Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [310,2,Mod(101,310)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(310, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("310.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 310 = 2 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 310.h (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: | \(2.47536246266\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.64000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 221.1 | ||
Root | \(1.14412 - 0.831254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 310.221 |
Dual form | 310.2.h.e.101.1 |
$q$-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 \(\left(\mathbb{Z}/310\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(251\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||
\(3\) | −0.579108 | + | 1.78231i | −0.334348 | + | 1.02902i | 0.632694 | + | 0.774402i | \(0.281949\pi\) |
−0.967042 | + | 0.254616i | \(0.918051\pi\) | |||||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.87403 | 0.765070 | ||||||||
\(7\) | 2.95314 | − | 2.14558i | 1.11618 | − | 0.810954i | 0.132556 | − | 0.991176i | \(-0.457682\pi\) |
0.983626 | + | 0.180222i | \(0.0576816\pi\) | |||||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | −0.414214 | − | 0.300944i | −0.138071 | − | 0.100315i | ||||
\(10\) | 0.309017 | + | 0.951057i | 0.0977198 | + | 0.300750i | ||||
\(11\) | −1.47923 | + | 1.07472i | −0.446004 | + | 0.324041i | −0.788016 | − | 0.615655i | \(-0.788892\pi\) |
0.342012 | + | 0.939696i | \(0.388892\pi\) | |||||||
\(12\) | −0.579108 | − | 1.78231i | −0.167174 | − | 0.514509i | ||||
\(13\) | −1.92418 | + | 5.92201i | −0.533671 | + | 1.64247i | 0.212832 | + | 0.977089i | \(0.431731\pi\) |
−0.746503 | + | 0.665382i | \(0.768269\pi\) | |||||||
\(14\) | −2.95314 | − | 2.14558i | −0.789260 | − | 0.573431i | ||||
\(15\) | 0.579108 | − | 1.78231i | 0.149525 | − | 0.460191i | ||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 2.86735 | + | 2.08325i | 0.695435 | + | 0.505263i | 0.878442 | − | 0.477848i | \(-0.158583\pi\) |
−0.183007 | + | 0.983112i | \(0.558583\pi\) | |||||||
\(18\) | −0.158216 | + | 0.486937i | −0.0372918 | + | 0.114772i | ||||
\(19\) | 2.03225 | + | 6.25461i | 0.466230 | + | 1.43491i | 0.857430 | + | 0.514601i | \(0.172060\pi\) |
−0.391200 | + | 0.920306i | \(0.627940\pi\) | |||||||
\(20\) | 0.809017 | − | 0.587785i | 0.180902 | − | 0.131433i | ||||
\(21\) | 2.11391 | + | 6.50593i | 0.461292 | + | 1.41971i | ||||
\(22\) | 1.47923 | + | 1.07472i | 0.315373 | + | 0.229132i | ||||
\(23\) | 4.36407 | + | 3.17068i | 0.909971 | + | 0.661133i | 0.941007 | − | 0.338386i | \(-0.109881\pi\) |
−0.0310366 | + | 0.999518i | \(0.509881\pi\) | |||||||
