Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 10 x^{10} - 15 x^{9} + 61 x^{8} - 25 x^{7} + 316 x^{6} + 50 x^{5} + 1336 x^{4} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 841.1 | ||
Root | \(0.784484 - 2.41439i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.841 |
Dual form | 930.2.n.f.721.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.03161 | + | 2.92914i | −1.52381 | + | 1.10711i | −0.564246 | + | 0.825607i | \(0.690833\pi\) |
−0.959560 | + | 0.281503i | \(0.909167\pi\) | |||||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | −0.309017 | − | 0.951057i | −0.0977198 | − | 0.300750i | ||||
\(11\) | 3.07834 | − | 2.23654i | 0.928154 | − | 0.674343i | −0.0173863 | − | 0.999849i | \(-0.505534\pi\) |
0.945540 | + | 0.325506i | \(0.105534\pi\) | |||||||
\(12\) | −0.309017 | − | 0.951057i | −0.0892055 | − | 0.274546i | ||||
\(13\) | −0.484838 | + | 1.49218i | −0.134470 | + | 0.413855i | −0.995507 | − | 0.0946863i | \(-0.969815\pi\) |
0.861037 | + | 0.508542i | \(0.169815\pi\) | |||||||
\(14\) | 4.03161 | + | 2.92914i | 1.07749 | + | 0.782845i | ||||
\(15\) | −0.309017 | + | 0.951057i | −0.0797878 | + | 0.245562i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −4.20814 | − | 3.05739i | −1.02062 | − | 0.741527i | −0.0542133 | − | 0.998529i | \(-0.517265\pi\) |
−0.966411 | + | 0.257003i | \(0.917265\pi\) | |||||||
\(18\) | −0.309017 | + | 0.951057i | −0.0728360 | + | 0.224166i | ||||
\(19\) | 1.24608 | + | 3.83505i | 0.285871 | + | 0.879821i | 0.986136 | + | 0.165938i | \(0.0530652\pi\) |
−0.700265 | + | 0.713883i | \(0.746935\pi\) | |||||||
\(20\) | −0.809017 | + | 0.587785i | −0.180902 | + | 0.131433i | ||||
\(21\) | −1.53994 | − | 4.73944i | −0.336042 | − | 1.03423i | ||||
\(22\) | −3.07834 | − | 2.23654i | −0.656304 | − | 0.476833i | ||||
\(23\) | −2.76439 | − | 2.00845i | −0.576415 | − | 0.418790i | 0.261015 | − | 0.965335i | \(-0.415943\pi\) |
−0.837430 | + | 0.546545i | \(0.815943\pi\) | |||||||
\(24\) | −0.809017 | + | 0.587785i | −0.165140 | + | 0.119981i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.56897 | 0.307700 | ||||||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | 1.53994 | − | 4.73944i | 0.291021 | − | 0.895671i | ||||
\(29\) | −1.32840 | − | 4.08841i | −0.246678 | − | 0.759198i | −0.995356 | − | 0.0962637i | \(-0.969311\pi\) |
0.748677 | − | 0.662934i | \(-0.230689\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −5.47277 | + | 1.02410i | −0.982939 | + | 0.183933i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.17582 | + | 3.61880i | 0.204684 | + | 0.629953i | ||||
\(34\) | −1.60737 | + | 4.94697i | −0.275661 | + | 0.848398i | ||||
\(35\) | −4.03161 | + | 2.92914i | −0.681467 | + | 0.495115i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.7227 | −1.76279 | −0.881397 | − | 0.472376i | \(-0.843397\pi\) | ||||
−0.881397 | + | 0.472376i | \(0.843397\pi\) | |||||||
\(38\) | 3.26229 | − | 2.37019i | 0.529213 | − | 0.384496i | ||||
\(39\) | −1.26932 | − | 0.922216i | −0.203254 | − | 0.147673i | ||||
\(40\) | 0.809017 | + | 0.587785i | 0.127917 | + | 0.0929370i | ||||
\(41\) | 1.39947 | + | 4.30712i | 0.218560 | + | 0.672660i | 0.998882 | + | 0.0472807i | \(0.0150555\pi\) |
−0.780321 | + | 0.625379i | \(0.784944\pi\) | |||||||
\(42\) | −4.03161 | + | 2.92914i | −0.622091 | + | 0.451976i | ||||
\(43\) | −2.13967 | − | 6.58522i | −0.326296 | − | 1.00424i | −0.970852 | − | 0.239680i | \(-0.922958\pi\) |
0.644556 | − | 0.764557i | \(-0.277042\pi\) | |||||||
\(44\) | −1.17582 | + | 3.61880i | −0.177262 | + | 0.545555i | ||||
\(45\) | −0.809017 | − | 0.587785i | −0.120601 | − | 0.0876219i | ||||
\(46\) | −1.05590 | + | 3.24973i | −0.155684 | + | 0.479147i | ||||
\(47\) | −0.665153 | + | 2.04713i | −0.0970226 | + | 0.298605i | −0.987776 | − | 0.155883i | \(-0.950178\pi\) |
0.890753 | + | 0.454488i | \(0.150178\pi\) | |||||||
\(48\) | 0.809017 | + | 0.587785i | 0.116772 | + | 0.0848395i | ||||
\(49\) | 5.51093 | − | 16.9609i | 0.787275 | − | 2.42298i | ||||
\(50\) | −0.309017 | − | 0.951057i | −0.0437016 | − | 0.134500i | ||||
\(51\) | 4.20814 | − | 3.05739i | 0.589258 | − | 0.428121i | ||||
\(52\) | −0.484838 | − | 1.49218i | −0.0672349 | − | 0.206928i | ||||
\(53\) | −8.26558 | − | 6.00530i | −1.13536 | − | 0.824891i | −0.148898 | − | 0.988853i | \(-0.547573\pi\) |
−0.986467 | + | 0.163962i | \(0.947573\pi\) | |||||||
\(54\) | −0.809017 | − | 0.587785i | −0.110093 | − | 0.0799874i | ||||
\(55\) | 3.07834 | − | 2.23654i | 0.415083 | − | 0.301575i | ||||
\(56\) | −4.98335 | −0.665928 | ||||||||
\(57\) | −4.03241 | −0.534106 | ||||||||
\(58\) | −3.47781 | + | 2.52677i | −0.456658 | + | 0.331782i | ||||
\(59\) | −1.59270 | + | 4.90182i | −0.207352 | + | 0.638163i | 0.792257 | + | 0.610188i | \(0.208906\pi\) |
−0.999609 | + | 0.0279754i | \(0.991094\pi\) | |||||||
\(60\) | −0.309017 | − | 0.951057i | −0.0398939 | − | 0.122781i | ||||
\(61\) | −8.45886 | −1.08305 | −0.541523 | − | 0.840686i | \(-0.682152\pi\) | ||||
−0.541523 | + | 0.840686i | \(0.682152\pi\) | |||||||
\(62\) | 2.66515 | + | 4.88845i | 0.338475 | + | 0.620834i | ||||
\(63\) | 4.98335 | 0.627843 | ||||||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | −0.484838 | + | 1.49218i | −0.0601367 | + | 0.185082i | ||||
\(66\) | 3.07834 | − | 2.23654i | 0.378917 | − | 0.275299i | ||||
\(67\) | −1.93515 | −0.236417 | −0.118208 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118208 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(68\) | 5.20155 | 0.630780 | ||||||||
\(69\) | 2.76439 | − | 2.00845i | 0.332793 | − | 0.241788i | ||||
\(70\) | 4.03161 | + | 2.92914i | 0.481870 | + | 0.350099i | ||||
\(71\) | 6.60268 | + | 4.79713i | 0.783594 | + | 0.569314i | 0.906055 | − | 0.423159i | \(-0.139079\pi\) |
−0.122462 | + | 0.992473i | \(0.539079\pi\) | |||||||
\(72\) | −0.309017 | − | 0.951057i | −0.0364180 | − | 0.112083i | ||||
\(73\) | 11.7344 | − | 8.52556i | 1.37341 | − | 0.997841i | 0.375949 | − | 0.926640i | \(-0.377317\pi\) |
0.997462 | − | 0.0712009i | \(-0.0226831\pi\) | |||||||
\(74\) | 3.31348 | + | 10.1979i | 0.385185 | + | 1.18548i | ||||
\(75\) | −0.309017 | + | 0.951057i | −0.0356822 | + | 0.109819i | ||||
\(76\) | −3.26229 | − | 2.37019i | −0.374210 | − | 0.271880i | ||||
\(77\) | −5.85952 | + | 18.0337i | −0.667754 | + | 2.05514i | ||||
\(78\) | −0.484838 | + | 1.49218i | −0.0548970 | + | 0.168956i | ||||
\(79\) | −7.75630 | − | 5.63528i | −0.872652 | − | 0.634019i | 0.0586450 | − | 0.998279i | \(-0.481322\pi\) |
−0.931297 | + | 0.364260i | \(0.881322\pi\) | |||||||
\(80\) | 0.309017 | − | 0.951057i | 0.0345492 | − | 0.106331i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 3.66386 | − | 2.66195i | 0.404605 | − | 0.293963i | ||||
\(83\) | 4.46803 | + | 13.7512i | 0.490430 | + | 1.50939i | 0.823959 | + | 0.566650i | \(0.191761\pi\) |
−0.333529 | + | 0.942740i | \(0.608239\pi\) | |||||||
\(84\) | 4.03161 | + | 2.92914i | 0.439885 | + | 0.319595i | ||||
\(85\) | −4.20814 | − | 3.05739i | −0.456437 | − | 0.331621i | ||||
\(86\) | −5.60172 | + | 4.06989i | −0.604049 | + | 0.438868i | ||||
\(87\) | 4.29881 | 0.460880 | ||||||||
\(88\) | 3.80504 | 0.405618 | ||||||||
\(89\) | −5.21612 | + | 3.78973i | −0.552908 | + | 0.401711i | −0.828856 | − | 0.559461i | \(-0.811008\pi\) |
0.275949 | + | 0.961172i | \(0.411008\pi\) | |||||||
\(90\) | −0.309017 | + | 0.951057i | −0.0325733 | + | 0.100250i | ||||
\(91\) | −2.41611 | − | 7.43603i | −0.253277 | − | 0.779508i | ||||
\(92\) | 3.41697 | 0.356244 | ||||||||
\(93\) | 0.717206 | − | 5.52138i | 0.0743708 | − | 0.572540i | ||||
\(94\) | 2.15248 | 0.222011 | ||||||||
\(95\) | 1.24608 | + | 3.83505i | 0.127846 | + | 0.393468i | ||||
\(96\) | 0.309017 | − | 0.951057i | 0.0315389 | − | 0.0970668i | ||||
\(97\) | −2.87578 | + | 2.08938i | −0.291992 | + | 0.212144i | −0.724131 | − | 0.689663i | \(-0.757759\pi\) |
0.432139 | + | 0.901807i | \(0.357759\pi\) | |||||||
\(98\) | −17.8337 | −1.80148 | ||||||||
\(99\) | −3.80504 | −0.382420 | ||||||||
\(100\) | −0.809017 | + | 0.587785i | −0.0809017 | + | 0.0587785i | ||||
\(101\) | −15.4559 | − | 11.2294i | −1.53792 | − | 1.11736i | −0.951625 | − | 0.307263i | \(-0.900587\pi\) |
−0.586292 | − | 0.810100i | \(-0.699413\pi\) | |||||||
\(102\) | −4.20814 | − | 3.05739i | −0.416668 | − | 0.302727i | ||||
\(103\) | 4.98486 | + | 15.3418i | 0.491172 | + | 1.51167i | 0.822838 | + | 0.568276i | \(0.192389\pi\) |
−0.331665 | + | 0.943397i | \(0.607611\pi\) | |||||||
\(104\) | −1.26932 | + | 0.922216i | −0.124467 | + | 0.0904307i | ||||
\(105\) | −1.53994 | − | 4.73944i | −0.150283 | − | 0.462522i | ||||
\(106\) | −3.15717 | + | 9.71677i | −0.306652 | + | 0.943777i | ||||
\(107\) | −2.91729 | − | 2.11953i | −0.282025 | − | 0.204903i | 0.437775 | − | 0.899084i | \(-0.355767\pi\) |
−0.719800 | + | 0.694181i | \(0.755767\pi\) | |||||||
\(108\) | −0.309017 | + | 0.951057i | −0.0297352 | + | 0.0915155i | ||||
\(109\) | −0.565181 | + | 1.73945i | −0.0541345 | + | 0.166609i | −0.974468 | − | 0.224525i | \(-0.927917\pi\) |
0.920334 | + | 0.391134i | \(0.127917\pi\) | |||||||
\(110\) | −3.07834 | − | 2.23654i | −0.293508 | − | 0.213246i | ||||
\(111\) | 3.31348 | − | 10.1979i | 0.314502 | − | 0.967938i | ||||
\(112\) | 1.53994 | + | 4.73944i | 0.145511 | + | 0.447835i | ||||
\(113\) | −5.70475 | + | 4.14474i | −0.536657 | + | 0.389904i | −0.822842 | − | 0.568270i | \(-0.807613\pi\) |
0.286185 | + | 0.958174i | \(0.407613\pi\) | |||||||
\(114\) | 1.24608 | + | 3.83505i | 0.116706 | + | 0.359186i | ||||
\(115\) | −2.76439 | − | 2.00845i | −0.257781 | − | 0.187289i | ||||
\(116\) | 3.47781 | + | 2.52677i | 0.322906 | + | 0.234605i | ||||
\(117\) | 1.26932 | − | 0.922216i | 0.117349 | − | 0.0852589i | ||||
\(118\) | 5.15408 | 0.474472 | ||||||||
\(119\) | 25.9211 | 2.37618 | ||||||||
\(120\) | −0.809017 | + | 0.587785i | −0.0738528 | + | 0.0536572i | ||||
