i | − | 0.0652653i | ||||||
\(181\) | −9.94903 | −0.739506 | −0.369753 | − | 0.929130i | \(-0.620558\pi\) | ||||
−0.369753 | + | 0.929130i | \(0.620558\pi\) | |||||||
\(182\) | 4.17740 | + | 3.34496i | 0.309649 | + | 0.247945i | ||||
\(183\) | −6.24908 | −0.461945 | ||||||||
\(184\) | 14.0483i | 1.03565i | ||||||||
\(185\) | −1.51901 | + | 2.63100i | −0.111680 | + | 0.193435i | ||||
\(186\) | 3.34240 | 0.245077 | ||||||||
\(187\) | 9.31241 | + | 5.37652i | 0.680991 | + | 0.393170i | ||||
\(188\) | −16.3367 | − | 9.43201i | −1.19148 | − | 0.687900i | ||||
\(189\) | −0.680125 | + | 2.55684i | −0.0494718 | + | 0.185983i | ||||
\(190\) | − | 1.60921i | − | 0.116744i | ||||||
\(191\) | −4.75437 | − | 8.23481i | −0.344014 | − | 0.595850i | 0.641160 | − | 0.767407i | \(-0.278454\pi\) |
−0.985174 | + | 0.171557i | \(0.945120\pi\) | |||||||
\(192\) | 0.703031 | − | 1.21769i | 0.0507369 | − | 0.0878789i | ||||
\(193\) | −2.69504 | − | 1.55598i | −0.193993 | − | 0.112002i | 0.399857 | − | 0.916577i | \(-0.369060\pi\) |
−0.593851 | + | 0.804575i | \(0.702393\pi\) | |||||||
\(194\) | −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 | −0.334467 | − | 0.942407i | \(-0.608556\pi\) |
0.648915 | + | 0.760861i | \(0.275223\pi\) | |||||||
\(198\) | −1.21597 | −0.0864150 | ||||||||
\(199\) | 13.9107 | 0.986105 | 0.493053 | − | 0.869999i | \(-0.335881\pi\) | ||||
0.493053 | + | 0.869999i | \(0.335881\pi\) | |||||||
\(200\) | 8.46891 | − | 4.88953i | 0.598842 | − | 0.345742i | ||||
\(201\) | −1.71581 | + | 0.990626i | −0.121024 | + | 0.0698734i | ||||
\(202\) | 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 | ||||
\(205\) | −5.53922 | −0.386876 | ||||||||
\(206\) | −8.57883 | − | 4.95299i | −0.597716 | − | 0.345091i | ||||
\(207\) | −3.39752 | − | 5.88468i | −0.236144 | − | 0.409014i | ||||
\(208\) | 7.29367 | + | 3.21528i | 0.505725 | + | 0.222939i | ||||
\(209\) | 11.9665 | 0.827738 | ||||||||
\(210\) | 0.744540 | − | 0.200950i | 0.0513781 | − | 0.0138669i | ||||
\(211\) | −6.30791 | − | 10.9256i | −0.434255 | − | 0.752151i | 0.562980 | − | 0.826471i | \(-0.309655\pi\) |
−0.997234 | + | 0.0743195i | \(0.976322\pi\) | |||||||
\(212\) | 1.76345 | + | 3.05439i | 0.121115 | + | 0.209777i | ||||
\(213\) | −8.61474 | + | 4.97372i | −0.590272 | + | 0.340794i | ||||
\(214\) | 10.9171i | 0.746275i | ||||||||
\(215\) | −1.90736 | + | 1.10122i | −0.130081 | + | 0.0751023i | ||||
\(216\) | − | 2.06743i | − | 0.140671i | ||||||
\(217\) | −4.10750 | − | 15.2187i | −0.278835 | − | 1.03311i | ||||
\(218\) | −4.58010 | − | 7.93296i | −0.310203 | − | 0.537288i | ||||
\(219\) | 2.85313i | 0.192796i | ||||||||
\(220\) | −0.948964 | − | 1.64365i | −0.0639791 | − | 0.110815i | ||||
\(221\) | −16.3674 | − | 7.21526i | −1.10099 | − | 0.485351i | ||||
\(222\) | −1.64012 | + | 2.84077i | −0.110078 | + | 0.190660i | ||||
\(223\) | 0.659526 | − | 0.380777i | 0.0441651 | − | 0.0254987i | −0.477755 | − | 0.878493i | \(-0.658549\pi\) |
0.521920 | + | 0.852994i | \(0.325216\pi\) | |||||||
\(224\) | 13.7432 | + | 3.65573i | 0.918259 | + | 0.244259i | ||||
\(225\) | −2.36502 | + | 4.09634i | −0.157668 | + | 0.273089i | ||||
\(226\) | 6.02437 | + | 3.47817i | 0.400735 | + | 0.231365i | ||||
\(227\) | 1.54056i | 0.102250i | 0.998692 | + | 0.0511252i | \(0.0162808\pi\) | ||||
−0.998692 | + | 0.0511252i | \(0.983719\pi\) | |||||||
\(228\) | 9.30418i | 0.616184i | ||||||||
\(229\) | −4.86535 | − | 2.80901i | −0.321512 | − | 0.185625i | 0.330555 | − | 0.943787i | \(-0.392764\pi\) |
−0.652066 | + | 0.758162i | \(0.726098\pi\) | |||||||
\(230\) | −0.990307 | + | 1.71526i | −0.0652989 | + | 0.113101i | ||||
\(231\) | 1.49431 | + | 5.53658i | 0.0983185 | + | 0.364280i | ||||
\(232\) | −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 | \(0.976794\pi\) | |||||||
\(234\) | 2.01083 | − | 0.218824i | 0.131452 | − | 0.0143050i | ||||
\(235\) | −2.90789 | − | 5.03662i | −0.189690 | − | 0.328553i | ||||
\(236\) | − | 5.13726i | − | 0.334407i | ||||||
\(237\) | −2.48141 | − | 4.29793i | −0.161185 | − | 0.279181i | ||||
\(238\) | −7.11599 | − | 1.89287i | −0.461261 | − | 0.122696i | ||||
\(239\) | − | 25.6658i | − | 1.66018i | −0.557628 | − | 0.830091i | \(-0.688289\pi\) | ||
0.557628 | − | 0.830091i | \(-0.311711\pi\) | |||||||
\(240\) | 0.994750 | − | 0.574319i | 0.0642109 | − | 0.0370722i | ||||
\(241\) | 4.71718i | 0.303861i | 0.988391 | + | 0.151930i | \(0.0485489\pi\) | ||||
−0.988391 | + | 0.151930i | \(0.951451\pi\) | |||||||
\(242\) | 3.06171 | − | 1.76768i | 0.196814 | − | 0.113631i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.26573 | − | 9.12050i | −0.337104 | − | 0.583880i | ||||
\(245\) | −1.82994 | − | 3.14311i | −0.116911 | − | 0.200806i | ||||
\(246\) | −5.98086 | −0.381325 | ||||||||
\(247\) | −19.7889 | + | 2.15347i | −1.25913 | + | 0.137022i | ||||
\(248\) | 6.15884 | + | 10.6674i | 0.391087 | + | 0.677382i | ||||
\(249\) | 3.16899 | + | 1.82961i | 0.200826 | + | 0.115947i | ||||
\(250\) | 2.83610 | 0.179371 | ||||||||
\(251\) | −0.0982527 | + | 0.170179i | −0.00620165 | + | 0.0107416i | −0.869110 | − | 0.494620i | \(-0.835307\pi\) |
0.862908 | + | 0.505361i | \(0.168641\pi\) | |||||||
\(252\) | −4.30480 | + | 1.16186i | −0.271177 | + | 0.0731902i | ||||
\(253\) | −12.7551 | − | 7.36416i | −0.801906 | − | 0.462981i | ||||
\(254\) | −9.87956 | + | 5.70397i | −0.619899 | + | 0.357899i | ||||
\(255\) | −2.23228 | + | 1.28880i | −0.139791 | + | 0.0807081i | ||||
\(256\) | −3.66121 | −0.228826 | ||||||||
\(257\) | −1.50601 | −0.0939422 | −0.0469711 | − | 0.998896i | \(-0.514957\pi\) | ||||
−0.0469711 | + | 0.998896i | \(0.514957\pi\) | |||||||
\(258\) | −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 | ||||
\(262\) | 6.69435 | + | 3.86498i | 0.413578 | + | 0.238779i | ||||
\(263\) | −3.44299 | + | 5.96344i | −0.212304 | + | 0.367721i | −0.952435 | − | 0.304741i | \(-0.901430\pi\) |
0.740131 | + | 0.672463i | \(0.234763\pi\) | |||||||
\(264\) | −2.24059 | − | 3.88082i | −0.137899 | − | 0.238848i | ||||
\(265\) | 1.08735i | 0.0667952i | ||||||||
\(266\) | −7.91129 | + | 2.13524i | −0.485072 | + | 0.130920i | ||||
\(267\) | 2.19138 | + | 1.26519i | 0.134110 | + | 0.0774285i | ||||
\(268\) | −2.89163 | − | 1.66948i | −0.176634 | − | 0.101980i | ||||
\(269\) | −11.8710 | −0.723785 | −0.361893 | − | 0.932220i | \(-0.617869\pi\) | ||||
−0.361893 | + | 0.932220i | \(0.617869\pi\) | |||||||
\(270\) | 0.145740 | − | 0.252428i | 0.00886943 | − | 0.0153623i | ||||
\(271\) | 13.7433i | 0.834843i | 0.908713 | + | 0.417422i | \(0.137066\pi\) | ||||
−0.908713 | + | 0.417422i | \(0.862934\pi\) | |||||||
\(272\) | −10.9675 | −0.665003 | ||||||||
\(273\) | −3.46749 | − | 8.88687i | −0.209862 | − | 0.537858i | ||||
\(274\) | 0.909537 | 0.0549472 | ||||||||
\(275\) | 10.2524i | 0.618244i | ||||||||
\(276\) | 5.72578 | − | 9.91734i | 0.344652 | − | 0.596954i | ||||
\(277\) | 11.2160 | 0.673905 | 0.336952 | − | 0.941522i | \(-0.390604\pi\) | ||||
0.336952 | + | 0.941522i | \(0.390604\pi\) | |||||||
\(278\) | 3.56484 | + | 2.05816i | 0.213805 | + | 0.123440i | ||||
\(279\) | −5.15974 | − | 2.97898i | −0.308906 | − | 0.178347i | ||||
\(280\) | 2.01326 | + | 2.00596i | 0.120315 | + | 0.119879i | ||||