\(24\) | −1.51612 | + | 1.10153i | −0.309477 | + | 0.224849i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.22677 | 1.22117 | ||||||||
\(27\) | −3.77212 | + | 2.74061i | −0.725945 | + | 0.527430i | ||||
\(28\) | −1.12800 | + | 3.47162i | −0.213172 | + | 0.656075i | ||||
\(29\) | −2.76419 | − | 8.50730i | −0.513297 | − | 1.57977i | −0.786360 | − | 0.617769i | \(-0.788037\pi\) |
0.273063 | − | 0.961996i | \(-0.411963\pi\) | |||||||
\(30\) | −1.87403 | −0.342150 | ||||||||
\(31\) | −5.56653 | − | 0.117415i | −0.999778 | − | 0.0210884i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.05886 | − | 3.25882i | −0.184323 | − | 0.567289i | ||||
\(34\) | 1.09523 | − | 3.37078i | 0.187831 | − | 0.578083i | ||||
\(35\) | −2.95314 | + | 2.14558i | −0.499172 | + | 0.362669i | ||||
\(36\) | 0.511996 | 0.0853327 | ||||||||
\(37\) | 10.9907 | 1.80686 | 0.903430 | − | 0.428735i | \(-0.141041\pi\) | ||||
0.903430 | + | 0.428735i | \(0.141041\pi\) | |||||||
\(38\) | 5.32049 | − | 3.86556i | 0.863098 | − | 0.627077i | ||||
\(39\) | −9.44056 | − | 6.85897i | −1.51170 | − | 1.09831i | ||||
\(40\) | −0.809017 | − | 0.587785i | −0.127917 | − | 0.0929370i | ||||
\(41\) | −2.48413 | − | 7.64537i | −0.387956 | − | 1.19401i | −0.934313 | − | 0.356454i | \(-0.883986\pi\) |
0.546357 | − | 0.837553i | \(-0.316014\pi\) | |||||||
\(42\) | 5.53428 | − | 4.02089i | 0.853958 | − | 0.620437i | ||||
\(43\) | 0.874032 | + | 2.68999i | 0.133289 | + | 0.410220i | 0.995320 | − | 0.0966349i | \(-0.0308079\pi\) |
−0.862031 | + | 0.506855i | \(0.830808\pi\) | |||||||
\(44\) | 0.565015 | − | 1.73894i | 0.0851792 | − | 0.262155i | ||||
\(45\) | 0.414214 | + | 0.300944i | 0.0617473 | + | 0.0448620i | ||||
\(46\) | 1.66693 | − | 5.13027i | 0.245775 | − | 0.756417i | ||||
\(47\) | 0.253967 | − | 0.781630i | 0.0370449 | − | 0.114012i | −0.930824 | − | 0.365468i | \(-0.880909\pi\) |
0.967869 | + | 0.251455i | \(0.0809091\pi\) | |||||||
\(48\) | 1.51612 | + | 1.10153i | 0.218834 | + | 0.158992i | ||||
\(49\) | 1.95440 | − | 6.01501i | 0.279199 | − | 0.859287i | ||||
\(50\) | −0.309017 | − | 0.951057i | −0.0437016 | − | 0.134500i | ||||
\(51\) | −5.37351 | + | 3.90409i | −0.752442 | + | 0.546681i | ||||
\(52\) | −1.92418 | − | 5.92201i | −0.266836 | − | 0.821235i | ||||
\(53\) | −3.32979 | − | 2.41923i | −0.457382 | − | 0.332307i | 0.335122 | − | 0.942175i | \(-0.391223\pi\) |
−0.792503 | + | 0.609868i | \(0.791223\pi\) | |||||||
\(54\) | 3.77212 | + | 2.74061i | 0.513321 | + | 0.372949i | ||||
\(55\) | 1.47923 | − | 1.07472i | 0.199459 | − | 0.144916i | ||||
\(56\) | 3.65028 | 0.487789 | ||||||||
\(57\) | −12.3246 | −1.63243 | ||||||||
\(58\) | −7.23674 | + | 5.25780i | −0.950230 | + | 0.690383i | ||||
\(59\) | −1.05792 | + | 3.25595i | −0.137730 | + | 0.423889i | −0.996005 | − | 0.0893017i | \(-0.971536\pi\) |