\(121\) | 1.07485 | − | 3.30805i | 0.0977138 | − | 0.300732i | ||||
\(122\) | 2.61393 | + | 8.04485i | 0.236654 | + | 0.728347i | ||||
\(123\) | −4.52878 | −0.408346 | ||||||||
\(124\) | 3.82562 | − | 4.04533i | 0.343550 | − | 0.363281i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.53994 | − | 4.73944i | −0.137189 | − | 0.422223i | ||||
\(127\) | −0.389015 | + | 1.19727i | −0.0345195 | + | 0.106240i | −0.966832 | − | 0.255415i | \(-0.917788\pi\) |
0.932312 | + | 0.361655i | \(0.117788\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | 6.92411 | 0.609634 | ||||||||
\(130\) | 1.56897 | 0.137608 | ||||||||
\(131\) | 14.1673 | − | 10.2932i | 1.23781 | − | 0.899319i | 0.240356 | − | 0.970685i | \(-0.422736\pi\) |
0.997450 | + | 0.0713662i | \(0.0227359\pi\) | |||||||
\(132\) | −3.07834 | − | 2.23654i | −0.267935 | − | 0.194666i | ||||
\(133\) | −16.2571 | − | 11.8115i | −1.40967 | − | 1.02419i | ||||
\(134\) | 0.597996 | + | 1.84044i | 0.0516590 | + | 0.158990i | ||||
\(135\) | 0.809017 | − | 0.587785i | 0.0696291 | − | 0.0505885i | ||||
\(136\) | −1.60737 | − | 4.94697i | −0.137831 | − | 0.424199i | ||||
\(137\) | −2.11477 | + | 6.50860i | −0.180677 | + | 0.556067i | −0.999847 | − | 0.0174837i | \(-0.994434\pi\) |
0.819170 | + | 0.573551i | \(0.194434\pi\) | |||||||
\(138\) | −2.76439 | − | 2.00845i | −0.235320 | − | 0.170970i | ||||
\(139\) | −4.20521 | + | 12.9423i | −0.356681 | + | 1.09775i | 0.598347 | + | 0.801237i | \(0.295825\pi\) |
−0.955028 | + | 0.296515i | \(0.904175\pi\) | |||||||
\(140\) | 1.53994 | − | 4.73944i | 0.130149 | − | 0.400556i | ||||
\(141\) | −1.74139 | − | 1.26520i | −0.146652 | − | 0.106549i | ||||
\(142\) | 2.52200 | − | 7.76191i | 0.211641 | − | 0.651365i | ||||
\(143\) | 1.84482 | + | 5.67778i | 0.154272 | + | 0.474800i | ||||
\(144\) | −0.809017 | + | 0.587785i | −0.0674181 | + | 0.0489821i | ||||
\(145\) | −1.32840 | − | 4.08841i | −0.110318 | − | 0.339524i | ||||
\(146\) | −11.7344 | − | 8.52556i | −0.971148 | − | 0.705580i | ||||
\(147\) | 14.4278 | + | 10.4824i | 1.18998 | + | 0.864574i | ||||
\(148\) | 8.67481 | − | 6.30262i | 0.713065 | − | 0.518072i | ||||
\(149\) | 7.64716 | 0.626480 | 0.313240 | − | 0.949674i | \(-0.398586\pi\) | ||||
0.313240 | + | 0.949674i | \(0.398586\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −8.09620 | + | 5.88224i | −0.658860 | + | 0.478690i | −0.866278 | − | 0.499563i | \(-0.833494\pi\) |
0.207418 | + | 0.978252i | \(0.433494\pi\) | |||||||
\(152\) | −1.24608 | + | 3.83505i | −0.101071 | + | 0.311064i | ||||
\(153\) | 1.60737 | + | 4.94697i | 0.129948 | + | 0.399938i | ||||
\(154\) | 18.9618 | 1.52799 | ||||||||
\(155\) | −5.47277 | + | 1.02410i | −0.439584 | + | 0.0822574i | ||||
\(156\) | 1.56897 | 0.125618 | ||||||||
\(157\) | −2.48662 | − | 7.65303i | −0.198454 | − | 0.610778i | −0.999919 | − | 0.0127365i | \(-0.995946\pi\) |
0.801465 | − | 0.598042i | \(-0.204054\pi\) | |||||||
\(158\) | −2.96264 | + | 9.11808i | −0.235695 | + | 0.725396i | ||||
\(159\) | 8.26558 | − | 6.00530i | 0.655503 | − | 0.476251i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 17.0280 | 1.34199 | ||||||||
\(162\) | 0.809017 | − | 0.587785i | 0.0635624 | − | 0.0461808i | ||||
\(163\) | 12.9789 | + | 9.42976i | 1.01659 | + | 0.738595i | 0.965581 | − | 0.260103i | \(-0.0837564\pi\) |
0.0510085 | + | 0.998698i | \(0.483756\pi\) | |||||||
\(164\) | −3.66386 | − | 2.66195i | −0.286099 | − | 0.207863i | ||||
\(165\) | 1.17582 | + | 3.61880i | 0.0915375 | + | 0.281723i | ||||
\(166\) | 11.6975 | − | 8.49870i | 0.907899 | − | 0.659627i | ||||
\(167\) | 1.97769 | + | 6.08669i | 0.153038 | + | 0.471002i | 0.997957 | − | 0.0638921i | \(-0.0203514\pi\) |
−0.844919 | + | 0.534894i | \(0.820351\pi\) | |||||||
\(168\) | 1.53994 | − | 4.73944i | 0.118809 | − | 0.365656i | ||||
\(169\) | 8.52570 | + | 6.19428i | 0.655823 | + | 0.476483i | ||||
\(170\) | −1.60737 | + | 4.94697i | −0.123279 | + | 0.379415i | ||||
\(171\) | 1.24608 | − | 3.83505i | 0.0952904 | − | 0.293274i | ||||
\(172\) | 5.60172 | + | 4.06989i | 0.427127 | + | 0.310326i | ||||
\(173\) | 0.240656 | − | 0.740662i | 0.0182967 | − | 0.0563115i | −0.941491 | − | 0.337037i | \(-0.890575\pi\) |
0.959788 | + | 0.280726i | \(0.0905752\pi\) | |||||||
\(174\) | −1.32840 | − | 4.08841i | −0.100706 | − | 0.309941i | ||||
\(175\) | −4.03161 | + | 2.92914i | −0.304761 | + | 0.221422i | ||||
\(176\) | −1.17582 | − | 3.61880i | −0.0886308 | − | 0.272778i | ||||
\(177\) | −4.16974 | − | 3.02949i | −0.313417 | − | 0.227711i | ||||
\(178\) | 5.21612 | + | 3.78973i | 0.390965 | + | 0.284053i | ||||
\(179\) | −2.43821 | + | 1.77147i | −0.182241 | + | 0.132406i | −0.675165 | − | 0.737666i | \(-0.735928\pi\) |
0.492925 | + | 0.870072i | \(0.335928\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 18.2338 | 1.35530 | 0.677652 | − | 0.735383i | \(-0.262998\pi\) | ||||
0.677652 | + | 0.735383i | \(0.262998\pi\) | |||||||
\(182\) | −6.32547 | + | 4.59572i | −0.468875 | + | 0.340657i | ||||
\(183\) | 2.61393 | − | 8.04485i | 0.193227 | − | 0.594693i | ||||
\(184\) | −1.05590 | − | 3.24973i | −0.0778422 | − | 0.239574i | ||||
\(185\) | −10.7227 | −0.788346 | ||||||||
\(186\) | −5.47277 | + | 1.02410i | −0.401283 | + | 0.0750904i | ||||
\(187\) | −19.7921 | −1.44734 | ||||||||
\(188\) | −0.665153 | − | 2.04713i | −0.0485113 | − | 0.149302i | ||||
\(189\) | −1.53994 | + | 4.73944i | −0.112014 | + | 0.344744i | ||||
\(190\) | 3.26229 | − | 2.37019i | 0.236671 | − | 0.171952i | ||||
\(191\) | 14.1453 | 1.02352 | 0.511759 | − | 0.859129i | \(-0.328994\pi\) | ||||
0.511759 | + | 0.859129i | \(0.328994\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.7511 | − | 9.26418i | 0.917841 | − | 0.666851i | −0.0251447 | − | 0.999684i | \(-0.508005\pi\) |
0.942986 | + | 0.332833i | \(0.108005\pi\) | |||||||
\(194\) | 2.87578 | + | 2.08938i | 0.206469 | + | 0.150009i | ||||
\(195\) | −1.26932 | − | 0.922216i | −0.0908980 | − | 0.0660412i | ||||
\(196\) | 5.51093 | + | 16.9609i | 0.393638 | + | 1.21149i | ||||
\(197\) | 5.36662 | − | 3.89908i | 0.382356 | − | 0.277798i | −0.379960 | − | 0.925003i | \(-0.624062\pi\) |
0.762316 | + | 0.647205i | \(0.224062\pi\) | |||||||
\(198\) | 1.17582 | + | 3.61880i | 0.0835619 | + | 0.257177i | ||||
\(199\) | 7.06054 | − | 21.7301i | 0.500508 | − | 1.54041i | −0.307685 | − | 0.951488i | \(-0.599554\pi\) |
0.808193 | − | 0.588918i | \(-0.200446\pi\) | |||||||
\(200\) | 0.809017 | + | 0.587785i | 0.0572061 | + | 0.0415627i | ||||
\(201\) | 0.597996 | − | 1.84044i | 0.0421794 | − | 0.129815i | ||||
\(202\) | −5.90362 | + | 18.1695i | −0.415377 | + | 1.27840i | ||||
\(203\) | 17.3311 | + | 12.5918i | 1.21641 | + | 0.883771i | ||||
\(204\) | −1.60737 | + | 4.94697i | −0.112538 | + | 0.346357i | ||||
\(205\) | 1.39947 | + | 4.30712i | 0.0977432 | + | 0.300822i | ||||
\(206\) | 13.0505 | − | 9.48176i | 0.909273 | − | 0.660625i | ||||
\(207\) | 1.05590 | + | 3.24973i | 0.0733903 | + | 0.225872i | ||||
\(208\) | 1.26932 | + | 0.922216i | 0.0880116 | + | 0.0639442i | ||||
\(209\) | 12.4131 | + | 9.01867i | 0.858634 | + | 0.623834i | ||||
\(210\) | −4.03161 | + | 2.92914i | −0.278208 | + | 0.202130i | ||||
\(211\) | −20.9742 | −1.44392 | −0.721962 | − | 0.691933i | \(-0.756759\pi\) | ||||
−0.721962 | + | 0.691933i | \(0.756759\pi\) | |||||||
\(212\) | 10.2168 | 0.701694 | ||||||||
\(213\) | −6.60268 | + | 4.79713i | −0.452408 | + | 0.328694i | ||||
\(214\) | −1.11430 | + | 3.42948i | −0.0761723 | + | 0.234434i | ||||
\(215\) | −2.13967 | − | 6.58522i | −0.145924 | − | 0.449108i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 19.0644 | − | 20.1593i | 1.29417 | − | 1.36850i | ||||
\(218\) | 1.82896 | 0.123873 | ||||||||
\(219\) | 4.48215 | + | 13.7946i | 0.302876 | + | 0.932156i | ||||
\(220\) | −1.17582 | + | 3.61880i | −0.0792738 | + | 0.243980i | ||||
\(221\) | 6.60243 | − | 4.79695i | 0.444128 | − | 0.322678i | ||||
\(222\) | −10.7227 | −0.719658 | ||||||||
\(223\) | 2.85280 | 0.191038 | 0.0955188 | − | 0.995428i | \(-0.469549\pi\) | ||||
0.0955188 | + | 0.995428i | \(0.469549\pi\) | |||||||
\(224\) | 4.03161 | − | 2.92914i | 0.269373 | − | 0.195711i | ||||
\(225\) | −0.809017 | − | 0.587785i | −0.0539345 | − | 0.0391857i | ||||
\(226\) | 5.70475 | + | 4.14474i | 0.379474 | + | 0.275704i | ||||
\(227\) | 1.05735 | + | 3.25419i | 0.0701787 | + | 0.215988i | 0.979995 | − | 0.199024i | \(-0.0637773\pi\) |
−0.909816 | + | 0.415012i | \(0.863777\pi\) | |||||||
\(228\) | 3.26229 | − | 2.37019i | 0.216050 | − | 0.156970i | ||||
\(229\) | 2.71639 | + | 8.36020i | 0.179504 | + | 0.552457i | 0.999810 | − | 0.0194672i | \(-0.00619699\pi\) |
−0.820306 | + | 0.571925i | \(0.806197\pi\) | |||||||
\(230\) | −1.05590 | + | 3.24973i | −0.0696241 | + | 0.214281i | ||||
\(231\) | −15.3404 | − | 11.1455i | −1.00933 | − | 0.733318i | ||||
\(232\) | 1.32840 | − | 4.08841i | 0.0872140 | − | 0.268417i | ||||
\(233\) | 4.73125 | − | 14.5613i | 0.309954 | − | 0.953941i | −0.667828 | − | 0.744316i | \(-0.732776\pi\) |
0.977782 | − | 0.209625i | \(-0.0672243\pi\) | |||||||
\(234\) | −1.26932 | − | 0.922216i | −0.0829781 | − | 0.0602871i | ||||
\(235\) | −0.665153 | + | 2.04713i | −0.0433898 | + | 0.133540i | ||||
\(236\) | −1.59270 | − | 4.90182i | −0.103676 | − | 0.319082i | ||||
\(237\) | 7.75630 | − | 5.63528i | 0.503826 | − | 0.366051i | ||||
\(238\) | −8.01006 | − | 24.6524i | −0.519215 | − | 1.59798i | ||||
\(239\) | −23.9532 | − | 17.4030i | −1.54940 | − | 1.12571i | −0.944075 | − | 0.329730i | \(-0.893042\pi\) |
−0.605327 | − | 0.795977i | \(-0.706958\pi\) | |||||||
\(240\) | 0.809017 | + | 0.587785i | 0.0522218 | + | 0.0379414i | ||||
\(241\) | −18.0030 | + | 13.0800i | −1.15968 | + | 0.842554i | −0.989737 | − | 0.142901i | \(-0.954357\pi\) |
−0.169939 | + | 0.985455i | \(0.554357\pi\) | |||||||