\(281\) | 1.81616i | 0.108343i | 0.998532 | + | 0.0541714i | \(0.0172517\pi\) | ||||
−0.998532 | + | 0.0541714i | \(0.982748\pi\) | |||||||
\(282\) | −3.13974 | − | 5.43818i | −0.186969 | − | 0.323839i | ||||
\(283\) | −15.4189 | + | 26.7063i | −0.916556 | + | 1.58752i | −0.111950 | + | 0.993714i | \(0.535710\pi\) |
−0.804606 | + | 0.593809i | \(0.797624\pi\) | |||||||
\(284\) | −14.5183 | − | 8.38212i | −0.861500 | − | 0.497387i | ||||
\(285\) | −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 | ||||
\(289\) | 7.61170 | 0.447747 | ||||||||
\(290\) | −2.22315 | −0.130548 | ||||||||
\(291\) | 8.01957 | − | 4.63010i | 0.470116 | − | 0.271421i | ||||
\(292\) | −4.16413 | + | 2.40416i | −0.243687 | + | 0.140693i | ||||
\(293\) | −0.948761 | − | 0.547767i | −0.0554272 | − | 0.0320009i | 0.472030 | − | 0.881582i | \(-0.343521\pi\) |
−0.527458 | + | 0.849581i | \(0.676855\pi\) | |||||||
\(294\) | −1.97584 | − | 3.39371i | −0.115233 | − | 0.197925i | ||||
\(295\) | 0.791910 | − | 1.37163i | 0.0461068 | − | 0.0798593i | ||||
\(296\) | −12.0886 | −0.702636 | ||||||||
\(297\) | 1.87712 | + | 1.08375i | 0.108921 | + | 0.0628858i | ||||
\(298\) | −0.301506 | − | 0.522223i | −0.0174658 | − | 0.0302516i | ||||
\(299\) | 22.4182 | + | 9.88265i | 1.29648 | + | 0.571528i | ||||
\(300\) | −7.97146 | −0.460232 | ||||||||
\(301\) | 7.94471 | + | 7.91588i | 0.457925 | + | 0.456264i | ||||
\(302\) | 3.52096 | + | 6.09848i | 0.202609 | + | 0.350928i | ||||
\(303\) | −4.52199 | − | 7.83231i | −0.259781 | − | 0.449955i | ||||
\(304\) | −10.5700 | + | 6.10257i | −0.606229 | + | 0.350006i | ||||
\(305\) | − | 3.24685i | − | 0.185914i | ||||||
\(306\) | −2.41025 | + | 1.39156i | −0.137785 | + | 0.0795502i | ||||
\(307\) | 4.90247i | 0.279799i | 0.990166 | + | 0.139899i | \(0.0446779\pi\) | ||||
−0.990166 | + | 0.139899i | \(0.955322\pi\) | |||||||
\(308\) | −6.82145 | + | 6.84629i | −0.388688 | + | 0.390104i | ||||
\(309\) | 8.82890 | + | 15.2921i | 0.502258 | + | 0.869937i | ||||
\(310\) | 1.73662i | 0.0986334i | ||||||||
\(311\) | −5.78751 | − | 10.0243i | −0.328179 | − | 0.568423i | 0.653971 | − | 0.756519i | \(-0.273102\pi\) |
−0.982151 | + | 0.188096i | \(0.939768\pi\) | |||||||
\(312\) | 4.40363 | + | 6.01446i | 0.249307 | + | 0.340502i | ||||
\(313\) | 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 | ||||
\(315\) | −1.32846 | − | 0.353374i | −0.0748505 | − | 0.0199104i | ||||
\(316\) | 4.18188 | − | 7.24322i | 0.235249 | − | 0.407463i | ||||
\(317\) | 14.8929 | + | 8.59841i | 0.836468 | + | 0.482935i | 0.856062 | − | 0.516873i | \(-0.172904\pi\) |
−0.0195943 | + | 0.999808i | \(0.506237\pi\) | |||||||
\(318\) | 1.17404i | 0.0658369i | ||||||||
\(319\) | − | 16.5319i | − | 0.925607i | ||||||
\(320\) | 0.632676 | + | 0.365276i | 0.0353677 | + | 0.0204195i | ||||
\(321\) | 9.73005 | − | 16.8529i | 0.543078 | − | 0.940639i | ||||
\(322\) | 9.74668 | + | 2.59264i | 0.543161 | + | 0.144482i | ||||
\(323\) | 23.7196 | − | 13.6945i | 1.31979 | − | 0.761983i | ||||
\(324\) | −0.842641 | + | 1.45950i | −0.0468134 | + | 0.0810831i | ||||
\(325\) | −1.84501 | − | 16.9543i | −0.102343 | − | 0.940457i | ||||
\(326\) | 2.91645 | + | 5.05143i | 0.161527 | + | 0.279773i | ||||
\(327\) | 16.3284i | 0.902963i | ||||||||
\(328\) | −11.0206 | − | 19.0882i | −0.608509 | − | 1.05397i | ||||
\(329\) | −20.9028 | + | 20.9790i | −1.15241 | + | 1.15661i | ||||
\(330\) | − | 0.631783i | − | 0.0347785i | ||||||
\(331\) | 17.6853 | − | 10.2106i | 0.972075 | − | 0.561228i | 0.0722066 | − | 0.997390i | \(-0.476996\pi\) |
0.899868 | + | 0.436162i | \(0.143663\pi\) | |||||||
\(332\) | 6.16683i | 0.338449i | ||||||||
\(333\) | 5.06378 | − | 2.92358i | 0.277494 | − | 0.160211i | ||||
\(334\) | 6.77275 | + | 11.7307i | 0.370588 | + | 0.641878i | ||||
\(335\) | −0.514702 | − | 0.891491i | −0.0281212 | − | 0.0487073i | ||||
\(336\) | −4.14342 | − | 4.12839i | −0.226042 | − | 0.225222i | ||||
\(337\) | −13.1872 | −0.718353 | −0.359176 | − | 0.933270i | \(-0.616942\pi\) | ||||
−0.359176 | + | 0.933270i | \(0.616942\pi\) | |||||||
\(338\) | −5.38371 | + | 4.91967i | −0.292835 | + | 0.267595i | ||||
\(339\) | −6.19998 | − | 10.7387i | −0.336736 | − | 0.583245i | ||||
\(340\) | −3.76201 | − | 2.17200i | −0.204024 | − | 0.117793i | ||||
\(341\) | −12.9139 | −0.699328 | ||||||||
\(342\) | −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 | ||||
\(345\) | 3.05752 | − | 1.76526i | 0.164611 | − | 0.0950384i | ||||
\(346\) | 1.81634 | − | 1.04867i | 0.0976473 | − | 0.0563767i | ||||
\(347\) | −8.68752 | −0.466371 | −0.233185 | − | 0.972432i | \(-0.574915\pi\) | ||||
−0.233185 | + | 0.972432i | \(0.574915\pi\) | |||||||
\(348\) | 12.8539 | 0.689039 | ||||||||
\(349\) | 30.2239 | − | 17.4498i | 1.61785 | − | 0.934064i | 0.630370 | − | 0.776294i | \(-0.282903\pi\) |
0.987476 | − | 0.157770i | \(-0.0504303\pi\) | |||||||
\(350\) | −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 | ||||
\(353\) | −12.5698 | − | 7.25715i | −0.669021 | − | 0.386259i | 0.126685 | − | 0.991943i | \(-0.459566\pi\) |
−0.795706 | + | 0.605684i | \(0.792900\pi\) | |||||||
\(354\) | 0.855048 | − | 1.48099i | 0.0454453 | − | 0.0787136i | ||||
\(355\) | −2.58421 | − | 4.47598i | −0.137156 | − | 0.237561i | ||||
\(356\) | 4.26441i | 0.226013i | ||||||||
\(357\) | 9.29807 | + | 9.26433i | 0.492106 | + | 0.490320i | ||||
\(358\) | 2.75864 | + | 1.59270i | 0.145798 | + | 0.0841768i | ||||
\(359\) | 0.460772 | + | 0.266027i | 0.0243186 | + | 0.0140404i | 0.512110 | − | 0.858920i | \(-0.328864\pi\) |
−0.487791 | + | 0.872960i | \(0.662197\pi\) | |||||||
\(360\) | 1.07418 | 0.0566144 | ||||||||
\(361\) | 5.73986 | − | 9.94173i | 0.302098 | − | 0.523249i | ||||
\(362\) | − | 5.58138i | − | 0.293351i | ||||||
\(363\) | −6.30191 | −0.330764 | ||||||||
\(364\) | 10.0485 | − | 12.5492i | 0.526685 | − | 0.657758i | ||||
\(365\) | −1.48241 | −0.0775927 | ||||||||
\(366\) | − | 3.50572i | − | 0.183247i | ||||||
\(367\) | −2.92633 | + | 5.06855i | −0.152753 | + | 0.264576i | −0.932239 | − | 0.361844i | \(-0.882147\pi\) |
0.779485 | + | 0.626420i | \(0.215481\pi\) | |||||||
\(368\) | 15.0221 | 0.783079 | ||||||||
\(369\) | 9.23279 | + | 5.33055i | 0.480640 | + | 0.277497i | ||||
\(370\) | −1.47599 | − | 0.852161i | −0.0767329 | − | 0.0443018i | ||||
\(371\) | 5.34567 | − | 1.44279i | 0.277533 | − | 0.0749058i | ||||
\(372\) | − | 10.0408i | − | 0.520593i | ||||||
\(373\) | −12.1259 | − | 21.0026i | −0.627853 | − | 1.08747i | −0.987982 | − | 0.154571i | \(-0.950600\pi\) |
0.360128 | − | 0.932903i | \(-0.382733\pi\) | |||||||
\(374\) | −3.01622 | + | 5.22424i | −0.155965 | + | 0.270139i | ||||
\(375\) | −4.37816 | − | 2.52773i | −0.226087 | − | 0.130532i | ||||
\(376\) | 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 | −0.530486 | − | 0.847694i | \(-0.677991\pi\) |
0.468881 | + | 0.883261i | \(0.344657\pi\) | |||||||
\(380\) | −4.83420 | −0.247989 | ||||||||
\(381\) | 20.3351 | 1.04180 | ||||||||
\(382\) | 4.61971 | − | 2.66719i | 0.236365 | − | 0.136465i | ||||
\(383\) | 17.0939 | − | 9.86915i | 0.873456 | − | 0.504290i | 0.00496051 | − | 0.999988i | \(-0.498421\pi\) |
0.868495 | + | 0.495698i | \(0.165088\pi\) | |||||||