0.858275 | + | 0.513190i | \(0.171536\pi\) | |||||||
\(60\) | 0.579108 | + | 1.78231i | 0.0747625 | + | 0.230095i | ||||
\(61\) | 9.38499 | 1.20162 | 0.600812 | − | 0.799390i | \(-0.294844\pi\) | ||||
0.600812 | + | 0.799390i | \(0.294844\pi\) | |||||||
\(62\) | 1.60848 | + | 5.33036i | 0.204278 | + | 0.676957i | ||||
\(63\) | −1.86893 | −0.235463 | ||||||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 1.92418 | − | 5.92201i | 0.238665 | − | 0.734535i | ||||
\(66\) | −2.77212 | + | 2.01406i | −0.341225 | + | 0.247914i | ||||
\(67\) | −0.182208 | −0.0222602 | −0.0111301 | − | 0.999938i | \(-0.503543\pi\) | ||||
−0.0111301 | + | 0.999938i | \(0.503543\pi\) | |||||||
\(68\) | −3.54424 | −0.429803 | ||||||||
\(69\) | −8.17840 | + | 5.94196i | −0.984564 | + | 0.715327i | ||||
\(70\) | 2.95314 | + | 2.14558i | 0.352968 | + | 0.256446i | ||||
\(71\) | −1.52473 | − | 1.10778i | −0.180952 | − | 0.131469i | 0.493622 | − | 0.869677i | \(-0.335673\pi\) |
−0.674574 | + | 0.738207i | \(0.735673\pi\) | |||||||
\(72\) | −0.158216 | − | 0.486937i | −0.0186459 | − | 0.0573861i | ||||
\(73\) | 12.8448 | − | 9.33230i | 1.50337 | − | 1.09226i | 0.534356 | − | 0.845259i | \(-0.320554\pi\) |
0.969015 | − | 0.247004i | \(-0.0794460\pi\) | |||||||
\(74\) | −3.39631 | − | 10.4528i | −0.394814 | − | 1.21511i | ||||
\(75\) | −0.579108 | + | 1.78231i | −0.0668696 | + | 0.205803i | ||||
\(76\) | −5.32049 | − | 3.86556i | −0.610302 | − | 0.443411i | ||||
\(77\) | −2.06246 | + | 6.34761i | −0.235040 | + | 0.723377i | ||||
\(78\) | −3.60597 | + | 11.0980i | −0.408296 | + | 1.25661i | ||||
\(79\) | −4.09398 | − | 2.97445i | −0.460608 | − | 0.334652i | 0.333162 | − | 0.942870i | \(-0.391885\pi\) |
−0.793770 | + | 0.608218i | \(0.791885\pi\) | |||||||
\(80\) | −0.309017 | + | 0.951057i | −0.0345492 | + | 0.106331i | ||||
\(81\) | −3.17479 | − | 9.77101i | −0.352755 | − | 1.08567i | ||||
\(82\) | −6.50354 | + | 4.72510i | −0.718196 | + | 0.521800i | ||||
\(83\) | 0.832595 | + | 2.56246i | 0.0913892 | + | 0.281267i | 0.986296 | − | 0.164986i | \(-0.0527580\pi\) |
−0.894907 | + | 0.446253i | \(0.852758\pi\) | |||||||
\(84\) | −5.53428 | − | 4.02089i | −0.603839 | − | 0.438715i | ||||
\(85\) | −2.86735 | − | 2.08325i | −0.311008 | − | 0.225961i | ||||
\(86\) | 2.28825 | − | 1.66251i | 0.246748 | − | 0.179273i | ||||
\(87\) | 16.7634 | 1.79723 | ||||||||
\(88\) | −1.82843 | −0.194911 | ||||||||
\(89\) | −8.21614 | + | 5.96937i | −0.870909 | + | 0.632752i | −0.930831 | − | 0.365451i | \(-0.880915\pi\) |
0.0599218 | + | 0.998203i | \(0.480915\pi\) | |||||||
\(90\) | 0.158216 | − | 0.486937i | 0.0166774 | − | 0.0513277i | ||||
\(91\) | 7.02379 | + | 21.6170i | 0.736294 | + | 2.26608i | ||||
\(92\) | −5.39428 | −0.562393 | ||||||||