\(242\) | −3.47829 | −0.223593 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.84336 | − | 4.97199i | 0.438101 | − | 0.318299i | ||||
\(245\) | 5.51093 | − | 16.9609i | 0.352080 | − | 1.08359i | ||||
\(246\) | 1.39947 | + | 4.30712i | 0.0892269 | + | 0.274612i | ||||
\(247\) | −6.32672 | −0.402560 | ||||||||
\(248\) | −5.02951 | − | 2.38830i | −0.319374 | − | 0.151657i | ||||
\(249\) | −14.4589 | −0.916293 | ||||||||
\(250\) | −0.309017 | − | 0.951057i | −0.0195440 | − | 0.0601501i | ||||
\(251\) | −0.442864 | + | 1.36300i | −0.0279533 | + | 0.0860316i | −0.964060 | − | 0.265685i | \(-0.914402\pi\) |
0.936107 | + | 0.351717i | \(0.114402\pi\) | |||||||
\(252\) | −4.03161 | + | 2.92914i | −0.253968 | + | 0.184518i | ||||
\(253\) | −13.0017 | −0.817410 | ||||||||
\(254\) | 1.25888 | 0.0789891 | ||||||||
\(255\) | 4.20814 | − | 3.05739i | 0.263524 | − | 0.191461i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −5.93986 | − | 4.31556i | −0.370518 | − | 0.269197i | 0.386907 | − | 0.922119i | \(-0.373543\pi\) |
−0.757426 | + | 0.652921i | \(0.773543\pi\) | |||||||
\(258\) | −2.13967 | − | 6.58522i | −0.133210 | − | 0.409978i | ||||
\(259\) | 43.2296 | − | 31.4081i | 2.68616 | − | 1.95161i | ||||
\(260\) | −0.484838 | − | 1.49218i | −0.0300683 | − | 0.0925409i | ||||
\(261\) | −1.32840 | + | 4.08841i | −0.0822261 | + | 0.253066i | ||||
\(262\) | −14.1673 | − | 10.2932i | −0.875261 | − | 0.635914i | ||||
\(263\) | 0.760163 | − | 2.33954i | 0.0468737 | − | 0.144262i | −0.924880 | − | 0.380258i | \(-0.875835\pi\) |
0.971754 | + | 0.235996i | \(0.0758352\pi\) | |||||||
\(264\) | −1.17582 | + | 3.61880i | −0.0723667 | + | 0.222722i | ||||
\(265\) | −8.26558 | − | 6.00530i | −0.507751 | − | 0.368902i | ||||
\(266\) | −6.20967 | + | 19.1114i | −0.380739 | + | 1.17179i | ||||
\(267\) | −1.99238 | − | 6.13192i | −0.121932 | − | 0.375267i | ||||
\(268\) | 1.56557 | − | 1.13746i | 0.0956326 | − | 0.0694811i | ||||
\(269\) | −6.02334 | − | 18.5379i | −0.367250 | − | 1.13028i | −0.948560 | − | 0.316596i | \(-0.897460\pi\) |
0.581311 | − | 0.813682i | \(-0.302540\pi\) | |||||||
\(270\) | −0.809017 | − | 0.587785i | −0.0492352 | − | 0.0357715i | ||||
\(271\) | −5.53896 | − | 4.02429i | −0.336468 | − | 0.244458i | 0.406702 | − | 0.913561i | \(-0.366679\pi\) |
−0.743170 | + | 0.669103i | \(0.766679\pi\) | |||||||
\(272\) | −4.20814 | + | 3.05739i | −0.255156 | + | 0.185382i | ||||
\(273\) | 7.81871 | 0.473210 | ||||||||
\(274\) | 6.84355 | 0.413434 | ||||||||
\(275\) | 3.07834 | − | 2.23654i | 0.185631 | − | 0.134869i | ||||
\(276\) | −1.05590 | + | 3.24973i | −0.0635579 | + | 0.195611i | ||||
\(277\) | −1.86603 | − | 5.74304i | −0.112119 | − | 0.345066i | 0.879217 | − | 0.476422i | \(-0.158067\pi\) |
−0.991335 | + | 0.131357i | \(0.958067\pi\) | |||||||
\(278\) | 13.6084 | 0.816175 | ||||||||
\(279\) | 5.02951 | + | 2.38830i | 0.301109 | + | 0.142984i | ||||
\(280\) | −4.98335 | −0.297812 | ||||||||
\(281\) | 9.75237 | + | 30.0147i | 0.581777 | + | 1.79053i | 0.611843 | + | 0.790979i | \(0.290428\pi\) |
−0.0300659 | + | 0.999548i | \(0.509572\pi\) | |||||||
\(282\) | −0.665153 | + | 2.04713i | −0.0396093 | + | 0.121905i | ||||
\(283\) | −3.06059 | + | 2.22365i | −0.181933 | + | 0.132182i | −0.675024 | − | 0.737795i | \(-0.735867\pi\) |
0.493091 | + | 0.869978i | \(0.335867\pi\) | |||||||
\(284\) | −8.16136 | −0.484287 | ||||||||
\(285\) | −4.03241 | −0.238860 | ||||||||
\(286\) | 4.82981 | − | 3.50906i | 0.285593 | − | 0.207495i | ||||
\(287\) | −18.2583 | − | 13.2654i | −1.07775 | − | 0.783032i | ||||
\(288\) | 0.809017 | + | 0.587785i | 0.0476718 | + | 0.0346356i | ||||
\(289\) | 3.10750 | + | 9.56392i | 0.182794 | + | 0.562583i | ||||
\(290\) | −3.47781 | + | 2.52677i | −0.204224 | + | 0.148377i | ||||
\(291\) | −1.09845 | − | 3.38069i | −0.0643924 | − | 0.198179i | ||||
\(292\) | −4.48215 | + | 13.7946i | −0.262298 | + | 0.807271i | ||||
\(293\) | −2.73649 | − | 1.98817i | −0.159867 | − | 0.116150i | 0.504976 | − | 0.863134i | \(-0.331501\pi\) |
−0.664843 | + | 0.746983i | \(0.731501\pi\) | |||||||
\(294\) | 5.51093 | − | 16.9609i | 0.321404 | − | 0.989179i | ||||
\(295\) | −1.59270 | + | 4.90182i | −0.0927305 | + | 0.285395i | ||||
\(296\) | −8.67481 | − | 6.30262i | −0.504213 | − | 0.366332i | ||||
\(297\) | 1.17582 | − | 3.61880i | 0.0682280 | − | 0.209984i | ||||
\(298\) | −2.36310 | − | 7.27289i | −0.136891 | − | 0.421307i | ||||
\(299\) | 4.33723 | − | 3.15119i | 0.250829 | − | 0.182238i | ||||
\(300\) | −0.309017 | − | 0.951057i | −0.0178411 | − | 0.0549093i | ||||
\(301\) | 27.9153 | + | 20.2817i | 1.60901 | + | 1.16902i | ||||
\(302\) | 8.09620 | + | 5.88224i | 0.465884 | + | 0.338485i | ||||
\(303\) | 15.4559 | − | 11.2294i | 0.887917 | − | 0.645109i | ||||
\(304\) | 4.03241 | 0.231275 | ||||||||
\(305\) | −8.45886 | −0.484353 | ||||||||
\(306\) | 4.20814 | − | 3.05739i | 0.240563 | − | 0.174780i | ||||
\(307\) | 1.61899 | − | 4.98273i | 0.0924004 | − | 0.284379i | −0.894167 | − | 0.447733i | \(-0.852231\pi\) |
0.986567 | + | 0.163354i | \(0.0522314\pi\) | |||||||
\(308\) | −5.85952 | − | 18.0337i | −0.333877 | − | 1.02757i | ||||
\(309\) | −16.1313 | −0.917679 | ||||||||
\(310\) | 2.66515 | + | 4.88845i | 0.151371 | + | 0.277645i | ||||
\(311\) | 14.8676 | 0.843066 | 0.421533 | − | 0.906813i | \(-0.361492\pi\) | ||||
0.421533 | + | 0.906813i | \(0.361492\pi\) | |||||||
\(312\) | −0.484838 | − | 1.49218i | −0.0274485 | − | 0.0844779i | ||||
\(313\) | −7.15490 | + | 22.0205i | −0.404419 | + | 1.24467i | 0.516960 | + | 0.856009i | \(0.327063\pi\) |
−0.921379 | + | 0.388664i | \(0.872937\pi\) | |||||||
\(314\) | −6.51005 | + | 4.72983i | −0.367384 | + | 0.266920i | ||||
\(315\) | 4.98335 | 0.280780 | ||||||||
\(316\) | 9.58732 | 0.539329 | ||||||||
\(317\) | −19.2994 | + | 14.0218i | −1.08396 | + | 0.787543i | −0.978369 | − | 0.206867i | \(-0.933673\pi\) |
−0.105591 | + | 0.994410i | \(0.533673\pi\) | |||||||
\(318\) | −8.26558 | − | 6.00530i | −0.463511 | − | 0.336760i | ||||
\(319\) | −13.2332 | − | 9.61447i | −0.740916 | − | 0.538307i | ||||
\(320\) | 0.309017 | + | 0.951057i | 0.0172746 | + | 0.0531657i | ||||
\(321\) | 2.91729 | − | 2.11953i | 0.162827 | − | 0.118301i | ||||
\(322\) | −5.26193 | − | 16.1945i | −0.293236 | − | 0.902487i | ||||
\(323\) | 6.48157 | − | 19.9482i | 0.360644 | − | 1.10995i | ||||
\(324\) | −0.809017 | − | 0.587785i | −0.0449454 | − | 0.0326547i | ||||
\(325\) | −0.484838 | + | 1.49218i | −0.0268939 | + | 0.0827711i | ||||
\(326\) | 4.95752 | − | 15.2577i | 0.274571 | − | 0.845044i | ||||
\(327\) | −1.47966 | − | 1.07504i | −0.0818255 | − | 0.0594497i | ||||
\(328\) | −1.39947 | + | 4.30712i | −0.0772727 | + | 0.237821i | ||||
\(329\) | −3.31469 | − | 10.2016i | −0.182745 | − | 0.562430i | ||||
\(330\) | 3.07834 | − | 2.23654i | 0.169457 | − | 0.123118i | ||||
\(331\) | 7.59627 | + | 23.3789i | 0.417529 | + | 1.28502i | 0.909969 | + | 0.414675i | \(0.136105\pi\) |
−0.492441 | + | 0.870346i | \(0.663895\pi\) | |||||||
\(332\) | −11.6975 | − | 8.49870i | −0.641982 | − | 0.466427i | ||||
\(333\) | 8.67481 | + | 6.30262i | 0.475377 | + | 0.345382i | ||||
\(334\) | 5.17765 | − | 3.76178i | 0.283308 | − | 0.205836i | ||||
\(335\) | −1.93515 | −0.105729 | ||||||||
\(336\) | −4.98335 | −0.271864 | ||||||||
\(337\) | −3.91658 | + | 2.84556i | −0.213350 | + | 0.155008i | −0.689328 | − | 0.724449i | \(-0.742094\pi\) |
0.475978 | + | 0.879457i | \(0.342094\pi\) | |||||||
\(338\) | 3.25653 | − | 10.0226i | 0.177132 | − | 0.545155i | ||||
\(339\) | −2.17902 | − | 6.70633i | −0.118348 | − | 0.364238i | ||||
\(340\) | 5.20155 | 0.282094 | ||||||||
\(341\) | −14.5566 | + | 15.3926i | −0.788284 | + | 0.833556i | ||||
\(342\) | −4.03241 | −0.218048 | ||||||||
\(343\) | 16.6833 | + | 51.3459i | 0.900813 | + | 2.77242i | ||||
\(344\) | 2.13967 | − | 6.58522i | 0.115363 | − | 0.355051i | ||||
\(345\) | 2.76439 | − | 2.00845i | 0.148830 | − | 0.108131i | ||||
\(346\) | −0.778778 | −0.0418674 | ||||||||
\(347\) | −15.3813 | −0.825709 | −0.412855 | − | 0.910797i | \(-0.635468\pi\) | ||||
−0.412855 | + | 0.910797i | \(0.635468\pi\) | |||||||
\(348\) | −3.47781 | + | 2.52677i | −0.186430 | + | 0.135449i | ||||
\(349\) | −18.1404 | − | 13.1798i | −0.971035 | − | 0.705498i | −0.0153478 | − | 0.999882i | \(-0.504886\pi\) |
−0.955687 | + | 0.294384i | \(0.904886\pi\) | |||||||
\(350\) | 4.03161 | + | 2.92914i | 0.215499 | + | 0.156569i | ||||
\(351\) | 0.484838 | + | 1.49218i | 0.0258787 | + | 0.0796465i | ||||
\(352\) | −3.07834 | + | 2.23654i | −0.164076 | + | 0.119208i | ||||
\(353\) | 10.3408 | + | 31.8257i | 0.550385 | + | 1.69391i | 0.707830 | + | 0.706383i | \(0.249674\pi\) |
−0.157444 | + | 0.987528i | \(0.550326\pi\) | |||||||
\(354\) | −1.59270 | + | 4.90182i | −0.0846510 | + | 0.260529i | ||||
\(355\) | 6.60268 | + | 4.79713i | 0.350434 | + | 0.254605i | ||||
\(356\) | 1.99238 | − | 6.13192i | 0.105596 | − | 0.324991i | ||||
\(357\) | −8.01006 | + | 24.6524i | −0.423938 | + | 1.30475i | ||||
\(358\) | 2.43821 | + | 1.77147i | 0.128864 | + | 0.0936249i | ||||
\(359\) | −7.59403 | + | 23.3720i | −0.400798 | + | 1.23353i | 0.523556 | + | 0.851991i | \(0.324605\pi\) |
−0.924354 | + | 0.381537i | \(0.875395\pi\) | |||||||
\(360\) | −0.309017 | − | 0.951057i | −0.0162866 | − | 0.0501251i | ||||
\(361\) | 2.21642 | − | 1.61032i | 0.116654 | − | 0.0847539i | ||||
\(362\) | −5.63454 | − | 17.3413i | −0.296145 | − | 0.911440i | ||||
\(363\) | 2.81400 | + | 2.04449i | 0.147697 | + | 0.107308i | ||||
\(364\) | 6.32547 | + | 4.59572i | 0.331545 | + | 0.240881i | ||||
\(365\) | 11.7344 | − | 8.52556i | 0.614208 | − | 0.446248i | ||||
\(366\) | −8.45886 | −0.442152 | ||||||||
\(367\) | −2.19500 | −0.114578 | −0.0572890 | − | 0.998358i | \(-0.518246\pi\) | ||||
−0.0572890 | + | 0.998358i | \(0.518246\pi\) | |||||||
\(368\) | −2.76439 | + | 2.00845i | −0.144104 | + | 0.104697i | ||||