\(384\) | 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 | ||||
\(387\) | 4.23893 | 0.215477 | ||||||||
\(388\) | 13.5152 | + | 7.80303i | 0.686132 | + | 0.396139i | ||||
\(389\) | 2.48623 | + | 4.30628i | 0.126057 | + | 0.218337i | 0.922146 | − | 0.386843i | \(-0.126434\pi\) |
−0.796089 | + | 0.605180i | \(0.793101\pi\) | |||||||
\(390\) | 0.113695 | + | 1.04477i | 0.00575718 | + | 0.0529042i | ||||
\(391\) | −33.7103 | −1.70480 | ||||||||
\(392\) | 7.19041 | − | 12.5594i | 0.363171 | − | 0.634344i | ||||
\(393\) | −6.88948 | − | 11.9329i | −0.347528 | − | 0.601937i | ||||
\(394\) | 1.42950 | + | 2.47596i | 0.0720170 | + | 0.124737i | ||||
\(395\) | 2.23309 | − | 1.28927i | 0.112359 | − | 0.0648704i | ||||
\(396\) | 3.65286i | 0.183563i | ||||||||
\(397\) | 8.50970 | − | 4.91308i | 0.427090 | − | 0.246580i | −0.271016 | − | 0.962575i | \(-0.587360\pi\) |
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(398\) | 7.80389i | 0.391173i | ||||||||
\(399\) | 14.1159 | + | 3.75486i | 0.706680 | + | 0.187978i | ||||
\(400\) | −5.22844 | − | 9.05593i | −0.261422 | − | 0.452796i | ||||
\(401\) | 29.2596i | 1.46115i | 0.682830 | + | 0.730577i | \(0.260749\pi\) | ||||
−0.682830 | + | 0.730577i | \(0.739251\pi\) | |||||||
\(402\) | −0.555739 | − | 0.962568i | −0.0277177 | − | 0.0480085i | ||||
\(403\) | 21.3556 | − | 2.32398i | 1.06380 | − | 0.115765i | ||||
\(404\) | 7.62082 | − | 13.1997i | 0.379150 | − | 0.656707i | ||||
\(405\) | −0.449963 | + | 0.259786i | −0.0223589 | + | 0.0129089i | ||||
\(406\) | 2.94987 | + | 10.9296i | 0.146400 | + | 0.542425i | ||||
\(407\) | 6.33688 | − | 10.9758i | 0.314107 | − | 0.544050i | ||||
\(408\) | −8.88246 | − | 5.12829i | −0.439747 | − | 0.253888i | ||||
\(409\) | 12.8399i | 0.634892i | 0.948276 | + | 0.317446i | \(0.102825\pi\) | ||||
−0.948276 | + | 0.317446i | \(0.897175\pi\) | |||||||
\(410\) | − | 3.10749i | − | 0.153468i | ||||||
\(411\) | −1.40407 | − | 0.810643i | −0.0692579 | − | 0.0399861i | ||||
\(412\) | −14.8792 | + | 25.7715i | −0.733045 | + | 1.26967i | ||||
\(413\) | −7.79405 | − | 2.07323i | −0.383520 | − | 0.102017i | ||||
\(414\) | 3.30129 | − | 1.90600i | 0.162250 | − | 0.0936749i | ||||
\(415\) | −0.950618 | + | 1.64652i | −0.0466640 | + | 0.0808244i | ||||
\(416\) | −7.81748 | + | 17.7335i | −0.383283 | + | 0.869457i | ||||
\(417\) | −3.66875 | − | 6.35446i | −0.179660 | − | 0.311179i | ||||
\(418\) | 6.71317i | 0.328352i | ||||||||
\(419\) | 13.1853 | + | 22.8376i | 0.644144 | + | 1.11569i | 0.984498 | + | 0.175393i | \(0.0561197\pi\) |
−0.340354 | + | 0.940297i | \(0.610547\pi\) | |||||||
\(420\) | −0.603670 | − | 2.23666i | −0.0294561 | − | 0.109138i | ||||
\(421\) | 2.71377i | 0.132261i | 0.997811 | + | 0.0661306i | \(0.0210654\pi\) | ||||
−0.997811 | + | 0.0661306i | \(0.978935\pi\) | |||||||
\(422\) | 6.12925 | − | 3.53873i | 0.298367 | − | 0.172262i | ||||
\(423\) | 11.1934i | 0.544242i | ||||||||
\(424\) | −3.74700 | + | 2.16333i | −0.181971 | + | 0.105061i | ||||
\(425\) | 11.7329 | + | 20.3220i | 0.569130 | + | 0.985762i | ||||
\(426\) | −2.79025 | − | 4.83285i | −0.135188 | − | 0.234152i | ||||
\(427\) | −15.9623 | + | 4.30821i | −0.772471 | + | 0.208489i | ||||
\(428\) | 32.7957 | 1.58524 | ||||||||
\(429\) | −7.76919 | + | 0.845464i | −0.375100 | + | 0.0408194i | ||||
\(430\) | −0.617779 | − | 1.07003i | −0.0297920 | − | 0.0516012i | ||||
\(431\) | −32.1180 | − | 18.5433i | −1.54707 | − | 0.893200i | −0.998364 | − | 0.0571837i | \(-0.981788\pi\) |
−0.548704 | − | 0.836016i | \(-0.684879\pi\) | |||||||
\(432\) | −2.21074 | −0.106364 | ||||||||
\(433\) | 7.21536 | − | 12.4974i | 0.346748 | − | 0.600585i | −0.638922 | − | 0.769272i | \(-0.720619\pi\) |
0.985670 | + | 0.168686i | \(0.0539525\pi\) | |||||||
\(434\) | 8.53766 | − | 2.30430i | 0.409821 | − | 0.110610i | ||||
\(435\) | 3.43193 | + | 1.98142i | 0.164548 | + | 0.0950020i | ||||
\(436\) | −23.8312 | + | 13.7590i | −1.14131 | + | 0.658936i | ||||
\(437\) | −32.4884 | + | 18.7572i | −1.55413 | + | 0.897278i | ||||
\(438\) | −1.60060 | −0.0764795 | ||||||||
\(439\) | 14.6300 | 0.698254 | 0.349127 | − | 0.937075i | \(-0.386478\pi\) | ||||
0.349127 | + | 0.937075i | \(0.386478\pi\) | |||||||
\(440\) | 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 | \(-0.169003\pi\) | |||||||
\(444\) | 8.53390 | + | 4.92705i | 0.405001 | + | 0.233827i | ||||
\(445\) | −0.657359 | + | 1.13858i | −0.0311618 | + | 0.0539738i | ||||
\(446\) | 0.213615 | + | 0.369993i | 0.0101150 | + | 0.0175197i | ||||
\(447\) | 1.07489i | 0.0508406i | ||||||||
\(448\) | 0.956298 | − | 3.59508i | 0.0451808 | − | 0.169851i | ||||
\(449\) | −5.59341 | − | 3.22935i | −0.263969 | − | 0.152403i | 0.362175 | − | 0.932110i | \(-0.382034\pi\) |
−0.626144 | + | 0.779708i | \(0.715368\pi\) | |||||||
\(450\) | −2.29804 | − | 1.32677i | −0.108330 | − | 0.0625446i | ||||
\(451\) | 23.1080 | 1.08811 | ||||||||
\(452\) | 10.4487 | − | 18.0977i | 0.491466 | − | 0.851244i | ||||
\(453\) | − | 12.5525i | − | 0.589768i | ||||||
\(454\) | −0.864250 | −0.0405613 | ||||||||
\(455\) | 4.61738 | − | 1.80161i | 0.216466 | − | 0.0844609i | ||||
\(456\) | −11.4140 | −0.534509 | ||||||||
\(457\) | − | 19.1940i | − | 0.897855i | −0.893568 | − | 0.448928i | \(-0.851806\pi\) | ||
0.893568 | − | 0.448928i | \(-0.148194\pi\) | |||||||
\(458\) | 1.57585 | − | 2.72945i | 0.0736346 | − | 0.127539i | ||||
\(459\) | 4.96102 | 0.231560 | ||||||||
\(460\) | 5.15278 | + | 2.97496i | 0.240250 | + | 0.138708i | ||||
\(461\) | −5.50203 | − | 3.17660i | −0.256255 | − | 0.147949i | 0.366370 | − | 0.930469i | \(-0.380600\pi\) |
−0.622625 | + | 0.782520i | \(0.713934\pi\) | |||||||
\(462\) | −3.10601 | + | 0.838306i | −0.144504 | + | 0.0390015i | ||||
\(463\) | − | 10.8299i | − | 0.503307i | −0.967817 | − | 0.251653i | \(-0.919026\pi\) | ||
0.967817 | − | 0.251653i | \(-0.0809743\pi\) | |||||||
\(464\) | 8.43079 | + | 14.6026i | 0.391390 | + | 0.677907i | ||||
\(465\) | 1.54780 | − | 2.68086i | 0.0717773 | − | 0.124322i | ||||
\(466\) | −8.33191 | − | 4.81043i | −0.385968 | − | 0.222839i | ||||
\(467\) | 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 | ||||
\(471\) | 0.692215 | 0.0318956 | ||||||||
\(472\) | 6.30219 | 0.290082 | ||||||||
\(473\) | 7.95696 | − | 4.59395i | 0.365862 | − | 0.211230i | ||||
\(474\) | 2.41113 | − | 1.39207i | 0.110747 | − | 0.0639397i | ||||
\(475\) | 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 | ||||
\(478\) | 14.3984 | 0.658570 | ||||||||
\(479\) | 20.8050 | + | 12.0118i | 0.950606 | + | 0.548833i | 0.893269 | − | 0.449522i | \(-0.148406\pi\) |
0.0573371 | + | 0.998355i | \(0.481739\pi\) | |||||||
\(480\) | 1.39637 | + | 2.41859i | 0.0637355 | + | 0.110393i | ||||
\(481\) | −8.50405 | + | 19.2909i | −0.387751 | + | 0.879592i | ||||
\(482\) | −2.64633 | −0.120537 | ||||||||
\(483\) | −12.7354 | − | 12.6892i | −0.579483 | − | 0.577380i | ||||
\(484\) | −5.31024 | − | 9.19761i | −0.241375 | − | 0.418073i | ||||
\(485\) | 2.40568 | + | 4.16675i | 0.109236 | + | 0.189202i | ||||
\(486\) | −0.485838 | + | 0.280499i | −0.0220381 | + | 0.0127237i | ||||
\(487\) | 6.04028i | 0.273711i | 0.990591 | + | 0.136856i | \(0.0436996\pi\) | ||||
−0.990591 | + | 0.136856i | \(0.956300\pi\) | |||||||