\(93\) | 3.43289 | − | 9.85328i | 0.355974 | − | 1.02174i | ||||
\(94\) | −0.821854 | −0.0847678 | ||||||||
\(95\) | −2.03225 | − | 6.25461i | −0.208504 | − | 0.641710i | ||||
\(96\) | 0.579108 | − | 1.78231i | 0.0591049 | − | 0.181906i | ||||
\(97\) | −4.61803 | + | 3.35520i | −0.468890 | + | 0.340669i | −0.797009 | − | 0.603968i | \(-0.793586\pi\) |
0.328118 | + | 0.944637i | \(0.393586\pi\) | |||||||
\(98\) | −6.32456 | −0.638877 | ||||||||
\(99\) | 0.936148 | 0.0940864 | ||||||||
\(100\) | −0.809017 | + | 0.587785i | −0.0809017 | + | 0.0587785i | ||||
\(101\) | −12.2062 | − | 8.86830i | −1.21456 | − | 0.882429i | −0.218923 | − | 0.975742i | \(-0.570254\pi\) |
−0.995637 | + | 0.0933130i | \(0.970254\pi\) | |||||||
\(102\) | 5.37351 | + | 3.90409i | 0.532057 | + | 0.386562i | ||||
\(103\) | 1.59236 | + | 4.90078i | 0.156900 | + | 0.482888i | 0.998348 | − | 0.0574492i | \(-0.0182967\pi\) |
−0.841449 | + | 0.540337i | \(0.818297\pi\) | |||||||
\(104\) | −5.03756 | + | 3.66001i | −0.493974 | + | 0.358893i | ||||
\(105\) | −2.11391 | − | 6.50593i | −0.206296 | − | 0.634914i | ||||
\(106\) | −1.27187 | + | 3.91440i | −0.123535 | + | 0.380200i | ||||
\(107\) | −11.9708 | − | 8.69728i | −1.15726 | − | 0.840797i | −0.167830 | − | 0.985816i | \(-0.553676\pi\) |
−0.989429 | + | 0.145019i | \(0.953676\pi\) | |||||||
\(108\) | 1.44082 | − | 4.43440i | 0.138643 | − | 0.426700i | ||||
\(109\) | 4.23397 | − | 13.0308i | 0.405541 | − | 1.24813i | −0.514902 | − | 0.857249i | \(-0.672172\pi\) |
0.920443 | − | 0.390877i | \(-0.127828\pi\) | |||||||
\(110\) | −1.47923 | − | 1.07472i | −0.141039 | − | 0.102471i | ||||
\(111\) | −6.36480 | + | 19.5888i | −0.604120 | + | 1.85929i | ||||
\(112\) | −1.12800 | − | 3.47162i | −0.106586 | − | 0.328038i | ||||
\(113\) | 11.6235 | − | 8.44497i | 1.09345 | − | 0.794436i | 0.113469 | − | 0.993542i | \(-0.463804\pi\) |
0.979978 | + | 0.199106i | \(0.0638037\pi\) | |||||||
\(114\) | 3.80850 | + | 11.7213i | 0.356698 | + | 1.09780i | ||||
\(115\) | −4.36407 | − | 3.17068i | −0.406951 | − | 0.295667i | ||||
\(116\) | 7.23674 | + | 5.25780i | 0.671914 | + | 0.488174i | ||||
\(117\) | 2.57921 | − | 1.87391i | 0.238448 | − | 0.173243i | ||||
\(118\) | 3.42351 | 0.315160 | ||||||||
\(119\) | 12.9375 | 1.18598 | ||||||||
\(120\) | 1.51612 | − | 1.10153i | 0.138403 | − | 0.100555i | ||||
\(121\) | −2.36610 | + | 7.28210i | −0.215100 | + | 0.662009i | ||||
\(122\) | −2.90012 | − | 8.92565i | −0.262565 | − | 0.808091i | ||||
\(123\) | 15.0650 | 1.35837 | ||||||||
\(124\) | 4.57243 | − | 3.17693i | 0.410616 | − | 0.285297i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.577531 | + | 1.77746i | 0.0514506 | + | 0.158349i | ||||
\(127\) | 0.509965 | − | 1.56951i | 0.0452521 | − | 0.139272i | −0.925878 | − | 0.377823i | \(-0.876673\pi\) |