\(369\) | 1.39947 | − | 4.30712i | 0.0728534 | − | 0.224220i | ||||
\(370\) | 3.31348 | + | 10.1979i | 0.172260 | + | 0.530161i | ||||
\(371\) | 50.9140 | 2.64332 | ||||||||
\(372\) | 2.66515 | + | 4.88845i | 0.138182 | + | 0.253454i | ||||
\(373\) | 4.40476 | 0.228070 | 0.114035 | − | 0.993477i | \(-0.463622\pi\) | ||||
0.114035 | + | 0.993477i | \(0.463622\pi\) | |||||||
\(374\) | 6.11609 | + | 18.8234i | 0.316255 | + | 0.973334i | ||||
\(375\) | −0.309017 | + | 0.951057i | −0.0159576 | + | 0.0491123i | ||||
\(376\) | −1.74139 | + | 1.26520i | −0.0898055 | + | 0.0652475i | ||||
\(377\) | 6.74469 | 0.347369 | ||||||||
\(378\) | 4.98335 | 0.256316 | ||||||||
\(379\) | −22.0796 | + | 16.0418i | −1.13415 | + | 0.824011i | −0.986294 | − | 0.164997i | \(-0.947238\pi\) |
−0.147860 | + | 0.989008i | \(0.547238\pi\) | |||||||
\(380\) | −3.26229 | − | 2.37019i | −0.167352 | − | 0.121588i | ||||
\(381\) | −1.01845 | − | 0.739951i | −0.0521770 | − | 0.0379088i | ||||
\(382\) | −4.37114 | − | 13.4530i | −0.223647 | − | 0.688314i | ||||
\(383\) | −19.9371 | + | 14.4852i | −1.01874 | + | 0.740158i | −0.966024 | − | 0.258451i | \(-0.916788\pi\) |
−0.0527161 | + | 0.998610i | \(0.516788\pi\) | |||||||
\(384\) | 0.309017 | + | 0.951057i | 0.0157695 | + | 0.0485334i | ||||
\(385\) | −5.85952 | + | 18.0337i | −0.298629 | + | 0.919085i | ||||
\(386\) | −12.7511 | − | 9.26418i | −0.649012 | − | 0.471535i | ||||
\(387\) | −2.13967 | + | 6.58522i | −0.108765 | + | 0.334746i | ||||
\(388\) | 1.09845 | − | 3.38069i | 0.0557654 | − | 0.171628i | ||||
\(389\) | 18.1578 | + | 13.1924i | 0.920635 | + | 0.668881i | 0.943682 | − | 0.330854i | \(-0.107337\pi\) |
−0.0230467 | + | 0.999734i | \(0.507337\pi\) | |||||||
\(390\) | −0.484838 | + | 1.49218i | −0.0245507 | + | 0.0755593i | ||||
\(391\) | 5.49233 | + | 16.9036i | 0.277759 | + | 0.854854i | ||||
\(392\) | 14.4278 | − | 10.4824i | 0.728714 | − | 0.529442i | ||||
\(393\) | 5.41144 | + | 16.6547i | 0.272971 | + | 0.840119i | ||||
\(394\) | −5.36662 | − | 3.89908i | −0.270367 | − | 0.196433i | ||||
\(395\) | −7.75630 | − | 5.63528i | −0.390262 | − | 0.283542i | ||||
\(396\) | 3.07834 | − | 2.23654i | 0.154692 | − | 0.112391i | ||||
\(397\) | 39.3286 | 1.97385 | 0.986924 | − | 0.161188i | \(-0.0515326\pi\) | ||||
0.986924 | + | 0.161188i | \(0.0515326\pi\) | |||||||
\(398\) | −22.8484 | −1.14529 | ||||||||
\(399\) | 16.2571 | − | 11.8115i | 0.813874 | − | 0.591314i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | 5.50521 | + | 16.9433i | 0.274917 | + | 0.846107i | 0.989241 | + | 0.146292i | \(0.0467340\pi\) |
−0.714325 | + | 0.699815i | \(0.753266\pi\) | |||||||
\(402\) | −1.93515 | −0.0965167 | ||||||||
\(403\) | 1.12527 | − | 8.66286i | 0.0560538 | − | 0.431528i | ||||
\(404\) | 19.1045 | 0.950485 | ||||||||
\(405\) | 0.309017 | + | 0.951057i | 0.0153552 | + | 0.0472584i | ||||
\(406\) | 6.61990 | − | 20.3739i | 0.328540 | − | 1.01114i | ||||
\(407\) | −33.0080 | + | 23.9817i | −1.63614 | + | 1.18873i | ||||
\(408\) | 5.20155 | 0.257515 | ||||||||
\(409\) | −22.3579 | −1.10553 | −0.552764 | − | 0.833338i | \(-0.686427\pi\) | ||||
−0.552764 | + | 0.833338i | \(0.686427\pi\) | |||||||
\(410\) | 3.66386 | − | 2.66195i | 0.180945 | − | 0.131464i | ||||
\(411\) | −5.53654 | − | 4.02253i | −0.273098 | − | 0.198417i | ||||
\(412\) | −13.0505 | − | 9.48176i | −0.642953 | − | 0.467133i | ||||
\(413\) | −7.93697 | − | 24.4275i | −0.390553 | − | 1.20200i | ||||
\(414\) | 2.76439 | − | 2.00845i | 0.135862 | − | 0.0987097i | ||||
\(415\) | 4.46803 | + | 13.7512i | 0.219327 | + | 0.675020i | ||||
\(416\) | 0.484838 | − | 1.49218i | 0.0237711 | − | 0.0731600i | ||||
\(417\) | −11.0094 | − | 7.99879i | −0.539132 | − | 0.391702i | ||||
\(418\) | 4.74139 | − | 14.5925i | 0.231909 | − | 0.713743i | ||||
\(419\) | −4.38617 | + | 13.4993i | −0.214279 | + | 0.659482i | 0.784925 | + | 0.619590i | \(0.212701\pi\) |
−0.999204 | + | 0.0398914i | \(0.987299\pi\) | |||||||
\(420\) | 4.03161 | + | 2.92914i | 0.196723 | + | 0.142927i | ||||
\(421\) | −5.51195 | + | 16.9640i | −0.268636 | + | 0.826776i | 0.722198 | + | 0.691687i | \(0.243132\pi\) |
−0.990833 | + | 0.135089i | \(0.956868\pi\) | |||||||
\(422\) | 6.48139 | + | 19.9477i | 0.315509 | + | 0.971037i | ||||
\(423\) | 1.74139 | − | 1.26520i | 0.0846694 | − | 0.0615160i | ||||
\(424\) | −3.15717 | − | 9.71677i | −0.153326 | − | 0.471888i | ||||
\(425\) | −4.20814 | − | 3.05739i | −0.204125 | − | 0.148305i | ||||
\(426\) | 6.60268 | + | 4.79713i | 0.319901 | + | 0.232421i | ||||
\(427\) | 34.1028 | − | 24.7772i | 1.65035 | − | 1.19905i | ||||
\(428\) | 3.60597 | 0.174301 | ||||||||
\(429\) | −5.96998 | −0.288233 | ||||||||
\(430\) | −5.60172 | + | 4.06989i | −0.270139 | + | 0.196268i | ||||
\(431\) | 7.88331 | − | 24.2623i | 0.379726 | − | 1.16868i | −0.560509 | − | 0.828148i | \(-0.689394\pi\) |
0.940235 | − | 0.340527i | \(-0.110606\pi\) | |||||||
\(432\) | −0.309017 | − | 0.951057i | −0.0148676 | − | 0.0457577i | ||||
\(433\) | −35.6182 | −1.71170 | −0.855852 | − | 0.517221i | \(-0.826966\pi\) | ||||
−0.855852 | + | 0.517221i | \(0.826966\pi\) | |||||||
\(434\) | −25.0638 | − | 11.9017i | −1.20310 | − | 0.571302i | ||||
\(435\) | 4.29881 | 0.206112 | ||||||||
\(436\) | −0.565181 | − | 1.73945i | −0.0270672 | − | 0.0833044i | ||||
\(437\) | 4.25783 | − | 13.1043i | 0.203680 | − | 0.626862i | ||||
\(438\) | 11.7344 | − | 8.52556i | 0.560693 | − | 0.407367i | ||||
\(439\) | −18.1281 | −0.865206 | −0.432603 | − | 0.901584i | \(-0.642405\pi\) | ||||
−0.432603 | + | 0.901584i | \(0.642405\pi\) | |||||||
\(440\) | 3.80504 | 0.181398 | ||||||||
\(441\) | −14.4278 | + | 10.4824i | −0.687038 | + | 0.499162i | ||||
\(442\) | −6.60243 | − | 4.79695i | −0.314046 | − | 0.228168i | ||||
\(443\) | 8.20713 | + | 5.96283i | 0.389933 | + | 0.283303i | 0.765428 | − | 0.643522i | \(-0.222527\pi\) |
−0.375495 | + | 0.926824i | \(0.622527\pi\) | |||||||
\(444\) | 3.31348 | + | 10.1979i | 0.157251 | + | 0.483969i | ||||
\(445\) | −5.21612 | + | 3.78973i | −0.247268 | + | 0.179651i | ||||
\(446\) | −0.881564 | − | 2.71317i | −0.0417432 | − | 0.128472i | ||||
\(447\) | −2.36310 | + | 7.27289i | −0.111771 | + | 0.343996i | ||||
\(448\) | −4.03161 | − | 2.92914i | −0.190476 | − | 0.138389i | ||||
\(449\) | 7.86329 | − | 24.2007i | 0.371092 | − | 1.14210i | −0.574986 | − | 0.818163i | \(-0.694992\pi\) |
0.946078 | − | 0.323940i | \(-0.105008\pi\) | |||||||
\(450\) | −0.309017 | + | 0.951057i | −0.0145672 | + | 0.0448332i | ||||
\(451\) | 13.9411 | + | 10.1288i | 0.656461 | + | 0.476947i | ||||
\(452\) | 2.17902 | − | 6.70633i | 0.102492 | − | 0.315439i | ||||
\(453\) | −3.09247 | − | 9.51766i | −0.145297 | − | 0.447179i | ||||
\(454\) | 2.76818 | − | 2.01120i | 0.129917 | − | 0.0943902i | ||||
\(455\) | −2.41611 | − | 7.43603i | −0.113269 | − | 0.348607i | ||||
\(456\) | −3.26229 | − | 2.37019i | −0.152771 | − | 0.110994i | ||||
\(457\) | −5.21387 | − | 3.78810i | −0.243895 | − | 0.177200i | 0.459122 | − | 0.888373i | \(-0.348164\pi\) |
−0.703017 | + | 0.711173i | \(0.748164\pi\) | |||||||
\(458\) | 7.11161 | − | 5.16689i | 0.332304 | − | 0.241433i | ||||
\(459\) | −5.20155 | −0.242787 | ||||||||
\(460\) | 3.41697 | 0.159317 | ||||||||
\(461\) | −24.9063 | + | 18.0955i | −1.16000 | + | 0.842789i | −0.989778 | − | 0.142616i | \(-0.954448\pi\) |
−0.170222 | + | 0.985406i | \(0.554448\pi\) | |||||||
\(462\) | −5.85952 | + | 18.0337i | −0.272610 | + | 0.839006i | ||||
\(463\) | 4.25118 | + | 13.0838i | 0.197569 | + | 0.608055i | 0.999937 | + | 0.0112253i | \(0.00357319\pi\) |
−0.802368 | + | 0.596830i | \(0.796427\pi\) | |||||||
\(464\) | −4.29881 | −0.199567 | ||||||||
\(465\) | 0.717206 | − | 5.52138i | 0.0332596 | − | 0.256048i | ||||
\(466\) | −15.3106 | −0.709251 | ||||||||
\(467\) | 4.11345 | + | 12.6599i | 0.190348 | + | 0.585830i | 0.999999 | − | 0.00108088i | \(-0.000344054\pi\) |
−0.809652 | + | 0.586910i | \(0.800344\pi\) | |||||||
\(468\) | −0.484838 | + | 1.49218i | −0.0224116 | + | 0.0689759i | ||||
\(469\) | 7.80179 | − | 5.66833i | 0.360253 | − | 0.261739i | ||||
\(470\) | 2.15248 | 0.0992865 | ||||||||
\(471\) | 8.04687 | 0.370780 | ||||||||
\(472\) | −4.16974 | + | 3.02949i | −0.191928 | + | 0.139444i | ||||
\(473\) | −21.3148 | − | 15.4861i | −0.980054 | − | 0.712051i | ||||
\(474\) | −7.75630 | − | 5.63528i | −0.356259 | − | 0.258837i | ||||
\(475\) | 1.24608 | + | 3.83505i | 0.0571743 | + | 0.175964i | ||||
\(476\) | −20.9706 | + | 15.2360i | −0.961187 | + | 0.698343i | ||||
\(477\) | 3.15717 | + | 9.71677i | 0.144557 | + | 0.444901i | ||||
\(478\) | −9.14930 | + | 28.1587i | −0.418479 | + | 1.28795i | ||||
\(479\) | 19.0548 | + | 13.8441i | 0.870638 | + | 0.632555i | 0.930758 | − | 0.365636i | \(-0.119148\pi\) |
−0.0601203 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(480\) | 0.309017 | − | 0.951057i | 0.0141046 | − | 0.0434096i | ||||
\(481\) | 5.19875 | − | 16.0001i | 0.237043 | − | 0.729542i | ||||
\(482\) | 18.0030 | + | 13.0800i | 0.820015 | + | 0.595776i | ||||
\(483\) | −5.26193 | + | 16.1945i | −0.239426 | + | 0.736877i | ||||
\(484\) | 1.07485 | + | 3.30805i | 0.0488569 | + | 0.150366i | ||||
\(485\) | −2.87578 | + | 2.08938i | −0.130583 | + | 0.0948738i | ||||
\(486\) | 0.309017 | + | 0.951057i | 0.0140173 | + | 0.0431408i | ||||
\(487\) | −25.7404 | − | 18.7015i | −1.16641 | − | 0.847446i | −0.175834 | − | 0.984420i | \(-0.556262\pi\) |
−0.990575 | + | 0.136974i | \(0.956262\pi\) | |||||||
\(488\) | −6.84336 | − | 4.97199i | −0.309784 | − | 0.225072i | ||||
\(489\) | −12.9789 | + | 9.42976i | −0.586928 | + | 0.426428i | ||||
\(490\) | −17.8337 | −0.805646 | ||||||||
\(491\) | −20.1959 | −0.911426 | −0.455713 | − | 0.890127i | \(-0.650616\pi\) | ||||
−0.455713 | + | 0.890127i | \(0.650616\pi\) | |||||||
\(492\) | 3.66386 | − | 2.66195i | 0.165179 | − | 0.120010i | ||||