\(488\) | 11.1887 | − | 6.45978i | 0.506487 | − | 0.292420i | ||||
\(489\) | − | 10.3974i | − | 0.470185i | ||||||
\(490\) | 1.76328 | − | 1.02659i | 0.0796568 | − | 0.0463768i | ||||
\(491\) | −7.05626 | − | 12.2218i | −0.318444 | − | 0.551562i | 0.661719 | − | 0.749752i | \(-0.269827\pi\) |
−0.980164 | + | 0.198190i | \(0.936494\pi\) | |||||||
\(492\) | 17.9670i | 0.810013i | ||||||||
\(493\) | −18.9192 | − | 32.7690i | −0.852076 | − | 1.47584i | ||||
\(494\) | −1.20809 | − | 11.1015i | −0.0543547 | − | 0.499480i | ||||
\(495\) | −0.563089 | + | 0.975299i | −0.0253090 | + | 0.0438364i | ||||
\(496\) | 11.4068 | − | 6.58574i | 0.512182 | − | 0.295708i | ||||
\(497\) | −18.5761 | + | 18.6438i | −0.833252 | + | 0.836287i | ||||
\(498\) | −1.02641 | + | 1.77779i | −0.0459945 | + | 0.0796648i | ||||
\(499\) | −28.4481 | − | 16.4245i | −1.27351 | − | 0.735263i | −0.297865 | − | 0.954608i | \(-0.596274\pi\) |
−0.975647 | + | 0.219345i | \(0.929608\pi\) | |||||||
\(500\) | − | 8.51988i | − | 0.381021i | ||||||
\(501\) | − | 24.1454i | − | 1.07874i | ||||||
\(502\) | −0.0954698 | − | 0.0551195i | −0.00426103 | − | 0.00246010i | ||||
\(503\) | −19.5590 | + | 33.8772i | −0.872093 | + | 1.51051i | −0.0122649 | + | 0.999925i | \(0.503904\pi\) |
−0.859828 | + | 0.510584i | \(0.829429\pi\) | |||||||
\(504\) | −1.42532 | − | 5.28095i | −0.0634888 | − | 0.235232i | ||||
\(505\) | 4.06946 | − | 2.34950i | 0.181088 | − | 0.104551i | ||||
\(506\) | 4.13127 | − | 7.15558i | 0.183658 | − | 0.318104i | ||||
\(507\) | 12.6957 | − | 2.79627i | 0.563836 | − | 0.124187i | ||||
\(508\) | 17.1352 | + | 29.6790i | 0.760250 | + | 1.31679i | ||||
\(509\) | − | 1.10833i | − | 0.0491260i | −0.999698 | − | 0.0245630i | \(-0.992181\pi\) | ||
0.999698 | − | 0.0245630i | \(-0.00781944\pi\) | |||||||
\(510\) | −0.723017 | − | 1.25230i | −0.0320157 | − | 0.0554528i | ||||
\(511\) | 1.96699 | + | 7.28789i | 0.0870144 | + | 0.322397i | ||||
\(512\) | 21.0240i | 0.929139i | ||||||||
\(513\) | 4.78119 | − | 2.76042i | 0.211095 | − | 0.121876i | ||||
\(514\) | − | 0.844867i | − | 0.0372655i | ||||||
\(515\) | −7.94536 | + | 4.58726i | −0.350114 | + | 0.202139i | ||||
\(516\) | 3.57189 | + | 6.18670i | 0.157244 | + | 0.272354i | ||||
\(517\) | 12.1309 | + | 21.0113i | 0.533516 | + | 0.924077i | ||||
\(518\) | −2.23097 | + | 8.38705i | −0.0980232 | + | 0.368506i | ||||
\(519\) | −3.73858 | −0.164105 | ||||||||
\(520\) | −3.12495 | + | 2.28801i | −0.137038 | + | 0.100336i | ||||
\(521\) | 6.87363 | + | 11.9055i | 0.301139 | + | 0.521589i | 0.976394 | − | 0.215996i | \(-0.0692997\pi\) |
−0.675255 | + | 0.737584i | \(0.735966\pi\) | |||||||
\(522\) | 3.70555 | + | 2.13940i | 0.162188 | + | 0.0936391i | ||||
\(523\) | −2.41355 | −0.105537 | −0.0527686 | − | 0.998607i | \(-0.516805\pi\) | ||||
−0.0527686 | + | 0.998607i | \(0.516805\pi\) | |||||||
\(524\) | 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 | ||||
\(527\) | −25.5976 | + | 14.7788i | −1.11505 | + | 0.643773i | ||||
\(528\) | −4.14981 | + | 2.39590i | −0.180597 | + | 0.104268i | ||||
\(529\) | 23.1726 | 1.00751 | ||||||||
\(530\) | −0.609999 | −0.0264967 | ||||||||
\(531\) | −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 | ||||
\(535\) | 8.75633 | + | 5.05547i | 0.378569 | + | 0.218567i | ||||
\(536\) | 2.04805 | − | 3.54733i | 0.0884625 | − | 0.153222i | ||||
\(537\) | −2.83905 | − | 4.91738i | −0.122514 | − | 0.212200i | ||||
\(538\) | − | 6.65958i | − | 0.287115i | ||||||
\(539\) | 7.63400 | + | 13.1122i | 0.328819 | + | 0.564780i | ||||
\(540\) | −0.758315 | − | 0.437813i | −0.0326327 | − | 0.0188405i | ||||
\(541\) | 7.81869 | + | 4.51412i | 0.336152 | + | 0.194077i | 0.658569 | − | 0.752520i | \(-0.271162\pi\) |
−0.322417 | + | 0.946598i | \(0.604495\pi\) | |||||||
\(542\) | −7.70993 | −0.331170 | ||||||||
\(543\) | −4.97451 | + | 8.61611i | −0.213477 | + | 0.369753i | ||||
\(544\) | − | 26.6659i | − | 1.14329i | ||||||
\(545\) | −8.48379 | −0.363406 | ||||||||
\(546\) | 4.98552 | − | 1.94525i | 0.213360 | − | 0.0832491i | ||||
\(547\) | −24.3206 | −1.03987 | −0.519936 | − | 0.854205i | \(-0.674044\pi\) | ||||
−0.519936 | + | 0.854205i | \(0.674044\pi\) | |||||||
\(548\) | − | 2.73232i | − | 0.116719i | ||||||
\(549\) | −3.12454 | + | 5.41186i | −0.133352 | + | 0.230972i | ||||
\(550\) | −5.75158 | −0.245248 | ||||||||
\(551\) | −36.4668 | − | 21.0541i | −1.55354 | − | 0.896935i | ||||
\(552\) | 12.1662 | + | 7.02415i | 0.517827 | + | 0.298968i | ||||
\(553\) | −9.30145 | − | 9.26770i | −0.395538 | − | 0.394103i | ||||
\(554\) | 6.29216i | 0.267328i | ||||||||
\(555\) | 1.51901 | + | 2.63100i | 0.0644784 | + | 0.111680i | ||||
\(556\) | 6.18288 | − | 10.7091i | 0.262212 | − | 0.454165i | ||||
\(557\) | 23.8965 | + | 13.7966i | 1.01253 | + | 0.584582i | 0.911930 | − | 0.410345i | \(-0.134592\pi\) |
0.100596 | + | 0.994927i | \(0.467925\pi\) | |||||||
\(558\) | 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 | ||||
\(562\) | −1.01886 | −0.0429780 | ||||||||
\(563\) | −7.70429 | −0.324697 | −0.162349 | − | 0.986733i | \(-0.551907\pi\) | ||||
−0.162349 | + | 0.986733i | \(0.551907\pi\) | |||||||
\(564\) | −16.3367 | + | 9.43201i | −0.687900 | + | 0.397159i | ||||
\(565\) | 5.57952 | − | 3.22134i | 0.234732 | − | 0.135523i | ||||
\(566\) | −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 | ||||
\(569\) | −23.2480 | −0.974605 | −0.487302 | − | 0.873233i | \(-0.662019\pi\) | ||||
−0.487302 | + | 0.873233i | \(0.662019\pi\) | |||||||
\(570\) | −1.39362 | − | 0.804605i | −0.0583722 | − | 0.0337012i | ||||
\(571\) | −2.06269 | − | 3.57268i | −0.0863209 | − | 0.149512i | 0.819632 | − | 0.572890i | \(-0.194178\pi\) |
−0.905953 | + | 0.423378i | \(0.860844\pi\) | |||||||
\(572\) | −7.78059 | − | 10.6267i | −0.325323 | − | 0.444324i | ||||
\(573\) | −9.50875 | −0.397234 | ||||||||
\(574\) | −15.2772 | + | 4.12329i | −0.637658 | + | 0.172103i | ||||
\(575\) | −16.0704 | − | 27.8348i | −0.670183 | − | 1.16079i | ||||
\(576\) | −0.703031 | − | 1.21769i | −0.0292930 | − | 0.0507369i | ||||
\(577\) | −6.14307 | + | 3.54670i | −0.255739 | + | 0.147651i | −0.622389 | − | 0.782708i | \(-0.713838\pi\) |
0.366650 | + | 0.930359i | \(0.380505\pi\) | |||||||
\(578\) | 4.27015i | 0.177615i | ||||||||
\(579\) | −2.69504 | + | 1.55598i | −0.112002 | + | 0.0646644i | ||||
\(580\) | 6.67852i | 0.277310i | ||||||||
\(581\) | 9.35606 | + | 2.48873i | 0.388155 | + | 0.103250i | ||||
\(582\) | 2.59748 | + | 4.49896i | 0.107669 | + | 0.186488i | ||||
\(583\) | − | 4.53610i | − | 0.187866i | ||||||
\(584\) | −2.94933 | − | 5.10838i | −0.122044 | − | 0.211386i | ||||
\(585\) | 0.755662 | − | 1.71418i | 0.0312428 | − | 0.0708725i | ||||
\(586\) | 0.307296 | − | 0.532253i | 0.0126943 | − | 0.0219871i | ||||
\(587\) | −1.42269 | + | 0.821391i | −0.0587208 | + | 0.0339025i | −0.529073 | − | 0.848576i | \(-0.677460\pi\) |
0.470352 | + | 0.882479i | \(0.344127\pi\) | |||||||
\(588\) | −10.1950 | + | 5.93559i | −0.420433 | + | 0.244779i | ||||
\(589\) | −16.4465 | + | 28.4861i | −0.677665 | + | 1.17375i | ||||
\(590\) | 0.769480 | + | 0.444260i | 0.0316790 | + | 0.0182899i | ||||
\(591\) | − | 5.09626i | − | 0.209632i | ||||||
\(592\) | 12.9265i | 0.531277i | ||||||||