0.971130 | + | 0.238552i | \(0.0766727\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | −5.30056 | −0.466689 | ||||||||
\(130\) | −6.22677 | −0.546124 | ||||||||
\(131\) | −0.636603 | + | 0.462519i | −0.0556202 | + | 0.0404105i | −0.615248 | − | 0.788334i | \(-0.710944\pi\) |
0.559628 | + | 0.828744i | \(0.310944\pi\) | |||||||
\(132\) | 2.77212 | + | 2.01406i | 0.241282 | + | 0.175302i | ||||
\(133\) | 19.4213 | + | 14.1104i | 1.68404 | + | 1.22353i | ||||
\(134\) | 0.0563053 | + | 0.173290i | 0.00486404 | + | 0.0149700i | ||||
\(135\) | 3.77212 | − | 2.74061i | 0.324653 | − | 0.235874i | ||||
\(136\) | 1.09523 | + | 3.37078i | 0.0939153 | + | 0.289042i | ||||
\(137\) | −4.76551 | + | 14.6667i | −0.407145 | + | 1.25306i | 0.511946 | + | 0.859018i | \(0.328925\pi\) |
−0.919091 | + | 0.394045i | \(0.871075\pi\) | |||||||
\(138\) | 8.17840 | + | 5.94196i | 0.696192 | + | 0.505813i | ||||
\(139\) | −1.10029 | + | 3.38635i | −0.0933256 | + | 0.287227i | −0.986814 | − | 0.161860i | \(-0.948251\pi\) |
0.893488 | + | 0.449087i | \(0.148251\pi\) | |||||||
\(140\) | 1.12800 | − | 3.47162i | 0.0953333 | − | 0.293406i | ||||
\(141\) | 1.24603 | + | 0.905296i | 0.104935 | + | 0.0762397i | ||||
\(142\) | −0.582394 | + | 1.79242i | −0.0488734 | + | 0.150417i | ||||
\(143\) | −3.51822 | − | 10.8280i | −0.294208 | − | 0.905480i | ||||
\(144\) | −0.414214 | + | 0.300944i | −0.0345178 | + | 0.0250786i | ||||
\(145\) | 2.76419 | + | 8.50730i | 0.229553 | + | 0.706492i | ||||
\(146\) | −12.8448 | − | 9.33230i | −1.06304 | − | 0.772347i | ||||
\(147\) | 9.58881 | + | 6.96668i | 0.790872 | + | 0.574602i | ||||
\(148\) | −8.89167 | + | 6.46017i | −0.730891 | + | 0.531023i | ||||
\(149\) | 17.0418 | 1.39612 | 0.698061 | − | 0.716038i | \(-0.254046\pi\) | ||||
0.698061 | + | 0.716038i | \(0.254046\pi\) | |||||||
\(150\) | 1.87403 | 0.153014 | ||||||||
\(151\) | 7.02634 | − | 5.10494i | 0.571796 | − | 0.415434i | −0.263961 | − | 0.964533i | \(-0.585029\pi\) |
0.835757 | + | 0.549099i | \(0.185029\pi\) | |||||||
\(152\) | −2.03225 | + | 6.25461i | −0.164837 | + | 0.507316i | ||||
\(153\) | −0.560754 | − | 1.72582i | −0.0453343 | − | 0.139525i | ||||
\(154\) | 6.67427 | 0.537828 | ||||||||
\(155\) | 5.56653 | + | 0.117415i | 0.447114 | + | 0.00943100i | ||||
\(156\) | 11.6692 | 0.934281 | ||||||||
\(157\) | −3.21117 | − | 9.88296i | −0.256279 | − | 0.788746i | −0.993575 | − | 0.113176i | \(-0.963898\pi\) |
0.737296 | − | 0.675570i | \(-0.236102\pi\) | |||||||
\(158\) | −1.56376 | + | 4.81276i | −0.124406 | + | 0.382882i | ||||
\(159\) | 6.24013 | − | 4.53372i | 0.494875 | − | 0.359547i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 19.6907 | 1.55184 | ||||||||