\(493\) | −6.90976 | + | 21.2660i | −0.311200 | + | 0.957774i | ||||
\(494\) | 1.95507 | + | 6.01707i | 0.0879625 | + | 0.270721i | ||||
\(495\) | −3.80504 | −0.171024 | ||||||||
\(496\) | −0.717206 | + | 5.52138i | −0.0322035 | + | 0.247917i | ||||
\(497\) | −40.6709 | −1.82434 | ||||||||
\(498\) | 4.46803 | + | 13.7512i | 0.200217 | + | 0.616206i | ||||
\(499\) | 7.26325 | − | 22.3540i | 0.325148 | − | 1.00070i | −0.646226 | − | 0.763146i | \(-0.723654\pi\) |
0.971374 | − | 0.237556i | \(-0.0763464\pi\) | |||||||
\(500\) | −0.809017 | + | 0.587785i | −0.0361803 | + | 0.0262866i | ||||
\(501\) | −6.39993 | −0.285928 | ||||||||
\(502\) | 1.43314 | 0.0639641 | ||||||||
\(503\) | −2.97500 | + | 2.16146i | −0.132649 | + | 0.0963749i | −0.652131 | − | 0.758106i | \(-0.726125\pi\) |
0.519482 | + | 0.854481i | \(0.326125\pi\) | |||||||
\(504\) | 4.03161 | + | 2.92914i | 0.179582 | + | 0.130474i | ||||
\(505\) | −15.4559 | − | 11.2294i | −0.687777 | − | 0.499700i | ||||
\(506\) | 4.01775 | + | 12.3653i | 0.178611 | + | 0.549707i | ||||
\(507\) | −8.52570 | + | 6.19428i | −0.378640 | + | 0.275098i | ||||
\(508\) | −0.389015 | − | 1.19727i | −0.0172598 | − | 0.0531201i | ||||
\(509\) | −0.442997 | + | 1.36340i | −0.0196355 | + | 0.0604318i | −0.960394 | − | 0.278645i | \(-0.910115\pi\) |
0.940759 | + | 0.339077i | \(0.110115\pi\) | |||||||
\(510\) | −4.20814 | − | 3.05739i | −0.186340 | − | 0.135384i | ||||
\(511\) | −22.3361 | + | 68.7435i | −0.988092 | + | 3.04103i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | 3.26229 | + | 2.37019i | 0.144034 | + | 0.104647i | ||||
\(514\) | −2.26883 | + | 6.98273i | −0.100074 | + | 0.307995i | ||||
\(515\) | 4.98486 | + | 15.3418i | 0.219659 | + | 0.676041i | ||||
\(516\) | −5.60172 | + | 4.06989i | −0.246602 | + | 0.179167i | ||||
\(517\) | 2.53093 | + | 7.78940i | 0.111310 | + | 0.342578i | ||||
\(518\) | −43.2296 | − | 31.4081i | −1.89940 | − | 1.37999i | ||||
\(519\) | 0.630045 | + | 0.457754i | 0.0276559 | + | 0.0200932i | ||||
\(520\) | −1.26932 | + | 0.922216i | −0.0556634 | + | 0.0404418i | ||||
\(521\) | 2.96602 | 0.129944 | 0.0649719 | − | 0.997887i | \(-0.479304\pi\) | ||||
0.0649719 | + | 0.997887i | \(0.479304\pi\) | |||||||
\(522\) | 4.29881 | 0.188154 | ||||||||
\(523\) | 7.65087 | − | 5.55868i | 0.334549 | − | 0.243064i | −0.407809 | − | 0.913067i | \(-0.633707\pi\) |
0.742358 | + | 0.670003i | \(0.233707\pi\) | |||||||
\(524\) | −5.41144 | + | 16.6547i | −0.236400 | + | 0.727564i | ||||
\(525\) | −1.53994 | − | 4.73944i | −0.0672084 | − | 0.206846i | ||||
\(526\) | −2.45994 | −0.107258 | ||||||||
\(527\) | 26.1613 | + | 12.4229i | 1.13960 | + | 0.541149i | ||||
\(528\) | 3.80504 | 0.165593 | ||||||||
\(529\) | −3.49940 | − | 10.7701i | −0.152148 | − | 0.468263i | ||||
\(530\) | −3.15717 | + | 9.71677i | −0.137139 | + | 0.422070i | ||||
\(531\) | 4.16974 | − | 3.02949i | 0.180951 | − | 0.131469i | ||||
\(532\) | 20.0949 | 0.871225 | ||||||||
\(533\) | −7.10550 | −0.307773 | ||||||||
\(534\) | −5.21612 | + | 3.78973i | −0.225724 | + | 0.163998i | ||||
\(535\) | −2.91729 | − | 2.11953i | −0.126125 | − | 0.0916354i | ||||
\(536\) | −1.56557 | − | 1.13746i | −0.0676224 | − | 0.0491306i | ||||
\(537\) | −0.931315 | − | 2.86629i | −0.0401892 | − | 0.123690i | ||||
\(538\) | −15.7693 | + | 11.4571i | −0.679863 | + | 0.493950i | ||||
\(539\) | −20.9693 | − | 64.5368i | −0.903211 | − | 2.77980i | ||||
\(540\) | −0.309017 | + | 0.951057i | −0.0132980 | + | 0.0409270i | ||||
\(541\) | −29.4923 | − | 21.4274i | −1.26797 | − | 0.921237i | −0.268854 | − | 0.963181i | \(-0.586645\pi\) |
−0.999120 | + | 0.0419442i | \(0.986645\pi\) | |||||||
\(542\) | −2.11569 | + | 6.51144i | −0.0908768 | + | 0.279690i | ||||
\(543\) | −5.63454 | + | 17.3413i | −0.241801 | + | 0.744188i | ||||
\(544\) | 4.20814 | + | 3.05739i | 0.180423 | + | 0.131085i | ||||
\(545\) | −0.565181 | + | 1.73945i | −0.0242097 | + | 0.0745097i | ||||
\(546\) | −2.41611 | − | 7.43603i | −0.103400 | − | 0.318233i | ||||
\(547\) | −11.1579 | + | 8.10670i | −0.477078 | + | 0.346618i | −0.800193 | − | 0.599742i | \(-0.795270\pi\) |
0.323115 | + | 0.946360i | \(0.395270\pi\) | |||||||
\(548\) | −2.11477 | − | 6.50860i | −0.0903386 | − | 0.278034i | ||||
\(549\) | 6.84336 | + | 4.97199i | 0.292068 | + | 0.212200i | ||||
\(550\) | −3.07834 | − | 2.23654i | −0.131261 | − | 0.0953665i | ||||
\(551\) | 14.0240 | − | 10.1890i | 0.597441 | − | 0.434066i | ||||
\(552\) | 3.41697 | 0.145436 | ||||||||
\(553\) | 47.7769 | 2.03168 | ||||||||
\(554\) | −4.88532 | + | 3.54939i | −0.207557 | + | 0.150799i | ||||
\(555\) | 3.31348 | − | 10.1979i | 0.140650 | − | 0.432875i | ||||
\(556\) | −4.20521 | − | 12.9423i | −0.178341 | − | 0.548876i | ||||
\(557\) | 29.2992 | 1.24145 | 0.620723 | − | 0.784030i | \(-0.286839\pi\) | ||||
0.620723 | + | 0.784030i | \(0.286839\pi\) | |||||||
\(558\) | 0.717206 | − | 5.52138i | 0.0303617 | − | 0.233739i | ||||
\(559\) | 10.8637 | 0.459486 | ||||||||
\(560\) | 1.53994 | + | 4.73944i | 0.0650743 | + | 0.200278i | ||||
\(561\) | 6.11609 | − | 18.8234i | 0.258221 | − | 0.794724i | ||||
\(562\) | 25.5320 | − | 18.5501i | 1.07700 | − | 0.782489i | ||||
\(563\) | 41.5662 | 1.75181 | 0.875904 | − | 0.482485i | \(-0.160266\pi\) | ||||
0.875904 | + | 0.482485i | \(0.160266\pi\) | |||||||
\(564\) | 2.15248 | 0.0906358 | ||||||||
\(565\) | −5.70475 | + | 4.14474i | −0.240000 | + | 0.174371i | ||||
\(566\) | 3.06059 | + | 2.22365i | 0.128646 | + | 0.0934670i | ||||
\(567\) | −4.03161 | − | 2.92914i | −0.169312 | − | 0.123012i | ||||
\(568\) | 2.52200 | + | 7.76191i | 0.105821 | + | 0.325683i | ||||
\(569\) | 21.0452 | − | 15.2902i | 0.882259 | − | 0.640999i | −0.0515890 | − | 0.998668i | \(-0.516429\pi\) |
0.933848 | + | 0.357670i | \(0.116429\pi\) | |||||||
\(570\) | 1.24608 | + | 3.83505i | 0.0521927 | + | 0.160633i | ||||
\(571\) | −2.56234 | + | 7.88607i | −0.107231 | + | 0.330022i | −0.990247 | − | 0.139319i | \(-0.955509\pi\) |
0.883017 | + | 0.469341i | \(0.155509\pi\) | |||||||
\(572\) | −4.82981 | − | 3.50906i | −0.201945 | − | 0.146721i | ||||
\(573\) | −4.37114 | + | 13.4530i | −0.182607 | + | 0.562006i | ||||
\(574\) | −6.97404 | + | 21.4639i | −0.291091 | + | 0.895885i | ||||
\(575\) | −2.76439 | − | 2.00845i | −0.115283 | − | 0.0837580i | ||||
\(576\) | 0.309017 | − | 0.951057i | 0.0128757 | − | 0.0396274i | ||||
\(577\) | −12.2400 | − | 37.6709i | −0.509559 | − | 1.56826i | −0.792969 | − | 0.609262i | \(-0.791466\pi\) |
0.283410 | − | 0.958999i | \(-0.408534\pi\) | |||||||
\(578\) | 8.13555 | − | 5.91083i | 0.338394 | − | 0.245858i | ||||
\(579\) | 4.87047 | + | 14.9898i | 0.202410 | + | 0.622953i | ||||
\(580\) | 3.47781 | + | 2.52677i | 0.144408 | + | 0.104919i | ||||
\(581\) | −58.2925 | − | 42.3520i | −2.41838 | − | 1.75706i | ||||
\(582\) | −2.87578 | + | 2.08938i | −0.119205 | + | 0.0866076i | ||||
\(583\) | −38.8754 | −1.61005 | ||||||||
\(584\) | 14.5045 | 0.600203 | ||||||||
\(585\) | 1.26932 | − | 0.922216i | 0.0524800 | − | 0.0381289i | ||||
\(586\) | −1.04524 | + | 3.21693i | −0.0431787 | + | 0.132890i | ||||
\(587\) | −12.2696 | − | 37.7619i | −0.506420 | − | 1.55860i | −0.798371 | − | 0.602166i | \(-0.794304\pi\) |
0.291951 | − | 0.956433i | \(-0.405696\pi\) | |||||||
\(588\) | −17.8337 | −0.735451 | ||||||||
\(589\) | −10.7470 | − | 19.7123i | −0.442822 | − | 0.812229i | ||||
\(590\) | 5.15408 | 0.212190 | ||||||||
\(591\) | 2.04987 | + | 6.30885i | 0.0843203 | + | 0.259511i | ||||
\(592\) | −3.31348 | + | 10.1979i | −0.136183 | + | 0.419129i | ||||
\(593\) | 21.1257 | − | 15.3487i | 0.867530 | − | 0.630297i | −0.0623930 | − | 0.998052i | \(-0.519873\pi\) |
0.929923 | + | 0.367754i | \(0.119873\pi\) | |||||||
\(594\) | −3.80504 | −0.156122 | ||||||||
\(595\) | 25.9211 | 1.06266 | ||||||||
\(596\) | −6.18669 | + | 4.49489i | −0.253417 | + | 0.184118i | ||||
\(597\) | 18.4847 | + | 13.4299i | 0.756530 | + | 0.549651i | ||||
\(598\) | −4.33723 | − | 3.15119i | −0.177363 | − | 0.128862i | ||||
\(599\) | 0.0829747 | + | 0.255370i | 0.00339026 | + | 0.0104341i | 0.952737 | − | 0.303795i | \(-0.0982539\pi\) |
−0.949347 | + | 0.314229i | \(0.898254\pi\) | |||||||
\(600\) | −0.809017 | + | 0.587785i | −0.0330280 | + | 0.0239962i | ||||
\(601\) | −5.57367 | − | 17.1540i | −0.227355 | − | 0.699726i | −0.998044 | − | 0.0625147i | \(-0.980088\pi\) |
0.770689 | − | 0.637211i | \(-0.219912\pi\) | |||||||
\(602\) | 10.6627 | − | 32.8164i | 0.434580 | − | 1.33750i | ||||
\(603\) | 1.56557 | + | 1.13746i | 0.0637551 | + | 0.0463208i | ||||
\(604\) | 3.09247 | − | 9.51766i | 0.125831 | − | 0.387268i | ||||
\(605\) | 1.07485 | − | 3.30805i | 0.0436989 | − | 0.134491i | ||||
\(606\) | −15.4559 | − | 11.2294i | −0.627852 | − | 0.456161i | ||||
\(607\) | −2.48114 | + | 7.63618i | −0.100707 | + | 0.309943i | −0.988699 | − | 0.149916i | \(-0.952100\pi\) |
0.887992 | + | 0.459858i | \(0.152100\pi\) | |||||||
\(608\) | −1.24608 | − | 3.83505i | −0.0505354 | − | 0.155532i | ||||
\(609\) | −17.3311 | + | 12.5918i | −0.702292 | + | 0.510245i | ||||
\(610\) | 2.61393 | + | 8.04485i | 0.105835 | + | 0.325727i | ||||
\(611\) | −2.73219 | − | 1.98505i | −0.110533 | − | 0.0803066i | ||||
\(612\) | −4.20814 | − | 3.05739i | −0.170104 | − | 0.123588i | ||||
\(613\) | −5.59613 | + | 4.06583i | −0.226026 | + | 0.164217i | −0.695035 | − | 0.718976i | \(-0.744611\pi\) |
0.469009 | + | 0.883193i | \(0.344611\pi\) | |||||||
\(614\) | −5.23915 | −0.211435 | ||||||||
\(615\) | −4.52878 | −0.182618 | ||||||||
\(616\) | −15.3404 | + | 11.1455i | −0.618083 | + | 0.449064i | ||||
\(617\) | 1.20568 | − | 3.71071i | 0.0485390 | − | 0.149388i | −0.923849 | − | 0.382756i | \(-0.874975\pi\) |
0.972388 | + | 0.233369i | \(0.0749749\pi\) | |||||||
\(618\) | 4.98486 | + | 15.3418i | 0.200520 | + | 0.617138i | ||||