\(593\) | 37.1597 | + | 21.4542i | 1.52597 | + | 0.881016i | 0.999525 | + | 0.0308039i | \(0.00980675\pi\) |
0.526440 | + | 0.850212i | \(0.323527\pi\) | |||||||
\(594\) | −0.607984 | + | 1.05306i | −0.0249459 | + | 0.0432075i | ||||
\(595\) | −4.81349 | + | 4.83102i | −0.197334 | + | 0.198053i | ||||
\(596\) | −1.56880 | + | 0.905747i | −0.0642606 | + | 0.0371009i | ||||
\(597\) | 6.95536 | − | 12.0470i | 0.284664 | − | 0.493053i | ||||
\(598\) | −5.54414 | + | 12.5766i | −0.226717 | + | 0.514295i | ||||
\(599\) | 15.5990 | + | 27.0183i | 0.637358 | + | 1.10394i | 0.986010 | + | 0.166684i | \(0.0533060\pi\) |
−0.348653 | + | 0.937252i | \(0.613361\pi\) | |||||||
\(600\) | − | 9.77906i | − | 0.399228i | ||||||
\(601\) | −17.5568 | − | 30.4093i | −0.716157 | − | 1.24042i | −0.962511 | − | 0.271241i | \(-0.912566\pi\) |
0.246354 | − | 0.969180i | \(-0.420767\pi\) | |||||||
\(602\) | −4.44079 | + | 4.45696i | −0.180993 | + | 0.181652i | ||||
\(603\) | 1.98125i | 0.0806828i | ||||||||
\(604\) | 18.3203 | − | 10.5772i | 0.745444 | − | 0.430382i | ||||
\(605\) | − | 3.27430i | − | 0.133119i | ||||||
\(606\) | 4.39391 | − | 2.53683i | 0.178490 | − | 0.103051i | ||||
\(607\) | 1.15886 | + | 2.00720i | 0.0470365 | + | 0.0814696i | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(608\) | −14.8375 | − | 25.6993i | −0.601741 | − | 1.04225i | ||||
\(609\) | 5.18740 | − | 19.5014i | 0.210204 | − | 0.790235i | ||||
\(610\) | 1.82148 | 0.0737494 | ||||||||
\(611\) | −23.8419 | − | 32.5632i | −0.964541 | − | 1.31737i | ||||
\(612\) | 4.18036 | + | 7.24059i | 0.168981 | + | 0.292683i | ||||
\(613\) | −14.7745 | − | 8.53004i | −0.596735 | − | 0.344525i | 0.171021 | − | 0.985267i | \(-0.445293\pi\) |
−0.767756 | + | 0.640742i | \(0.778627\pi\) | |||||||
\(614\) | −2.75027 | −0.110992 | ||||||||
\(615\) | −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 | 0.0265537 | − | 0.999647i | \(-0.491547\pi\) |
−0.852443 | + | 0.522820i | \(0.824880\pi\) | |||||||
\(618\) | −8.57883 | + | 4.95299i | −0.345091 | + | 0.199239i | ||||
\(619\) | −13.5416 | + | 7.81825i | −0.544283 | + | 0.314242i | −0.746813 | − | 0.665034i | \(-0.768417\pi\) |
0.202530 | + | 0.979276i | \(0.435084\pi\) | |||||||
\(620\) | 5.21694 | 0.209517 | ||||||||
\(621\) | −6.79504 | −0.272676 | ||||||||
\(622\) | 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 | ||||
\(626\) | 2.46301 | + | 1.42202i | 0.0984416 | + | 0.0568353i | ||||
\(627\) | 5.98324 | − | 10.3633i | 0.238948 | − | 0.413869i | ||||
\(628\) | 0.583289 | + | 1.01029i | 0.0232758 | + | 0.0403148i | ||||
\(629\) | − | 29.0078i | − | 1.15662i | ||||||
\(630\) | 0.198242 | − | 0.745265i | 0.00789815 | − | 0.0296921i | ||||
\(631\) | −19.8241 | − | 11.4455i | −0.789186 | − | 0.455637i | 0.0504898 | − | 0.998725i | \(-0.483922\pi\) |
−0.839676 | + | 0.543088i | \(0.817255\pi\) | |||||||
\(632\) | 8.88569 | + | 5.13015i | 0.353454 | + | 0.204067i | ||||
\(633\) | −12.6158 | −0.501434 | ||||||||
\(634\) | −4.82369 | + | 8.35487i | −0.191573 | + | 0.331814i | ||||
\(635\) | 10.5656i | 0.419281i | ||||||||
\(636\) | 3.52691 | 0.139851 | ||||||||
\(637\) | −14.9839 | − | 20.3097i | −0.593685 | − | 0.804698i | ||||
\(638\) | 9.27434 | 0.367175 | ||||||||
\(639\) | 9.94745i | 0.393515i | ||||||||
\(640\) | −2.99767 | + | 5.19211i | −0.118493 | + | 0.205236i | ||||
\(641\) | −46.2048 | −1.82498 | −0.912490 | − | 0.409100i | \(-0.865843\pi\) | ||||
−0.912490 | + | 0.409100i | \(0.865843\pi\) | |||||||
\(642\) | 9.45446 | + | 5.45853i | 0.373138 | + | 0.215431i | ||||
\(643\) | 8.19662 | + | 4.73232i | 0.323243 | + | 0.186625i | 0.652837 | − | 0.757498i | \(-0.273579\pi\) |
−0.329594 | + | 0.944123i | \(0.606912\pi\) | |||||||
\(644\) | 7.78849 | − | 29.2798i | 0.306909 | − | 1.15379i | ||||
\(645\) | 2.20243i | 0.0867206i | ||||||||
\(646\) | 7.68259 | + | 13.3066i | 0.302267 | + | 0.523542i | ||||
\(647\) | −2.85296 | + | 4.94148i | −0.112162 | + | 0.194270i | −0.916642 | − | 0.399710i | \(-0.869111\pi\) |
0.804480 | + | 0.593980i | \(0.202444\pi\) | |||||||
\(648\) | −1.79045 | − | 1.03372i | −0.0703355 | − | 0.0406082i | ||||
\(649\) | −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 | ||||
\(653\) | 33.0133 | 1.29191 | 0.645956 | − | 0.763375i | \(-0.276459\pi\) | ||||
0.645956 | + | 0.763375i | \(0.276459\pi\) | |||||||
\(654\) | −9.16020 | −0.358192 | ||||||||
\(655\) | 6.20002 | − | 3.57959i | 0.242255 | − | 0.139866i | ||||
\(656\) | −20.4113 | + | 11.7845i | −0.796926 | + | 0.460106i | ||||
\(657\) | 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 | −0.998036 | − | 0.0626408i | \(-0.980048\pi\) |
0.553267 | + | 0.833004i | \(0.313381\pi\) | |||||||
\(660\) | −1.89793 | −0.0738767 | ||||||||
\(661\) | −1.58812 | − | 0.916900i | −0.0617706 | − | 0.0356633i | 0.468797 | − | 0.883306i | \(-0.344688\pi\) |
−0.530567 | + | 0.847643i | \(0.678021\pi\) | |||||||
\(662\) | 5.72815 | + | 9.92144i | 0.222631 | + | 0.385608i | ||||
\(663\) | −14.4323 | + | 10.5670i | −0.560504 | + | 0.410387i | ||||
\(664\) | −7.56522 | −0.293587 | ||||||||
\(665\) | −1.95092 | + | 7.33425i | −0.0756536 | + | 0.284410i | ||||
\(666\) | 1.64012 | + | 2.84077i | 0.0635533 | + | 0.110078i | ||||
\(667\) | 25.9133 | + | 44.8832i | 1.00337 | + | 1.73789i | ||||
\(668\) | 35.2401 | − | 20.3459i | 1.36348 | − | 0.787206i | ||||
\(669\) | − | 0.761555i | − | 0.0294434i | ||||||
\(670\) | 0.500124 | − | 0.288747i | 0.0193215 | − | 0.0111553i | ||||
\(671\) | 13.5449i | 0.522896i | ||||||||
\(672\) | 10.0376 | − | 10.0741i | 0.387208 | − | 0.388618i | ||||
\(673\) | 14.8231 | + | 25.6743i | 0.571387 | + | 0.989672i | 0.996424 | + | 0.0844955i | \(0.0269278\pi\) |
−0.425037 | + | 0.905176i | \(0.639739\pi\) | |||||||
\(674\) | − | 7.39799i | − | 0.284960i | ||||||
\(675\) | 2.36502 | + | 4.09634i | 0.0910297 | + | 0.157668i | ||||
\(676\) | 14.7791 | + | 16.1731i | 0.568426 | + | 0.622042i | ||||
\(677\) | −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 | ||||
\(679\) | 17.2927 | − | 17.3557i | 0.663635 | − | 0.666051i | ||||
\(680\) | 2.66452 | − | 4.61508i | 0.102180 | − | 0.176980i | ||||
\(681\) | 1.33416 | + | 0.770280i | 0.0511252 | + | 0.0295172i | ||||
\(682\) | − | 7.24468i | − | 0.277413i | ||||||
\(683\) | 24.8889i | 0.952347i | 0.879351 | + | 0.476173i | \(0.157977\pi\) | ||||
−0.879351 | + | 0.476173i | \(0.842023\pi\) | |||||||
\(684\) | 8.05765 | + | 4.65209i | 0.308092 | + | 0.177877i | ||||
\(685\) | 0.421188 | − | 0.729519i | 0.0160928 | − | 0.0278735i | ||||
\(686\) | −7.38667 | − | 7.30654i | −0.282024 | − | 0.278965i | ||||
\(687\) | −4.86535 | + | 2.80901i | −0.185625 | + | 0.107171i | ||||
\(688\) | −4.68558 | + | 8.11566i | −0.178636 | + | 0.309407i | ||||
\(689\) | 0.816312 | + | 7.50131i | 0.0310990 | + | 0.285777i | ||||
\(690\) | 0.990307 | + | 1.71526i | 0.0377003 | + | 0.0652989i | ||||
\(691\) | − | 37.5585i | − | 1.42879i | −0.699741 | − | 0.714396i | \(-0.746701\pi\) | ||
0.699741 | − | 0.714396i | \(-0.253299\pi\) | |||||||
\(692\) | −3.15028 | − | 5.45644i | −0.119756 | − | 0.207423i | ||||
\(693\) | 5.54197 | + | 1.47418i | 0.210522 | + | 0.0559993i | ||||
\(694\) | − | 4.87368i | − | 0.185002i | ||||||