\(162\) | −8.31172 | + | 6.03882i | −0.653030 | + | 0.474454i | ||||
\(163\) | −5.15983 | − | 3.74884i | −0.404149 | − | 0.293632i | 0.367080 | − | 0.930190i | \(-0.380358\pi\) |
−0.771229 | + | 0.636558i | \(0.780358\pi\) | |||||||
\(164\) | 6.50354 | + | 4.72510i | 0.507841 | + | 0.368968i | ||||
\(165\) | 1.05886 | + | 3.25882i | 0.0824319 | + | 0.253699i | ||||
\(166\) | 2.17976 | − | 1.58369i | 0.169182 | − | 0.122918i | ||||
\(167\) | 1.90983 | + | 5.87785i | 0.147787 | + | 0.454842i | 0.997359 | − | 0.0726311i | \(-0.0231396\pi\) |
−0.849572 | + | 0.527473i | \(0.823140\pi\) | |||||||
\(168\) | −2.11391 | + | 6.50593i | −0.163091 | + | 0.501944i | ||||
\(169\) | −20.8506 | − | 15.1488i | −1.60389 | − | 1.16529i | ||||
\(170\) | −1.09523 | + | 3.37078i | −0.0840004 | + | 0.258527i | ||||
\(171\) | 1.04050 | − | 3.20234i | 0.0795692 | − | 0.244889i | ||||
\(172\) | −2.28825 | − | 1.66251i | −0.174477 | − | 0.126765i | ||||
\(173\) | 3.96623 | − | 12.2068i | 0.301547 | − | 0.928067i | −0.679396 | − | 0.733772i | \(-0.737758\pi\) |
0.980943 | − | 0.194295i | \(-0.0622418\pi\) | |||||||
\(174\) | −5.18018 | − | 15.9429i | −0.392708 | − | 1.20863i | ||||
\(175\) | 2.95314 | − | 2.14558i | 0.223236 | − | 0.162191i | ||||
\(176\) | 0.565015 | + | 1.73894i | 0.0425896 | + | 0.131077i | ||||
\(177\) | −5.19046 | − | 3.77109i | −0.390139 | − | 0.283453i | ||||
\(178\) | 8.21614 | + | 5.96937i | 0.615826 | + | 0.447423i | ||||
\(179\) | 11.4200 | − | 8.29709i | 0.853568 | − | 0.620153i | −0.0725597 | − | 0.997364i | \(-0.523117\pi\) |
0.926127 | + | 0.377211i | \(0.123117\pi\) | |||||||
\(180\) | −0.511996 | −0.0381619 | ||||||||
\(181\) | 2.20654 | 0.164011 | 0.0820055 | − | 0.996632i | \(-0.473867\pi\) | ||||
0.0820055 | + | 0.996632i | \(0.473867\pi\) | |||||||
\(182\) | 18.3885 | − | 13.3600i | 1.36305 | − | 0.990313i | ||||
\(183\) | −5.43492 | + | 16.7270i | −0.401761 | + | 1.23649i | ||||
\(184\) | 1.66693 | + | 5.13027i | 0.122887 | + | 0.378208i | ||||
\(185\) | −10.9907 | −0.808053 | ||||||||
\(186\) | −10.4318 | − | 0.220039i | −0.764900 | − | 0.0161341i | ||||
\(187\) | −6.48039 | −0.473893 | ||||||||
\(188\) | 0.253967 | + | 0.781630i | 0.0185224 | + | 0.0570062i | ||||
\(189\) | −5.25941 | + | 16.1868i | −0.382566 | + | 1.17742i | ||||
\(190\) | −5.32049 | + | 3.86556i | −0.385989 | + | 0.280438i | ||||
\(191\) | 18.4221 | 1.33298 | 0.666489 | − | 0.745515i | \(-0.267796\pi\) | ||||
0.666489 | + | 0.745515i | \(0.267796\pi\) | |||||||
\(192\) | −1.87403 | −0.135247 | ||||||||
\(193\) | −4.13839 | + | 3.00672i | −0.297888 | + | 0.216428i | −0.726682 | − | 0.686974i | \(-0.758939\pi\) |
0.428794 | + | 0.903402i | \(0.358939\pi\) | |||||||
\(194\) | 4.61803 | + | 3.35520i | 0.331556 | + | 0.240889i | ||||