\(619\) | 4.39207 | 0.176532 | 0.0882662 | − | 0.996097i | \(-0.471867\pi\) | ||||
0.0882662 | + | 0.996097i | \(0.471867\pi\) | |||||||
\(620\) | 3.82562 | − | 4.04533i | 0.153640 | − | 0.162464i | ||||
\(621\) | −3.41697 | −0.137118 | ||||||||
\(622\) | −4.59435 | − | 14.1400i | −0.184217 | − | 0.566960i | ||||
\(623\) | 9.92873 | − | 30.5575i | 0.397786 | − | 1.22426i | ||||
\(624\) | −1.26932 | + | 0.922216i | −0.0508135 | + | 0.0369182i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.1538 | 0.925410 | ||||||||
\(627\) | −12.4131 | + | 9.01867i | −0.495733 | + | 0.360171i | ||||
\(628\) | 6.51005 | + | 4.72983i | 0.259779 | + | 0.188741i | ||||
\(629\) | 45.1225 | + | 32.7834i | 1.79915 | + | 1.30716i | ||||
\(630\) | −1.53994 | − | 4.73944i | −0.0613526 | − | 0.188824i | ||||
\(631\) | 9.73418 | − | 7.07230i | 0.387512 | − | 0.281544i | −0.376923 | − | 0.926244i | \(-0.623018\pi\) |
0.764435 | + | 0.644701i | \(0.223018\pi\) | |||||||
\(632\) | −2.96264 | − | 9.11808i | −0.117848 | − | 0.362698i | ||||
\(633\) | 6.48139 | − | 19.9477i | 0.257612 | − | 0.792848i | ||||
\(634\) | 19.2994 | + | 14.0218i | 0.766475 | + | 0.556877i | ||||
\(635\) | −0.389015 | + | 1.19727i | −0.0154376 | + | 0.0475120i | ||||
\(636\) | −3.15717 | + | 9.71677i | −0.125190 | + | 0.385295i | ||||
\(637\) | 22.6367 | + | 16.4466i | 0.896900 | + | 0.651636i | ||||
\(638\) | −5.05462 | + | 15.5565i | −0.200114 | + | 0.615889i | ||||
\(639\) | −2.52200 | − | 7.76191i | −0.0997687 | − | 0.307056i | ||||
\(640\) | 0.809017 | − | 0.587785i | 0.0319792 | − | 0.0232343i | ||||
\(641\) | −8.53173 | − | 26.2580i | −0.336983 | − | 1.03713i | −0.965737 | − | 0.259523i | \(-0.916435\pi\) |
0.628754 | − | 0.777604i | \(-0.283565\pi\) | |||||||
\(642\) | −2.91729 | − | 2.11953i | −0.115136 | − | 0.0836513i | ||||
\(643\) | 5.24286 | + | 3.80916i | 0.206758 | + | 0.150219i | 0.686346 | − | 0.727275i | \(-0.259214\pi\) |
−0.479588 | + | 0.877494i | \(0.659214\pi\) | |||||||
\(644\) | −13.7759 | + | 10.0088i | −0.542847 | + | 0.394401i | ||||
\(645\) | 6.92411 | 0.272637 | ||||||||
\(646\) | −20.9748 | −0.825242 | ||||||||
\(647\) | −15.3169 | + | 11.1284i | −0.602168 | + | 0.437501i | −0.846648 | − | 0.532154i | \(-0.821383\pi\) |
0.244480 | + | 0.969654i | \(0.421383\pi\) | |||||||
\(648\) | −0.309017 | + | 0.951057i | −0.0121393 | + | 0.0373610i | ||||
\(649\) | 6.06028 | + | 18.6516i | 0.237887 | + | 0.732140i | ||||
\(650\) | 1.56897 | 0.0615400 | ||||||||
\(651\) | 13.2814 | + | 24.3608i | 0.520538 | + | 0.954777i | ||||
\(652\) | −16.0429 | −0.628287 | ||||||||
\(653\) | 7.57673 | + | 23.3188i | 0.296500 | + | 0.912534i | 0.982713 | + | 0.185134i | \(0.0592718\pi\) |
−0.686213 | + | 0.727401i | \(0.740728\pi\) | |||||||
\(654\) | −0.565181 | + | 1.73945i | −0.0221003 | + | 0.0680178i | ||||
\(655\) | 14.1673 | − | 10.2932i | 0.553564 | − | 0.402188i | ||||
\(656\) | 4.52878 | 0.176819 | ||||||||
\(657\) | −14.5045 | −0.565876 | ||||||||
\(658\) | −8.67797 | + | 6.30491i | −0.338302 | + | 0.245791i | ||||
\(659\) | −22.2006 | − | 16.1297i | −0.864811 | − | 0.628322i | 0.0643785 | − | 0.997926i | \(-0.479494\pi\) |
−0.929190 | + | 0.369604i | \(0.879494\pi\) | |||||||
\(660\) | −3.07834 | − | 2.23654i | −0.119824 | − | 0.0870573i | ||||
\(661\) | 8.77090 | + | 26.9940i | 0.341148 | + | 1.04995i | 0.963614 | + | 0.267299i | \(0.0861312\pi\) |
−0.622465 | + | 0.782647i | \(0.713869\pi\) | |||||||
\(662\) | 19.8873 | − | 14.4490i | 0.772942 | − | 0.561575i | ||||
\(663\) | 2.52191 | + | 7.76163i | 0.0979427 | + | 0.301437i | ||||
\(664\) | −4.46803 | + | 13.7512i | −0.173393 | + | 0.533650i | ||||
\(665\) | −16.2571 | − | 11.8115i | −0.630424 | − | 0.458030i | ||||
\(666\) | 3.31348 | − | 10.1979i | 0.128395 | − | 0.395159i | ||||
\(667\) | −4.53912 | + | 13.9700i | −0.175755 | + | 0.540920i | ||||
\(668\) | −5.17765 | − | 3.76178i | −0.200329 | − | 0.145548i | ||||
\(669\) | −0.881564 | + | 2.71317i | −0.0340832 | + | 0.104897i | ||||
\(670\) | 0.597996 | + | 1.84044i | 0.0231026 | + | 0.0711025i | ||||
\(671\) | −26.0392 | + | 18.9186i | −1.00523 | + | 0.730345i | ||||
\(672\) | 1.53994 | + | 4.73944i | 0.0594044 | + | 0.182828i | ||||
\(673\) | −10.1374 | − | 7.36523i | −0.390767 | − | 0.283909i | 0.375003 | − | 0.927024i | \(-0.377642\pi\) |
−0.765770 | + | 0.643115i | \(0.777642\pi\) | |||||||
\(674\) | 3.91658 | + | 2.84556i | 0.150861 | + | 0.109607i | ||||
\(675\) | 0.809017 | − | 0.587785i | 0.0311391 | − | 0.0226239i | ||||
\(676\) | −10.5383 | −0.405321 | ||||||||
\(677\) | 20.5948 | 0.791522 | 0.395761 | − | 0.918353i | \(-0.370481\pi\) | ||||
0.395761 | + | 0.918353i | \(0.370481\pi\) | |||||||
\(678\) | −5.70475 | + | 4.14474i | −0.219089 | + | 0.159178i | ||||
\(679\) | 5.47397 | − | 16.8471i | 0.210072 | − | 0.646534i | ||||
\(680\) | −1.60737 | − | 4.94697i | −0.0616397 | − | 0.189707i | ||||
\(681\) | −3.42165 | −0.131118 | ||||||||
\(682\) | 19.1375 | + | 9.08758i | 0.732812 | + | 0.347981i | ||||
\(683\) | 0.601320 | 0.0230089 | 0.0115044 | − | 0.999934i | \(-0.496338\pi\) | ||||
0.0115044 | + | 0.999934i | \(0.496338\pi\) | |||||||
\(684\) | 1.24608 | + | 3.83505i | 0.0476452 | + | 0.146637i | ||||
\(685\) | −2.11477 | + | 6.50860i | −0.0808013 | + | 0.248681i | ||||
\(686\) | 43.6774 | − | 31.7335i | 1.66761 | − | 1.21159i | ||||
\(687\) | −8.79043 | −0.335376 | ||||||||
\(688\) | −6.92411 | −0.263979 | ||||||||
\(689\) | 12.9684 | − | 9.42211i | 0.494058 | − | 0.358954i | ||||
\(690\) | −2.76439 | − | 2.00845i | −0.105238 | − | 0.0764602i | ||||
\(691\) | 22.7457 | + | 16.5257i | 0.865287 | + | 0.628668i | 0.929318 | − | 0.369280i | \(-0.120396\pi\) |
−0.0640308 | + | 0.997948i | \(0.520396\pi\) | |||||||
\(692\) | 0.240656 | + | 0.740662i | 0.00914836 | + | 0.0281558i | ||||
\(693\) | 15.3404 | − | 11.1455i | 0.582735 | − | 0.423381i | ||||
\(694\) | 4.75307 | + | 14.6284i | 0.180424 | + | 0.555288i | ||||
\(695\) | −4.20521 | + | 12.9423i | −0.159513 | + | 0.490930i | ||||
\(696\) | 3.47781 | + | 2.52677i | 0.131826 | + | 0.0957771i | ||||
\(697\) | 7.27940 | − | 22.4037i | 0.275727 | − | 0.848601i | ||||
\(698\) | −6.92903 | + | 21.3254i | −0.262268 | + | 0.807177i | ||||
\(699\) | 12.3866 | + | 8.99936i | 0.468503 | + | 0.340387i | ||||
\(700\) | 1.53994 | − | 4.73944i | 0.0582042 | − | 0.179134i | ||||
\(701\) | −1.08461 | − | 3.33810i | −0.0409653 | − | 0.126078i | 0.928482 | − | 0.371377i | \(-0.121114\pi\) |
−0.969448 | + | 0.245298i | \(0.921114\pi\) | |||||||
\(702\) | 1.26932 | − | 0.922216i | 0.0479074 | − | 0.0348068i | ||||
\(703\) | −13.3613 | − | 41.1220i | −0.503932 | − | 1.55094i | ||||
\(704\) | 3.07834 | + | 2.23654i | 0.116019 | + | 0.0842929i | ||||
\(705\) | −1.74139 | − | 1.26520i | −0.0655847 | − | 0.0476501i | ||||
\(706\) | 27.0726 | − | 19.6694i | 1.01889 | − | 0.740266i | ||||
\(707\) | 95.2044 | 3.58053 | ||||||||
\(708\) | 5.15408 | 0.193702 | ||||||||
\(709\) | −27.9955 | + | 20.3399i | −1.05139 | + | 0.763881i | −0.972477 | − | 0.233000i | \(-0.925146\pi\) |
−0.0789152 | + | 0.996881i | \(0.525146\pi\) | |||||||
\(710\) | 2.52200 | − | 7.76191i | 0.0946489 | − | 0.291299i | ||||
\(711\) | 2.96264 | + | 9.11808i | 0.111108 | + | 0.341955i | ||||
\(712\) | −6.44748 | −0.241630 | ||||||||
\(713\) | 17.1857 | + | 8.16076i | 0.643610 | + | 0.305623i | ||||
\(714\) | 25.9211 | 0.970073 | ||||||||
\(715\) | 1.84482 | + | 5.67778i | 0.0689925 | + | 0.212337i | ||||
\(716\) | 0.931315 | − | 2.86629i | 0.0348049 | − | 0.107118i | ||||
\(717\) | 23.9532 | − | 17.4030i | 0.894548 | − | 0.649927i | ||||
\(718\) | 24.5748 | 0.917123 | ||||||||
\(719\) | 1.86816 | 0.0696707 | 0.0348353 | − | 0.999393i | \(-0.488909\pi\) | ||||
0.0348353 | + | 0.999393i | \(0.488909\pi\) | |||||||
\(720\) | −0.809017 | + | 0.587785i | −0.0301503 | + | 0.0219055i | ||||
\(721\) | −65.0353 | − | 47.2509i | −2.42204 | − | 1.75971i | ||||
\(722\) | −2.21642 | − | 1.61032i | −0.0824866 | − | 0.0599300i | ||||
\(723\) | −6.87654 | − | 21.1638i | −0.255741 | − | 0.787091i | ||||
\(724\) | −14.7514 | + | 10.7175i | −0.548232 | + | 0.398314i | ||||
\(725\) | −1.32840 | − | 4.08841i | −0.0493357 | − | 0.151840i | ||||
\(726\) | 1.07485 | − | 3.30805i | 0.0398915 | − | 0.122773i | ||||
\(727\) | 40.6115 | + | 29.5060i | 1.50620 | + | 1.09432i | 0.967830 | + | 0.251606i | \(0.0809588\pi\) |
0.538368 | + | 0.842710i | \(0.319041\pi\) | |||||||
\(728\) | 2.41611 | − | 7.43603i | 0.0895471 | − | 0.275598i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −11.7344 | − | 8.52556i | −0.434311 | − | 0.315545i | ||||
\(731\) | −11.1296 | + | 34.2533i | −0.411643 | + | 1.26691i | ||||
\(732\) | 2.61393 | + | 8.04485i | 0.0966137 | + | 0.297346i | ||||
\(733\) | 22.8889 | − | 16.6298i | 0.845421 | − | 0.614234i | −0.0784587 | − | 0.996917i | \(-0.525000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(734\) | 0.678292 | + | 2.08757i | 0.0250362 | + | 0.0770536i | ||||
\(735\) | 14.4278 | + | 10.4824i | 0.532177 | + | 0.386649i | ||||
\(736\) | 2.76439 | + | 2.00845i | 0.101897 | + | 0.0740323i | ||||
\(737\) | −5.95706 | + | 4.32806i | −0.219431 | + | 0.159426i | ||||
\(738\) | −4.52878 | −0.166707 | ||||||||
\(739\) | −26.6202 | −0.979240 | −0.489620 | − | 0.871936i | \(-0.662864\pi\) | ||||
−0.489620 | + | 0.871936i | \(0.662864\pi\) | |||||||
\(740\) | 8.67481 | − | 6.30262i | 0.318893 | − | 0.231689i | ||||
\(741\) | 1.95507 | − | 6.01707i | 0.0718211 | − | 0.221043i | ||||
\(742\) | −15.7333 | − | 48.4220i | −0.577587 | − | 1.77763i | ||||
\(743\) | 1.62566 | 0.0596399 | 0.0298199 | − | 0.999555i | \(-0.490507\pi\) | ||||
0.0298199 | + | 0.999555i | \(0.490507\pi\) | |||||||
\(744\) | 3.82562 | − | 4.04533i | 0.140254 | − | 0.148309i | ||||
\(745\) | 7.64716 | 0.280170 | ||||||||
\(746\) | −1.36114 | − | 4.18917i | −0.0498351 | − | 0.153377i | ||||