\(695\) | 3.30161 | − | 1.90618i | 0.125237 | − | 0.0723057i | ||||
\(696\) | 15.7686i | 0.597707i | ||||||||
\(697\) | 45.8040 | − | 26.4450i | 1.73495 | − | 1.00167i | ||||
\(698\) | 9.78927 | + | 16.9555i | 0.370529 | + | 0.641776i | ||||
\(699\) | 8.57478 | + | 14.8520i | 0.324328 | + | 0.561753i | ||||
\(700\) | −20.3619 | + | 5.49564i | −0.769607 | + | 0.207716i | ||||
\(701\) | 36.1312 | 1.36466 | 0.682328 | − | 0.731046i | \(-0.260968\pi\) | ||||
0.682328 | + | 0.731046i | \(0.260968\pi\) | |||||||
\(702\) | 0.815910 | − | 1.85085i | 0.0307945 | − | 0.0698557i | ||||
\(703\) | −16.1406 | − | 27.9564i | −0.608755 | − | 1.05439i | ||||
\(704\) | −2.63934 | − | 1.52383i | −0.0994740 | − | 0.0574314i | ||||
\(705\) | −5.81579 | −0.219035 | ||||||||
\(706\) | 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 | ||||
\(709\) | −21.6643 | + | 12.5079i | −0.813619 | + | 0.469743i | −0.848211 | − | 0.529659i | \(-0.822320\pi\) |
0.0345923 | + | 0.999402i | \(0.488987\pi\) | |||||||
\(710\) | 2.51102 | − | 1.44974i | 0.0942368 | − | 0.0544076i | ||||
\(711\) | −4.96282 | −0.186120 | ||||||||
\(712\) | −5.23140 | −0.196055 | ||||||||
\(713\) | 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 | ||||
\(717\) | −22.2272 | − | 12.8329i | −0.830091 | − | 0.479253i | ||||
\(718\) | −0.149240 | + | 0.258492i | −0.00556960 | + | 0.00964684i | ||||
\(719\) | 3.31824 | + | 5.74736i | 0.123749 | + | 0.214340i | 0.921243 | − | 0.388987i | \(-0.127175\pi\) |
−0.797494 | + | 0.603327i | \(0.793841\pi\) | |||||||
\(720\) | − | 1.14864i | − | 0.0428072i | ||||||
\(721\) | 33.0947 | + | 32.9746i | 1.23251 | + | 1.22804i | ||||
\(722\) | 5.57729 | + | 3.22005i | 0.207565 | + | 0.119838i | ||||
\(723\) | 4.08520 | + | 2.35859i | 0.151930 | + | 0.0877170i | ||||
\(724\) | −16.7669 | −0.623138 | ||||||||
\(725\) | 18.0383 | − | 31.2433i | 0.669927 | − | 1.16035i | ||||
\(726\) | − | 3.53536i | − | 0.131209i | ||||||
\(727\) | 18.2640 | 0.677375 | 0.338688 | − | 0.940899i | \(-0.390017\pi\) | ||||
0.338688 | + | 0.940899i | \(0.390017\pi\) | |||||||
\(728\) | 15.3949 | + | 12.3271i | 0.570572 | + | 0.456873i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 0.831627i | − | 0.0307799i | ||||||
\(731\) | 10.5147 | − | 18.2120i | 0.388900 | − | 0.673595i | ||||
\(732\) | −10.5315 | −0.389254 | ||||||||
\(733\) | 26.5047 | + | 15.3025i | 0.978972 | + | 0.565210i | 0.901960 | − | 0.431820i | \(-0.142129\pi\) |
0.0770123 | + | 0.997030i | \(0.475462\pi\) | |||||||
\(734\) | −2.84345 | − | 1.64166i | −0.104953 | − | 0.0605949i | ||||
\(735\) | −3.63699 | + | 0.0132216i | −0.134152 | + | 0.000487686i | ||||
\(736\) | 36.5240i | 1.34629i | ||||||||
\(737\) | 2.14719 | + | 3.71904i | 0.0790928 | + | 0.136993i | ||||
\(738\) | −2.99043 | + | 5.17957i | −0.110079 | + | 0.190663i | ||||
\(739\) | −30.3042 | − | 17.4962i | −1.11476 | − | 0.643607i | −0.174702 | − | 0.984621i | \(-0.555896\pi\) |
−0.940058 | + | 0.341014i | \(0.889229\pi\) | |||||||
\(740\) | −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 | −0.368567 | − | 0.929601i | \(-0.620151\pi\) |
0.620775 | + | 0.783989i | \(0.286818\pi\) | |||||||
\(744\) | 12.3177 | 0.451588 | ||||||||
\(745\) | −0.558484 | −0.0204613 | ||||||||
\(746\) | 11.7824 | − | 6.80258i | 0.431385 | − | 0.249060i | ||||
\(747\) | 3.16899 | − | 1.82961i | 0.115947 | − | 0.0669421i | ||||
\(748\) | 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 | ||||
\(751\) | −30.8388 | −1.12532 | −0.562662 | − | 0.826687i | \(-0.690223\pi\) | ||||
−0.562662 | + | 0.826687i | \(0.690223\pi\) | |||||||
\(752\) | −21.4304 | − | 12.3728i | −0.781485 | − | 0.451191i | ||||
\(753\) | 0.0982527 | + | 0.170179i | 0.00358053 | + | 0.00620165i | ||||
\(754\) | −15.3369 | + | 1.66900i | −0.558537 | + | 0.0607814i | ||||
\(755\) | 6.52194 | 0.237358 | ||||||||
\(756\) | −1.14620 | + | 4.30900i | −0.0416869 | + | 0.156717i | ||||
\(757\) | 3.83594 | + | 6.64405i | 0.139420 | + | 0.241482i | 0.927277 | − | 0.374376i | \(-0.122143\pi\) |
−0.787857 | + | 0.615858i | \(0.788810\pi\) | |||||||
\(758\) | −0.388451 | − | 0.672816i | −0.0141092 | − | 0.0244378i | ||||
\(759\) | −12.7551 | + | 7.36416i | −0.462981 | + | 0.267302i | ||||
\(760\) | − | 5.93040i | − | 0.215118i | ||||||
\(761\) | 24.5371 | − | 14.1665i | 0.889470 | − | 0.513535i | 0.0157006 | − | 0.999877i | \(-0.495002\pi\) |
0.873769 | + | 0.486341i | \(0.161669\pi\) | |||||||
\(762\) | 11.4079i | 0.413266i | ||||||||
\(763\) | 11.2570 | + | 41.7085i | 0.407532 | + | 1.50995i | ||||
\(764\) | −8.01246 | − | 13.8780i | −0.289881 | − | 0.502088i | ||||
\(765\) | 2.57761i | 0.0931937i | ||||||||
\(766\) | 5.53657 | + | 9.58962i | 0.200044 | + | 0.346487i | ||||
\(767\) | 4.43344 | − | 10.0570i | 0.160082 | − | 0.363137i | ||||
\(768\) | −1.83061 | + | 3.17070i | −0.0660563 | + | 0.114413i | ||||
\(769\) | 8.61926 | − | 4.97633i | 0.310819 | − | 0.179451i | −0.336474 | − | 0.941693i | \(-0.609234\pi\) |
0.647293 | + | 0.762242i | \(0.275901\pi\) | |||||||
\(770\) | −0.435561 | − | 1.61380i | −0.0156965 | − | 0.0581572i | ||||
\(771\) | −0.753004 | + | 1.30424i | −0.0271188 | + | 0.0469711i | ||||
\(772\) | −4.54190 | − | 2.62227i | −0.163466 | − | 0.0943774i | ||||
\(773\) | − | 36.8023i | − | 1.32369i | −0.749641 | − | 0.661844i | \(-0.769774\pi\) | ||
0.749641 | − | 0.661844i | \(-0.230226\pi\) | |||||||
\(774\) | 2.37803i | 0.0854765i | ||||||||
\(775\) | −24.4058 | − | 14.0907i | −0.876682 | − | 0.506153i | ||||
\(776\) | −9.57244 | + | 16.5799i | −0.343630 | + | 0.595185i | ||||
\(777\) | 10.9191 | − | 10.9589i | 0.391721 | − | 0.393148i | ||||
\(778\) | −2.41581 | + | 1.39477i | −0.0866111 | + | 0.0500050i | ||||
\(779\) | 29.4292 | − | 50.9728i | 1.05441 | − | 1.82629i | ||||
\(780\) | 3.13859 | − | 0.341549i | 0.112379 | − | 0.0122294i | ||||
\(781\) | 10.7806 | + | 18.6725i | 0.385760 | + | 0.668155i | ||||
\(782\) | − | 18.9114i | − | 0.676271i | ||||||
\(783\) | −3.81357 | − | 6.60529i | −0.136286 | − | 0.236054i | ||||
\(784\) | −13.4299 | − | 7.68881i | −0.479640 | − | 0.274600i | ||||
\(785\) | 0.359656i | 0.0128367i | ||||||||
\(786\) | 6.69435 | − | 3.86498i | 0.238779 | − | 0.137859i | ||||
\(787\) | − | 14.3887i | − | 0.512903i | −0.966557 | − | 0.256451i | \(-0.917447\pi\) | ||
0.966557 | − | 0.256451i | \(-0.0825534\pi\) | |||||||
\(788\) | 7.43798 | − | 4.29432i | 0.264967 | − | 0.152979i | ||||
\(789\) | 3.44299 | + | 5.96344i | 0.122574 | + | 0.212304i | ||||
\(790\) | 0.723279 | + | 1.25276i | 0.0257331 | + | 0.0445711i | ||||
\(791\) | −23.2403 | − | 23.1560i | −0.826330 | − | 0.823332i | ||||
\(792\) | −4.48118 | −0.159232 | ||||||||
\(793\) | −2.43753 | − | 22.3991i | −0.0865592 | − | 0.795416i | ||||
\(794\) | 2.75623 | + | 4.77392i | 0.0978148 | + | 0.169420i | ||||
\(795\) | 0.941670 | + | 0.543673i | 0.0333976 | + | 0.0192821i | ||||
\(796\) | 23.4435 | 0.830933 | ||||||||
\(797\) | 15.6589 | − | 27.1221i | 0.554668 | − | 0.960712i | −0.443262 | − | 0.896392i | \(-0.646179\pi\) |
0.997929 | − | 0.0643202i | \(-0.0204879\pi\) | |||||||
\(798\) | −2.10647 | + | 7.91900i | −0.0745682 | + | 0.280329i | ||||
\(799\) | 48.0910 | + | 27.7653i | 1.70134 | + | 0.982267i | ||||
\(800\) | 22.0182 | − | 12.7122i | 0.778460 | − | 0.449444i | ||||