\(747\) | 4.46803 | − | 13.7512i | 0.163477 | − | 0.503130i | ||||
\(748\) | 16.0121 | − | 11.6335i | 0.585461 | − | 0.425362i | ||||
\(749\) | 17.9698 | 0.656601 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −31.8327 | + | 23.1278i | −1.16159 | + | 0.843946i | −0.989978 | − | 0.141219i | \(-0.954898\pi\) |
−0.171613 | + | 0.985164i | \(0.554898\pi\) | |||||||
\(752\) | 1.74139 | + | 1.26520i | 0.0635021 | + | 0.0461370i | ||||
\(753\) | −1.15943 | − | 0.842378i | −0.0422521 | − | 0.0306980i | ||||
\(754\) | −2.08422 | − | 6.41458i | −0.0759029 | − | 0.233605i | ||||
\(755\) | −8.09620 | + | 5.88224i | −0.294651 | + | 0.214076i | ||||
\(756\) | −1.53994 | − | 4.73944i | −0.0560070 | − | 0.172372i | ||||
\(757\) | 5.32651 | − | 16.3933i | 0.193595 | − | 0.595825i | −0.806395 | − | 0.591378i | \(-0.798584\pi\) |
0.999990 | − | 0.00444753i | \(-0.00141570\pi\) | |||||||
\(758\) | 22.0796 | + | 16.0418i | 0.801968 | + | 0.582664i | ||||
\(759\) | 4.01775 | − | 12.3653i | 0.145835 | − | 0.448834i | ||||
\(760\) | −1.24608 | + | 3.83505i | −0.0452002 | + | 0.139112i | ||||
\(761\) | −43.6264 | − | 31.6964i | −1.58145 | − | 1.14899i | −0.915004 | − | 0.403446i | \(-0.867812\pi\) |
−0.666451 | − | 0.745549i | \(-0.732188\pi\) | |||||||
\(762\) | −0.389015 | + | 1.19727i | −0.0140925 | + | 0.0433724i | ||||
\(763\) | −2.81649 | − | 8.66827i | −0.101964 | − | 0.313812i | ||||
\(764\) | −11.4438 | + | 8.31440i | −0.414022 | + | 0.300804i | ||||
\(765\) | 1.60737 | + | 4.94697i | 0.0581145 | + | 0.178858i | ||||
\(766\) | 19.9371 | + | 14.4852i | 0.720358 | + | 0.523371i | ||||
\(767\) | −6.54219 | − | 4.75318i | −0.236225 | − | 0.171627i | ||||
\(768\) | 0.809017 | − | 0.587785i | 0.0291929 | − | 0.0212099i | ||||
\(769\) | −43.1821 | −1.55719 | −0.778593 | − | 0.627530i | \(-0.784066\pi\) | ||||
−0.778593 | + | 0.627530i | \(0.784066\pi\) | |||||||
\(770\) | 18.9618 | 0.683336 | ||||||||
\(771\) | 5.93986 | − | 4.31556i | 0.213919 | − | 0.155421i | ||||
\(772\) | −4.87047 | + | 14.9898i | −0.175292 | + | 0.539493i | ||||
\(773\) | −4.62611 | − | 14.2377i | −0.166390 | − | 0.512095i | 0.832746 | − | 0.553655i | \(-0.186767\pi\) |
−0.999136 | + | 0.0415601i | \(0.986767\pi\) | |||||||
\(774\) | 6.92411 | 0.248882 | ||||||||
\(775\) | −5.47277 | + | 1.02410i | −0.196588 | + | 0.0367866i | ||||
\(776\) | −3.55467 | −0.127605 | ||||||||
\(777\) | 16.5122 | + | 50.8194i | 0.592373 | + | 1.82314i | ||||
\(778\) | 6.93565 | − | 21.3457i | 0.248655 | − | 0.765282i | ||||
\(779\) | −14.7742 | + | 10.7341i | −0.529340 | + | 0.384588i | ||||
\(780\) | 1.56897 | 0.0561780 | ||||||||
\(781\) | 31.0542 | 1.11121 | ||||||||
\(782\) | 14.3791 | − | 10.4470i | 0.514195 | − | 0.373585i | ||||
\(783\) | −3.47781 | − | 2.52677i | −0.124287 | − | 0.0902996i | ||||
\(784\) | −14.4278 | − | 10.4824i | −0.515278 | − | 0.374372i | ||||
\(785\) | −2.48662 | − | 7.65303i | −0.0887513 | − | 0.273148i | ||||
\(786\) | 14.1673 | − | 10.2932i | 0.505332 | − | 0.367145i | ||||
\(787\) | −6.64094 | − | 20.4387i | −0.236724 | − | 0.728561i | −0.996888 | − | 0.0788303i | \(-0.974881\pi\) |
0.760164 | − | 0.649731i | \(-0.225119\pi\) | |||||||
\(788\) | −2.04987 | + | 6.30885i | −0.0730235 | + | 0.224743i | ||||
\(789\) | 1.99013 | + | 1.44592i | 0.0708506 | + | 0.0514760i | ||||
\(790\) | −2.96264 | + | 9.11808i | −0.105406 | + | 0.324407i | ||||
\(791\) | 10.8588 | − | 33.4200i | 0.386095 | − | 1.18828i | ||||
\(792\) | −3.07834 | − | 2.23654i | −0.109384 | − | 0.0794721i | ||||
\(793\) | 4.10117 | − | 12.6221i | 0.145637 | − | 0.448224i | ||||
\(794\) | −12.1532 | − | 37.4038i | −0.431301 | − | 1.32741i | ||||
\(795\) | 8.26558 | − | 6.00530i | 0.293150 | − | 0.212986i | ||||
\(796\) | 7.06054 | + | 21.7301i | 0.250254 | + | 0.770203i | ||||
\(797\) | 14.9776 | + | 10.8819i | 0.530535 | + | 0.385456i | 0.820558 | − | 0.571564i | \(-0.193663\pi\) |
−0.290023 | + | 0.957020i | \(0.593663\pi\) | |||||||
\(798\) | −16.2571 | − | 11.8115i | −0.575496 | − | 0.418122i | ||||
\(799\) | 9.05794 | − | 6.58098i | 0.320447 | − | 0.232818i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 6.44748 | 0.227811 | ||||||||
\(802\) | 14.4128 | − | 10.4715i | 0.508934 | − | 0.369762i | ||||
\(803\) | 17.0547 | − | 52.4891i | 0.601849 | − | 1.85230i | ||||
\(804\) | 0.597996 | + | 1.84044i | 0.0210897 | + | 0.0649074i | ||||
\(805\) | 17.0280 | 0.600156 | ||||||||
\(806\) | −8.58660 | + | 1.60677i | −0.302450 | + | 0.0565962i | ||||
\(807\) | 19.4919 | 0.686149 | ||||||||
\(808\) | −5.90362 | − | 18.1695i | −0.207689 | − | 0.639200i | ||||
\(809\) | −6.97549 | + | 21.4683i | −0.245245 | + | 0.754787i | 0.750351 | + | 0.661040i | \(0.229884\pi\) |
−0.995596 | + | 0.0937470i | \(0.970116\pi\) | |||||||
\(810\) | 0.809017 | − | 0.587785i | 0.0284260 | − | 0.0206527i | ||||
\(811\) | 5.39634 | 0.189491 | 0.0947456 | − | 0.995502i | \(-0.469796\pi\) | ||||
0.0947456 | + | 0.995502i | \(0.469796\pi\) | |||||||
\(812\) | −21.4224 | −0.751780 | ||||||||
\(813\) | 5.53896 | − | 4.02429i | 0.194260 | − | 0.141138i | ||||
\(814\) | 33.0080 | + | 23.9817i | 1.15693 | + | 0.840558i | ||||
\(815\) | 12.9789 | + | 9.42976i | 0.454633 | + | 0.330310i | ||||
\(816\) | −1.60737 | − | 4.94697i | −0.0562691 | − | 0.173178i | ||||
\(817\) | 22.5885 | − | 16.4115i | 0.790270 | − | 0.574165i | ||||
\(818\) | 6.90898 | + | 21.2637i | 0.241567 | + | 0.743466i | ||||
\(819\) | −2.41611 | + | 7.43603i | −0.0844258 | + | 0.259836i | ||||
\(820\) | −3.66386 | − | 2.66195i | −0.127947 | − | 0.0929593i | ||||
\(821\) | 2.23099 | − | 6.86630i | 0.0778623 | − | 0.239635i | −0.904548 | − | 0.426373i | \(-0.859791\pi\) |
0.982410 | + | 0.186737i | \(0.0597913\pi\) | |||||||
\(822\) | −2.11477 | + | 6.50860i | −0.0737611 | + | 0.227013i | ||||
\(823\) | −8.10046 | − | 5.88533i | −0.282364 | − | 0.205150i | 0.437584 | − | 0.899178i | \(-0.355834\pi\) |
−0.719948 | + | 0.694028i | \(0.755834\pi\) | |||||||
\(824\) | −4.98486 | + | 15.3418i | −0.173656 | + | 0.534457i | ||||
\(825\) | 1.17582 | + | 3.61880i | 0.0409368 | + | 0.125991i | ||||
\(826\) | −20.7793 | + | 15.0970i | −0.723003 | + | 0.525292i | ||||
\(827\) | 0.492566 | + | 1.51596i | 0.0171282 | + | 0.0527152i | 0.959255 | − | 0.282541i | \(-0.0911772\pi\) |
−0.942127 | + | 0.335256i | \(0.891177\pi\) | |||||||
\(828\) | −2.76439 | − | 2.00845i | −0.0960691 | − | 0.0697983i | ||||
\(829\) | −34.4916 | − | 25.0596i | −1.19794 | − | 0.870357i | −0.203863 | − | 0.978999i | \(-0.565350\pi\) |
−0.994081 | + | 0.108642i | \(0.965350\pi\) | |||||||
\(830\) | 11.6975 | − | 8.49870i | 0.406025 | − | 0.294994i | ||||
\(831\) | 6.03859 | 0.209476 | ||||||||
\(832\) | −1.56897 | −0.0543941 | ||||||||
\(833\) | −75.0469 | + | 54.5247i | −2.60022 | + | 1.88917i | ||||
\(834\) | −4.20521 | + | 12.9423i | −0.145615 | + | 0.448156i | ||||
\(835\) | 1.97769 | + | 6.08669i | 0.0684406 | + | 0.210639i | ||||
\(836\) | −15.3435 | −0.530665 | ||||||||
\(837\) | −3.82562 | + | 4.04533i | −0.132233 | + | 0.139827i | ||||
\(838\) | 14.1940 | 0.490322 | ||||||||
\(839\) | −9.81630 | − | 30.2115i | −0.338896 | − | 1.04302i | −0.964771 | − | 0.263092i | \(-0.915258\pi\) |
0.625875 | − | 0.779924i | \(-0.284742\pi\) | |||||||
\(840\) | 1.53994 | − | 4.73944i | 0.0531329 | − | 0.163526i | ||||
\(841\) | 8.51108 | − | 6.18366i | 0.293485 | − | 0.213230i | ||||
\(842\) | 17.8370 | 0.614705 | ||||||||
\(843\) | −31.5593 | −1.08696 | ||||||||
\(844\) | 16.9685 | − | 12.3283i | 0.584080 | − | 0.424359i | ||||
\(845\) | 8.52570 | + | 6.19428i | 0.293293 | + | 0.213090i | ||||
\(846\) | −1.74139 | − | 1.26520i | −0.0598703 | − | 0.0434983i | ||||
\(847\) | 5.35636 | + | 16.4852i | 0.184047 | + | 0.566437i | ||||
\(848\) | −8.26558 | + | 6.00530i | −0.283841 | + | 0.206223i | ||||
\(849\) | −1.16904 | − | 3.59794i | −0.0401214 | − | 0.123481i | ||||
\(850\) | −1.60737 | + | 4.94697i | −0.0551322 | + | 0.169680i | ||||
\(851\) | 29.6416 | + | 21.5359i | 1.01610 | + | 0.738240i | ||||
\(852\) | 2.52200 | − | 7.76191i | 0.0864022 | − | 0.265919i | ||||
\(853\) | −9.52156 | + | 29.3044i | −0.326012 | + | 1.00336i | 0.644970 | + | 0.764208i | \(0.276870\pi\) |
−0.970982 | + | 0.239154i | \(0.923130\pi\) | |||||||
\(854\) | −34.1028 | − | 24.7772i | −1.16698 | − | 0.847857i | ||||
\(855\) | 1.24608 | − | 3.83505i | 0.0426152 | − | 0.131156i | ||||
\(856\) | −1.11430 | − | 3.42948i | −0.0380861 | − | 0.117217i | ||||
\(857\) | −7.23014 | + | 5.25300i | −0.246977 | + | 0.179439i | −0.704386 | − | 0.709817i | \(-0.748778\pi\) |
0.457409 | + | 0.889256i | \(0.348778\pi\) | |||||||
\(858\) | 1.84482 | + | 5.67778i | 0.0629812 | + | 0.193836i | ||||
\(859\) | −17.5357 | − | 12.7404i | −0.598309 | − | 0.434697i | 0.246969 | − | 0.969023i | \(-0.420565\pi\) |
−0.845278 | + | 0.534326i | \(0.820565\pi\) | |||||||
\(860\) | 5.60172 | + | 4.06989i | 0.191017 | + | 0.138782i | ||||
\(861\) | 18.2583 | − | 13.2654i | 0.622240 | − | 0.452084i | ||||
\(862\) | −25.5109 | −0.868906 | ||||||||
\(863\) | 26.0672 | 0.887339 | 0.443670 | − | 0.896190i | \(-0.353676\pi\) | ||||
0.443670 | + | 0.896190i | \(0.353676\pi\) | |||||||
\(864\) | −0.809017 | + | 0.587785i | −0.0275233 | + | 0.0199969i | ||||
\(865\) | 0.240656 | − | 0.740662i | 0.00818254 | − | 0.0251833i | ||||
\(866\) | 11.0066 | + | 33.8750i | 0.374021 | + | 1.15112i | ||||
\(867\) | −10.0561 | −0.341523 | ||||||||
\(868\) | −3.57408 | + | 27.5149i | −0.121312 | + | 0.933918i | ||||
\(869\) | −36.4801 | −1.23750 | ||||||||
\(870\) | −1.32840 | − | 4.08841i | −0.0450371 | − | 0.138610i | ||||
\(871\) | 0.938235 | − | 2.88759i | 0.0317909 | − | 0.0978423i | ||||
\(872\) | −1.47966 | + | 1.07504i | −0.0501077 | + | 0.0364054i | ||||
\(873\) | 3.55467 | 0.120307 | ||||||||
\(874\) | −13.7786 | −0.466070 | ||||||||
\(875\) | −4.03161 | + | 2.92914i | −0.136293 | + | 0.0990229i | ||||