\(801\) | 2.19138 | − | 1.26519i | 0.0774285 | − | 0.0447034i | ||||
\(802\) | −16.4146 | −0.579618 | ||||||||
\(803\) | 6.18417 | 0.218235 | ||||||||
\(804\) | −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 | ||||
\(808\) | 16.1928 | + | 9.34892i | 0.569661 | + | 0.328894i | ||||
\(809\) | −27.7311 | + | 48.0316i | −0.974973 | + | 1.68870i | −0.294947 | + | 0.955514i | \(0.595302\pi\) |
−0.680026 | + | 0.733188i | \(0.738031\pi\) | |||||||
\(810\) | −0.145740 | − | 0.252428i | −0.00512077 | − | 0.00886943i | ||||
\(811\) | 8.46874i | 0.297378i | 0.988884 | + | 0.148689i | \(0.0475053\pi\) | ||||
−0.988884 | + | 0.148689i | \(0.952495\pi\) | |||||||
\(812\) | 32.8333 | − | 8.86164i | 1.15222 | − | 0.310983i | ||||
\(813\) | 11.9020 | + | 6.87163i | 0.417422 | + | 0.240998i | ||||
\(814\) | 6.15739 | + | 3.55497i | 0.215817 | + | 0.124602i | ||||
\(815\) | 5.40218 | 0.189230 | ||||||||
\(816\) | −5.48375 | + | 9.49814i | −0.191970 | + | 0.332501i | ||||
\(817\) | − | 23.4025i | − | 0.818748i | ||||||
\(818\) | −7.20315 | −0.251852 | ||||||||
\(819\) | −9.43000 | − | 1.44050i | −0.329511 | − | 0.0503353i | ||||
\(820\) | −9.33515 | −0.325997 | ||||||||
\(821\) | 26.5861i | 0.927862i | 0.885871 | + | 0.463931i | \(0.153561\pi\) | ||||
−0.885871 | + | 0.463931i | \(0.846439\pi\) | |||||||
\(822\) | 0.454769 | − | 0.787682i | 0.0158619 | − | 0.0274736i | ||||
\(823\) | −48.9627 | −1.70673 | −0.853366 | − | 0.521312i | \(-0.825443\pi\) | ||||
−0.853366 | + | 0.521312i | \(0.825443\pi\) | |||||||
\(824\) | −31.6154 | − | 18.2532i | −1.10138 | − | 0.635879i | ||||
\(825\) | 8.87885 | + | 5.12620i | 0.309122 | + | 0.178472i | ||||
\(826\) | 1.16308 | − | 4.37244i | 0.0404687 | − | 0.152137i | ||||
\(827\) | 16.8817i | 0.587034i | 0.955954 | + | 0.293517i | \(0.0948257\pi\) | ||||
−0.955954 | + | 0.293517i | \(0.905174\pi\) | |||||||
\(828\) | −5.72578 | − | 9.91734i | −0.198985 | − | 0.344652i | ||||
\(829\) | −4.72080 | + | 8.17666i | −0.163960 | + | 0.283987i | −0.936286 | − | 0.351240i | \(-0.885760\pi\) |
0.772325 | + | 0.635227i | \(0.219093\pi\) | |||||||
\(830\) | −0.923693 | − | 0.533294i | −0.0320619 | − | 0.0185109i | ||||
\(831\) | 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 | ||||
\(835\) | 12.5453 | 0.434147 | ||||||||
\(836\) | 20.1669 | 0.697486 | ||||||||
\(837\) | −5.15974 | + | 2.97898i | −0.178347 | + | 0.102969i | ||||
\(838\) | −12.8119 | + | 7.39693i | −0.442578 | + | 0.255523i | ||||
\(839\) | −32.5016 | − | 18.7648i | −1.12208 | − | 0.647833i | −0.180149 | − | 0.983639i | \(-0.557658\pi\) |
−0.941931 | + | 0.335806i | \(0.890991\pi\) | |||||||
\(840\) | 2.74384 | − | 0.740558i | 0.0946714 | − | 0.0255517i | ||||
\(841\) | −14.5866 | + | 25.2647i | −0.502985 | + | 0.871195i | ||||
\(842\) | −1.52242 | −0.0524661 | ||||||||
\(843\) | 1.57284 | + | 0.908078i | 0.0541714 | + | 0.0312759i | ||||
\(844\) | −10.6306 | − | 18.4128i | −0.365921 | − | 0.633793i | ||||
\(845\) | 1.45287 | + | 6.59634i | 0.0499802 | + | 0.226921i | ||||
\(846\) | −6.27947 | −0.215893 | ||||||||
\(847\) | −16.0973 | + | 4.34463i | −0.553109 | + | 0.149283i | ||||
\(848\) | 2.31328 | + | 4.00672i | 0.0794385 | + | 0.137591i | ||||
\(849\) | 15.4189 | + | 26.7063i | 0.529174 | + | 0.916556i | ||||
\(850\) | −11.4006 | + | 6.58214i | −0.391037 | + | 0.225766i | ||||
\(851\) | 39.7317i | 1.36198i | ||||||||
\(852\) | −14.5183 | + | 8.38212i | −0.497387 | + | 0.287167i | ||||
\(853\) | 35.3664i | 1.21092i | 0.795875 | + | 0.605461i | \(0.207011\pi\) | ||||
−0.795875 | + | 0.605461i | \(0.792989\pi\) | |||||||
\(854\) | −2.41689 | − | 8.95483i | −0.0827044 | − | 0.306428i | ||||
\(855\) | 1.43424 | + | 2.48418i | 0.0490500 | + | 0.0849571i | ||||
\(856\) | 40.2325i | 1.37512i | ||||||||
\(857\) | −2.53098 | − | 4.38379i | −0.0864568 | − | 0.149748i | 0.819554 | − | 0.573002i | \(-0.194221\pi\) |
−0.906011 | + | 0.423254i | \(0.860888\pi\) | |||||||
\(858\) | −0.474303 | − | 4.35850i | −0.0161924 | − | 0.148797i | ||||
\(859\) | 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 | ||||
\(861\) | 27.2587 | + | 7.25088i | 0.928975 | + | 0.247109i | ||||
\(862\) | 10.4028 | − | 18.0181i | 0.354319 | − | 0.613699i | ||||
\(863\) | −1.53116 | − | 0.884017i | −0.0521214 | − | 0.0300923i | 0.473713 | − | 0.880679i | \(-0.342913\pi\) |
−0.525834 | + | 0.850587i | \(0.676247\pi\) | |||||||
\(864\) | − | 5.37509i | − | 0.182864i | ||||||
\(865\) | − | 1.94246i | − | 0.0660458i | ||||||
\(866\) | 7.01100 | + | 4.04780i | 0.238243 | + | 0.137550i | ||||
\(867\) | 3.80585 | − | 6.59193i | 0.129253 | − | 0.223874i | ||||
\(868\) | −6.92230 | − | 25.6478i | −0.234958 | − | 0.870543i | ||||
\(869\) | −9.31580 | + | 5.37848i | −0.316017 | + | 0.182452i | ||||
\(870\) | −1.11157 | + | 1.92530i | −0.0376859 | + | 0.0652739i | ||||
\(871\) | −4.22007 | − | 5.76374i | −0.142991 | − | 0.195297i | ||||
\(872\) | −16.8790 | − | 29.2352i | −0.571593 | − | 0.990029i | ||||
\(873\) | − | 9.26021i | − | 0.313411i | ||||||
\(874\) | −10.5227 | − | 18.2259i | −0.355937 | − | 0.616501i | ||||
\(875\) | −12.9260 | − | 3.43835i | −0.436979 | − | 0.116237i | ||||
\(876\) | 4.80832i | 0.162458i | ||||||||
\(877\) | 49.2185 | − | 28.4163i | 1.66199 | − | 0.959550i | 0.690227 | − | 0.723593i | \(-0.257511\pi\) |
0.971763 | − | 0.235957i | \(-0.0758225\pi\) | |||||||
\(878\) | 8.20742i | 0.276987i | ||||||||
\(879\) | −0.948761 | + | 0.547767i | −0.0320009 | + | 0.0184757i | ||||
\(880\) | −1.24484 | − | 2.15613i | −0.0419636 | − | 0.0726831i | ||||
\(881\) | 20.9164 | + | 36.2283i | 0.704693 | + | 1.22056i | 0.966802 | + | 0.255525i | \(0.0822484\pi\) |
−0.262110 | + | 0.965038i | \(0.584418\pi\) | |||||||
\(882\) | −3.92696 | + | 0.0142757i | −0.132228 | + | 0.000480689i | ||||
\(883\) | −8.23784 | −0.277225 | −0.138613 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138613 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(884\) | −27.5837 | − | 12.1597i | −0.927740 | − | 0.408976i | ||||
\(885\) | −0.791910 | − | 1.37163i | −0.0266198 | − | 0.0461068i | ||||
\(886\) | 17.7860 | + | 10.2688i | 0.597533 | + | 0.344986i | ||||
\(887\) | −54.7544 | −1.83847 | −0.919236 | − | 0.393706i | \(-0.871193\pi\) | ||||
−0.919236 | + | 0.393706i | \(0.871193\pi\) | |||||||
\(888\) | −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 | ||||
\(891\) | 1.87712 | − | 1.08375i | 0.0628858 | − | 0.0363071i | ||||
\(892\) | 1.11149 | − | 0.641717i | 0.0372153 | − | 0.0214863i | ||||
\(893\) | 61.7970 | 2.06796 | ||||||||
\(894\) | −0.603012 | −0.0201677 | ||||||||
\(895\) | 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 | ||||
\(899\) | 39.3540 | + | 22.7211i | 1.31253 | + | 0.757789i | ||||
\(900\) | −3.98573 | + | 6.90348i | −0.132858 | + | 0.230116i | ||||
\(901\) | −5.19114 | − | 8.99131i | −0.172942 | − | 0.299544i | ||||
\(902\) | 12.9636i | 0.431639i | ||||||||
\(903\) | 10.8277 | − | 2.92238i | 0.360323 | − | 0.0972507i | ||||
\(904\) | 22.2015 | + | 12.8180i | 0.738411 | + | 0.426322i | ||||
\(905\) | −4.47670 | − | 2.58462i | −0.148810 | − | 0.0859158i | ||||
\(906\) | 7.04192 | 0.233952 | ||||||||
\(907\) | −5.77857 | + | 10.0088i | −0.191874 | + | 0.332336i | −0.945871 | − | 0.324542i | \(-0.894790\pi\) |