\(876\) | −11.7344 | − | 8.52556i | −0.396470 | − | 0.288052i | ||||
\(877\) | −1.18834 | − | 0.863383i | −0.0401275 | − | 0.0291544i | 0.567541 | − | 0.823345i | \(-0.307895\pi\) |
−0.607668 | + | 0.794191i | \(0.707895\pi\) | |||||||
\(878\) | 5.60189 | + | 17.2408i | 0.189054 | + | 0.581850i | ||||
\(879\) | 2.73649 | − | 1.98817i | 0.0922994 | − | 0.0670594i | ||||
\(880\) | −1.17582 | − | 3.61880i | −0.0396369 | − | 0.121990i | ||||
\(881\) | −12.1428 | + | 37.3716i | −0.409100 | + | 1.25908i | 0.508322 | + | 0.861167i | \(0.330266\pi\) |
−0.917423 | + | 0.397914i | \(0.869734\pi\) | |||||||
\(882\) | 14.4278 | + | 10.4824i | 0.485809 | + | 0.352961i | ||||
\(883\) | 16.2008 | − | 49.8610i | 0.545201 | − | 1.67796i | −0.175310 | − | 0.984513i | \(-0.556093\pi\) |
0.720511 | − | 0.693443i | \(-0.243907\pi\) | |||||||
\(884\) | −2.52191 | + | 7.76163i | −0.0848209 | + | 0.261052i | ||||
\(885\) | −4.16974 | − | 3.02949i | −0.140164 | − | 0.101835i | ||||
\(886\) | 3.13485 | − | 9.64806i | 0.105317 | − | 0.324133i | ||||
\(887\) | −7.69179 | − | 23.6729i | −0.258265 | − | 0.794858i | −0.993169 | − | 0.116686i | \(-0.962773\pi\) |
0.734904 | − | 0.678171i | \(-0.237227\pi\) | |||||||
\(888\) | 8.67481 | − | 6.30262i | 0.291108 | − | 0.211502i | ||||
\(889\) | −1.93860 | − | 5.96639i | −0.0650185 | − | 0.200106i | ||||
\(890\) | 5.21612 | + | 3.78973i | 0.174845 | + | 0.127032i | ||||
\(891\) | 3.07834 | + | 2.23654i | 0.103128 | + | 0.0749270i | ||||
\(892\) | −2.30796 | + | 1.67683i | −0.0772763 | + | 0.0561445i | ||||
\(893\) | −8.67969 | −0.290455 | ||||||||
\(894\) | 7.64716 | 0.255759 | ||||||||
\(895\) | −2.43821 | + | 1.77147i | −0.0815005 | + | 0.0592136i | ||||
\(896\) | −1.53994 | + | 4.73944i | −0.0514457 | + | 0.158334i | ||||
\(897\) | 1.65668 | + | 5.09872i | 0.0553148 | + | 0.170241i | ||||
\(898\) | −25.4462 | −0.849149 | ||||||||
\(899\) | 11.4570 | + | 21.0145i | 0.382112 | + | 0.700873i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 16.4222 | + | 50.5423i | 0.547102 | + | 1.68381i | ||||
\(902\) | 5.32503 | − | 16.3888i | 0.177304 | − | 0.545686i | ||||
\(903\) | −27.9153 | + | 20.2817i | −0.928964 | + | 0.674932i | ||||
\(904\) | −7.05145 | −0.234528 | ||||||||
\(905\) | 18.2338 | 0.606111 | ||||||||
\(906\) | −8.09620 | + | 5.88224i | −0.268978 | + | 0.195424i | ||||
\(907\) | −2.22906 | − | 1.61951i | −0.0740148 | − | 0.0537749i | 0.550163 | − | 0.835058i | \(-0.314566\pi\) |
−0.624177 | + | 0.781283i | \(0.714566\pi\) | |||||||
\(908\) | −2.76818 | − | 2.01120i | −0.0918651 | − | 0.0667439i | ||||
\(909\) | 5.90362 | + | 18.1695i | 0.195811 | + | 0.602643i | ||||
\(910\) | −6.32547 | + | 4.59572i | −0.209687 | + | 0.152347i | ||||
\(911\) | −9.38427 | − | 28.8818i | −0.310915 | − | 0.956897i | −0.977403 | − | 0.211382i | \(-0.932204\pi\) |
0.666489 | − | 0.745515i | \(-0.267796\pi\) | |||||||
\(912\) | −1.24608 | + | 3.83505i | −0.0412620 | + | 0.126991i | ||||
\(913\) | 44.5093 | + | 32.3379i | 1.47304 | + | 1.07023i | ||||
\(914\) | −1.99152 | + | 6.12928i | −0.0658737 | + | 0.202738i | ||||
\(915\) | 2.61393 | − | 8.04485i | 0.0864139 | − | 0.265955i | ||||
\(916\) | −7.11161 | − | 5.16689i | −0.234974 | − | 0.170719i | ||||
\(917\) | −26.9671 | + | 82.9961i | −0.890532 | + | 2.74077i | ||||
\(918\) | 1.60737 | + | 4.94697i | 0.0530510 | + | 0.163274i | ||||
\(919\) | −16.6589 | + | 12.1034i | −0.549526 | + | 0.399254i | −0.827611 | − | 0.561302i | \(-0.810300\pi\) |
0.278085 | + | 0.960557i | \(0.410300\pi\) | |||||||
\(920\) | −1.05590 | − | 3.24973i | −0.0348121 | − | 0.107141i | ||||
\(921\) | 4.23856 | + | 3.07949i | 0.139665 | + | 0.101473i | ||||
\(922\) | 24.9063 | + | 18.0955i | 0.820244 | + | 0.595942i | ||||
\(923\) | −10.3594 | + | 7.52653i | −0.340983 | + | 0.247739i | ||||
\(924\) | 18.9618 | 0.623798 | ||||||||
\(925\) | −10.7227 | −0.352559 | ||||||||
\(926\) | 11.1297 | − | 8.08622i | 0.365746 | − | 0.265730i | ||||
\(927\) | 4.98486 | − | 15.3418i | 0.163724 | − | 0.503891i | ||||
\(928\) | 1.32840 | + | 4.08841i | 0.0436070 | + | 0.134209i | ||||
\(929\) | 35.4821 | 1.16413 | 0.582065 | − | 0.813142i | \(-0.302245\pi\) | ||||
0.582065 | + | 0.813142i | \(0.302245\pi\) | |||||||
\(930\) | −5.47277 | + | 1.02410i | −0.179459 | + | 0.0335815i | ||||
\(931\) | 71.9130 | 2.35685 | ||||||||
\(932\) | 4.73125 | + | 14.5613i | 0.154977 | + | 0.476971i | ||||
\(933\) | −4.59435 | + | 14.1400i | −0.150412 | + | 0.462921i | ||||
\(934\) | 10.7691 | − | 7.82424i | 0.352377 | − | 0.256017i | ||||
\(935\) | −19.7921 | −0.647270 | ||||||||
\(936\) | 1.56897 | 0.0512833 | ||||||||
\(937\) | −22.6986 | + | 16.4915i | −0.741530 | + | 0.538753i | −0.893190 | − | 0.449680i | \(-0.851538\pi\) |
0.151660 | + | 0.988433i | \(0.451538\pi\) | |||||||
\(938\) | −7.80179 | − | 5.66833i | −0.254738 | − | 0.185078i | ||||
\(939\) | −18.7318 | − | 13.6094i | −0.611288 | − | 0.444127i | ||||
\(940\) | −0.665153 | − | 2.04713i | −0.0216949 | − | 0.0667700i | ||||
\(941\) | 40.6679 | − | 29.5470i | 1.32574 | − | 0.963204i | 0.325896 | − | 0.945406i | \(-0.394334\pi\) |
0.999842 | − | 0.0177987i | \(-0.00566580\pi\) | |||||||
\(942\) | −2.48662 | − | 7.65303i | −0.0810184 | − | 0.249349i | ||||
\(943\) | 4.78195 | − | 14.7173i | 0.155722 | − | 0.479262i | ||||
\(944\) | 4.16974 | + | 3.02949i | 0.135714 | + | 0.0986016i | ||||
\(945\) | −1.53994 | + | 4.73944i | −0.0500942 | + | 0.154174i | ||||
\(946\) | −8.14151 | + | 25.0570i | −0.264703 | + | 0.814673i | ||||
\(947\) | −7.48246 | − | 5.43633i | −0.243147 | − | 0.176657i | 0.459537 | − | 0.888159i | \(-0.348015\pi\) |
−0.702684 | + | 0.711502i | \(0.748015\pi\) | |||||||
\(948\) | −2.96264 | + | 9.11808i | −0.0962222 | + | 0.296142i | ||||
\(949\) | 7.03235 | + | 21.6433i | 0.228280 | + | 0.702573i | ||||
\(950\) | 3.26229 | − | 2.37019i | 0.105843 | − | 0.0768992i | ||||
\(951\) | −7.37170 | − | 22.6878i | −0.239044 | − | 0.735701i | ||||
\(952\) | 20.9706 | + | 15.2360i | 0.679662 | + | 0.493803i | ||||
\(953\) | 2.11820 | + | 1.53896i | 0.0686152 | + | 0.0498519i | 0.621564 | − | 0.783363i | \(-0.286498\pi\) |
−0.552949 | + | 0.833215i | \(0.686498\pi\) | |||||||
\(954\) | 8.26558 | − | 6.00530i | 0.267608 | − | 0.194429i | ||||
\(955\) | 14.1453 | 0.457731 | ||||||||
\(956\) | 29.6078 | 0.957583 | ||||||||
\(957\) | 13.2332 | − | 9.61447i | 0.427768 | − | 0.310792i | ||||
\(958\) | 7.27830 | − | 22.4003i | 0.235151 | − | 0.723721i | ||||
\(959\) | −10.5386 | − | 32.4346i | −0.340310 | − | 1.04737i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 28.9025 | − | 11.2093i | 0.932337 | − | 0.361590i | ||||
\(962\) | −16.8235 | −0.542411 | ||||||||
\(963\) | 1.11430 | + | 3.42948i | 0.0359080 | + | 0.110513i | ||||
\(964\) | 6.87654 | − | 21.1638i | 0.221478 | − | 0.681640i | ||||
\(965\) | 12.7511 | − | 9.26418i | 0.410471 | − | 0.298225i | ||||
\(966\) | 17.0280 | 0.547865 | ||||||||
\(967\) | −41.1785 | −1.32421 | −0.662106 | − | 0.749411i | \(-0.730337\pi\) | ||||
−0.662106 | + | 0.749411i | \(0.730337\pi\) | |||||||
\(968\) | 2.81400 | − | 2.04449i | 0.0904453 | − | 0.0657124i | ||||
\(969\) | 16.9690 | + | 12.3287i | 0.545122 | + | 0.396054i | ||||
\(970\) | 2.87578 | + | 2.08938i | 0.0923359 | + | 0.0670859i | ||||
\(971\) | −10.7806 | − | 33.1792i | −0.345965 | − | 1.06477i | −0.961065 | − | 0.276322i | \(-0.910884\pi\) |
0.615100 | − | 0.788449i | \(-0.289116\pi\) | |||||||
\(972\) | 0.809017 | − | 0.587785i | 0.0259492 | − | 0.0188532i | ||||
\(973\) | −20.9560 | − | 64.4960i | −0.671819 | − | 2.06765i | ||||
\(974\) | −9.83196 | + | 30.2597i | −0.315036 | + | 0.969582i | ||||
\(975\) | −1.26932 | − | 0.922216i | −0.0406508 | − | 0.0295345i | ||||
\(976\) | −2.61393 | + | 8.04485i | −0.0836699 | + | 0.257510i | ||||
\(977\) | 7.98866 | − | 24.5866i | 0.255580 | − | 0.786594i | −0.738135 | − | 0.674653i | \(-0.764293\pi\) |
0.993715 | − | 0.111941i | \(-0.0357067\pi\) | |||||||
\(978\) | 12.9789 | + | 9.42976i | 0.415021 | + | 0.301530i | ||||
\(979\) | −7.58108 | + | 23.3322i | −0.242292 | + | 0.745699i | ||||
\(980\) | 5.51093 | + | 16.9609i | 0.176040 | + | 0.541796i | ||||
\(981\) | 1.47966 | − | 1.07504i | 0.0472420 | − | 0.0343233i | ||||
\(982\) | 6.24086 | + | 19.2074i | 0.199154 | + | 0.612933i | ||||
\(983\) | −9.58528 | − | 6.96411i | −0.305723 | − | 0.222121i | 0.424336 | − | 0.905505i | \(-0.360508\pi\) |
−0.730059 | + | 0.683384i | \(0.760508\pi\) | |||||||
\(984\) | −3.66386 | − | 2.66195i | −0.116800 | − | 0.0848598i | ||||
\(985\) | 5.36662 | − | 3.89908i | 0.170995 | − | 0.124235i | ||||
\(986\) | 22.3604 | 0.712102 | ||||||||
\(987\) | 10.7266 | 0.341430 | ||||||||
\(988\) | 5.11843 | − | 3.71875i | 0.162839 | − | 0.118309i | ||||
\(989\) | −7.31119 | + | 22.5015i | −0.232482 | + | 0.715507i | ||||
\(990\) | 1.17582 | + | 3.61880i | 0.0373700 | + | 0.115013i | ||||
\(991\) | 13.4917 | 0.428577 | 0.214289 | − | 0.976770i | \(-0.431257\pi\) | ||||
0.214289 | + | 0.976770i | \(0.431257\pi\) | |||||||
\(992\) | 5.47277 | − | 1.02410i | 0.173761 | − | 0.0325151i | ||||
\(993\) | −24.5820 | −0.780088 | ||||||||
\(994\) | 12.5680 | + | 38.6803i | 0.398632 | + | 1.22686i | ||||
\(995\) | 7.06054 | − | 21.7301i | 0.223834 | − | 0.688890i | ||||
\(996\) | 11.6975 | − | 8.49870i | 0.370648 | − | 0.269292i | ||||
\(997\) | 46.3656 | 1.46841 | 0.734207 | − | 0.678926i | \(-0.237554\pi\) | ||||
0.734207 | + | 0.678926i | \(0.237554\pi\) | |||||||
\(998\) | −23.5044 | −0.744018 | ||||||||
\(999\) | −8.67481 | + | 6.30262i | −0.274459 | + | 0.199406i |
(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 | 930.2.n.f.841.1 | yes | 12 | |
31.8 | even | 5 | inner | 930.2.n.f.721.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.f.721.1 | ✓ | 12 | 31.8 | even | 5 | inner | |
930.2.n.f.841.1 | yes | 12 | 1.1 | even | 1 | trivial |