0.753997 | + | 0.656878i | \(0.228123\pi\) | |||||||
\(908\) | 2.59628i | 0.0861604i | ||||||||
\(909\) | −9.04398 | −0.299970 | ||||||||
\(910\) | 1.01070 | + | 2.59034i | 0.0335044 | + | 0.0858689i | ||||
\(911\) | 23.9338 | 0.792961 | 0.396481 | − | 0.918043i | \(-0.370231\pi\) | ||||
0.396481 | + | 0.918043i | \(0.370231\pi\) | |||||||
\(912\) | 12.2051i | 0.404152i | ||||||||
\(913\) | 3.96570 | − | 6.86880i | 0.131246 | − | 0.227324i | ||||
\(914\) | 10.7678 | 0.356166 | ||||||||
\(915\) | −2.81185 | − | 1.62342i | −0.0929570 | − | 0.0536688i | ||||
\(916\) | −8.19949 | − | 4.73398i | −0.270919 | − | 0.156415i | ||||
\(917\) | −25.8249 | − | 25.7312i | −0.852813 | − | 0.849718i | ||||
\(918\) | 2.78312i | 0.0918566i | ||||||||
\(919\) | −1.56904 | − | 2.71766i | −0.0517580 | − | 0.0896474i | 0.838986 | − | 0.544154i | \(-0.183149\pi\) |
−0.890744 | + | 0.454506i | \(0.849816\pi\) | |||||||
\(920\) | −3.64956 | + | 6.32122i | −0.120322 | + | 0.208405i | ||||
\(921\) | 4.24566 | + | 2.45124i | 0.139899 | + | 0.0807709i | ||||
\(922\) | 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 | ||||
\(926\) | 6.07553 | 0.199654 | ||||||||
\(927\) | 17.6578 | 0.579958 | ||||||||
\(928\) | −35.5040 | + | 20.4982i | −1.16548 | + | 0.672888i | ||||
\(929\) | 18.3572 | − | 10.5986i | 0.602282 | − | 0.347728i | −0.167657 | − | 0.985845i | \(-0.553620\pi\) |
0.769939 | + | 0.638118i | \(0.220287\pi\) | |||||||
\(930\) | 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 | ||||
\(933\) | −11.5750 | −0.378949 | ||||||||
\(934\) | 5.67470 | + | 3.27629i | 0.185682 | + | 0.107204i | ||||
\(935\) | 2.79350 | + | 4.83848i | 0.0913571 | + | 0.158235i | ||||
\(936\) | 7.41049 | − | 0.806429i | 0.242219 | − | 0.0263590i | ||||
\(937\) | −26.0293 | −0.850339 | −0.425169 | − | 0.905114i | \(-0.639786\pi\) | ||||
−0.425169 | + | 0.905114i | \(0.639786\pi\) | |||||||
\(938\) | −2.08316 | − | 2.07560i | −0.0680176 | − | 0.0677708i | ||||
\(939\) | −2.53480 | − | 4.39041i | −0.0827201 | − | 0.143275i | ||||
\(940\) | −4.90062 | − | 8.48812i | −0.159841 | − | 0.276852i | ||||
\(941\) | 14.2589 | − | 8.23240i | 0.464828 | − | 0.268369i | −0.249244 | − | 0.968441i | \(-0.580182\pi\) |
0.714072 | + | 0.700072i | \(0.246849\pi\) | |||||||
\(942\) | 0.388331i | 0.0126525i | ||||||||
\(943\) | −62.7372 | + | 36.2213i | −2.04300 | + | 1.17953i | ||||
\(944\) | − | 6.73902i | − | 0.219336i | ||||||
\(945\) | −0.970263 | + | 0.973797i | −0.0315627 | + | 0.0316776i | ||||
\(946\) | 2.57720 | + | 4.46384i | 0.0837919 | + | 0.145132i | ||||
\(947\) | − | 14.2330i | − | 0.462511i | −0.972893 | − | 0.231255i | \(-0.925717\pi\) | ||
0.972893 | − | 0.231255i | \(-0.0742833\pi\) | |||||||
\(948\) | −4.18188 | − | 7.24322i | −0.135821 | − | 0.235249i | ||||
\(949\) | −10.2267 | + | 1.11290i | −0.331973 | + | 0.0361262i | ||||
\(950\) | −7.32490 | + | 12.6871i | −0.237651 | + | 0.411624i | ||||
\(951\) | 14.8929 | − | 8.59841i | 0.482935 | − | 0.278823i | ||||
\(952\) | −26.2244 | − | 6.97575i | −0.849939 | − | 0.226085i | ||||
\(953\) | −22.2750 | + | 38.5815i | −0.721559 | + | 1.24978i | 0.238815 | + | 0.971065i | \(0.423241\pi\) |
−0.960375 | + | 0.278712i | \(0.910092\pi\) | |||||||
\(954\) | 1.01675 | + | 0.587020i | 0.0329184 | + | 0.0190055i | ||||
\(955\) | − | 4.94049i | − | 0.159870i | ||||||
\(956\) | − | 43.2541i | − | 1.39894i | ||||||
\(957\) | −14.3170 | − | 8.26593i | −0.462803 | − | 0.267200i | ||||
\(958\) | −6.73859 | + | 11.6716i | −0.217714 | + | 0.377092i | ||||
\(959\) | −4.14537 | − | 1.10268i | −0.133861 | − | 0.0356073i | ||||
\(960\) | 0.632676 | − | 0.365276i | 0.0204195 | − | 0.0117892i | ||||
\(961\) | 2.24861 | − | 3.89472i | 0.0725360 | − | 0.125636i | ||||
\(962\) | −10.8222 | − | 4.77075i | −0.348921 | − | 0.153815i | ||||
\(963\) | −9.73005 | − | 16.8529i | −0.313546 | − | 0.543078i | ||||
\(964\) | 7.94978i | 0.256045i | ||||||||
\(965\) | −0.808445 | − | 1.40027i | −0.0260248 | − | 0.0450762i | ||||
\(966\) | 7.11863 | − | 7.14456i | 0.229038 | − | 0.229872i | ||||
\(967\) | − | 17.7030i | − | 0.569289i | −0.958633 | − | 0.284645i | \(-0.908124\pi\) | ||
0.958633 | − | 0.284645i | \(-0.0918756\pi\) | |||||||
\(968\) | 11.2833 | − | 6.51439i | 0.362658 | − | 0.209380i | ||||
\(969\) | − | 27.3890i | − | 0.879862i | ||||||
\(970\) | −2.33754 | + | 1.34958i | −0.0750538 | + | 0.0433324i | ||||
\(971\) | −3.16344 | − | 5.47924i | −0.101520 | − | 0.175837i | 0.810791 | − | 0.585335i | \(-0.199037\pi\) |
−0.912311 | + | 0.409498i | \(0.865704\pi\) | |||||||
\(972\) | 0.842641 | + | 1.45950i | 0.0270277 | + | 0.0468134i | ||||
\(973\) | −13.7521 | − | 13.7022i | −0.440873 | − | 0.439274i | ||||
\(974\) | −3.38858 | −0.108577 | ||||||||
\(975\) | −15.6054 | − | 6.87933i | −0.499772 | − | 0.220315i | ||||
\(976\) | −6.90753 | − | 11.9642i | −0.221105 | − | 0.382965i | ||||
\(977\) | −7.94569 | − | 4.58744i | −0.254205 | − | 0.146765i | 0.367483 | − | 0.930030i | \(-0.380220\pi\) |
−0.621688 | + | 0.783265i | \(0.713553\pi\) | |||||||
\(978\) | 5.83289 | 0.186515 | ||||||||
\(979\) | 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 | ||||
\(982\) | 6.85640 | − | 3.95854i | 0.218796 | − | 0.126322i | ||||
\(983\) | 42.7704 | − | 24.6935i | 1.36416 | − | 0.787601i | 0.373990 | − | 0.927433i | \(-0.377990\pi\) |
0.990175 | + | 0.139832i | \(0.0446562\pi\) | |||||||
\(984\) | −22.0411 | −0.702646 | ||||||||
\(985\) | 2.64788 | 0.0843685 | ||||||||
\(986\) | 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 | ||||
\(990\) | −0.547140 | − | 0.315892i | −0.0173893 | − | 0.0100397i | ||||
\(991\) | −17.9465 | + | 31.0842i | −0.570088 | + | 0.987421i | 0.426468 | + | 0.904502i | \(0.359758\pi\) |
−0.996556 | + | 0.0829187i | \(0.973576\pi\) | |||||||
\(992\) | 16.0123 | + | 27.7341i | 0.508390 | + | 0.880557i | ||||
\(993\) | − | 20.4213i | − | 0.648050i | ||||||
\(994\) | −10.4591 | − | 10.4212i | −0.331743 | − | 0.330539i | ||||
\(995\) | 6.25932 | + | 3.61382i | 0.198434 | + | 0.114566i | ||||
\(996\) | 5.34063 | + | 3.08342i | 0.169224 | + | 0.0977018i | ||||
\(997\) | 42.2451 | 1.33791 | 0.668957 | − | 0.743301i | \(-0.266741\pi\) | ||||
0.668957 | + | 0.743301i | \(0.266741\pi\) | |||||||
\(998\) | 9.21412 | − | 15.9593i | 0.291668 | − | 0.505184i | ||||
\(999\) | − | 5.84715i | − | 0.184996i |
(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.t.d.205.6 | yes | 20 | |
3.2 | odd | 2 | 819.2.bm.g.478.5 | 20 | |||
7.4 | even | 3 | 273.2.bl.d.88.5 | yes | 20 | ||
13.4 | even | 6 | 273.2.bl.d.121.5 | yes | 20 | ||
21.11 | odd | 6 | 819.2.do.g.361.6 | 20 | |||
39.17 | odd | 6 | 819.2.do.g.667.6 | 20 | |||
91.4 | even | 6 | inner | 273.2.t.d.4.5 | ✓ | 20 | |
273.95 | odd | 6 | 819.2.bm.g.550.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.d.4.5 | ✓ | 20 | 91.4 | even | 6 | inner | |
273.2.t.d.205.6 | yes | 20 | 1.1 | even | 1 | trivial | |
273.2.bl.d.88.5 | yes | 20 | 7.4 | even | 3 | ||
273.2.bl.d.121.5 | yes | 20 | 13.4 | even | 6 | ||
819.2.bm.g.478.5 | 20 | 3.2 | odd | 2 | |||
819.2.bm.g.550.6 | 20 | 273.95 | odd | 6 | |||
819.2.do.g.361.6 | 20 | 21.11 | odd | 6 | |||
819.2.do.g.667.6 | 20 | 39.17 | odd | 6 |