\(195\) | 9.44056 | + | 6.85897i | 0.676052 | + | 0.491181i | ||||
\(196\) | 1.95440 | + | 6.01501i | 0.139600 | + | 0.429644i | ||||
\(197\) | −3.84438 | + | 2.79311i | −0.273901 | + | 0.199001i | −0.716253 | − | 0.697841i | \(-0.754144\pi\) |
0.442352 | + | 0.896842i | \(0.354144\pi\) | |||||||
\(198\) | −0.289286 | − | 0.890329i | −0.0205586 | − | 0.0632729i | ||||
\(199\) | 2.59836 | − | 7.99693i | 0.184193 | − | 0.566887i | −0.815741 | − | 0.578418i | \(-0.803670\pi\) |
0.999934 | + | 0.0115305i | \(0.00367036\pi\) | |||||||
\(200\) | 0.809017 | + | 0.587785i | 0.0572061 | + | 0.0415627i | ||||
\(201\) | 0.105518 | − | 0.324751i | 0.00744266 | − | 0.0229062i | ||||
\(202\) | −4.66234 | + | 14.3492i | −0.328041 | + | 1.00961i | ||||
\(203\) | −26.4161 | − | 19.1924i | −1.85405 | − | 1.34705i | ||||
\(204\) | 2.05250 | − | 6.31694i | 0.143704 | − | 0.442274i | ||||
\(205\) | 2.48413 | + | 7.64537i | 0.173499 | + | 0.533976i | ||||
\(206\) | 4.16885 | − | 3.02885i | 0.290458 | − | 0.211030i | ||||
\(207\) | −0.853459 | − | 2.62668i | −0.0593195 | − | 0.182567i | ||||
\(208\) | 5.03756 | + | 3.66001i | 0.349292 | + | 0.253776i | ||||
\(209\) | −9.72813 | − | 7.06790i | −0.672909 | − | 0.488897i | ||||
\(210\) | −5.53428 | + | 4.02089i | −0.381902 | + | 0.277468i | ||||
\(211\) | −11.1672 | −0.768780 | −0.384390 | − | 0.923171i | \(-0.625588\pi\) | ||||
−0.384390 | + | 0.923171i | \(0.625588\pi\) | |||||||
\(212\) | 4.11584 | 0.282677 | ||||||||
\(213\) | 2.85739 | − | 2.07601i | 0.195785 | − | 0.142246i | ||||
\(214\) | −4.57243 | + | 14.0725i | −0.312565 | + | 0.961976i | ||||
\(215\) | −0.874032 | − | 2.68999i | −0.0596085 | − | 0.183456i | ||||
\(216\) | −4.66260 | −0.317250 | ||||||||
\(217\) | −16.6907 | + | 11.5967i | −1.13304 | + | 0.787235i | ||||
\(218\) | −13.7014 | −0.927977 | ||||||||
\(219\) | 9.19453 | + | 28.2978i | 0.621308 | + | 1.91219i | ||||
\(220\) | −0.565015 | + | 1.73894i | −0.0380933 | + | 0.117239i | ||||
\(221\) | −17.8544 | + | 12.9720i | −1.20101 | + | 0.872588i | ||||
\(222\) | 20.5969 | 1.38238 | ||||||||
\(223\) | −1.86150 | −0.124655 | −0.0623277 | − | 0.998056i | \(-0.519852\pi\) | ||||
−0.0623277 | + | 0.998056i | \(0.519852\pi\) | |||||||
\(224\) | −2.95314 | + | 2.14558i | −0.197315 | + | 0.143358i | ||||
\(225\) | −0.414214 | − | 0.300944i | −0.0276142 | − | 0.0200629i | ||||
\(226\) | −11.6235 | − | 8.44497i | −0.773184 | − | 0.561751i | ||||
\(227\) | 0.927209 | + | 2.85366i | 0.0615410 | + | 0.189404i | 0.977100 | − | 0.212779i | \(-0.0682515\pi\) |
−0.915559 | + | 0.402183i | \(0.868252\pi\) | |||||||
\(228\) | 9.97077 | − | 7.24419i | 0.660331 | − | 0.479758i | ||||
\(229\) | 4.68843 | + | 14.4295i | 0.309820 | + | 0.953529i | 0.977834 | + | 0.209380i | \(0.0671446\pi\) |
−0.668014 | + | 0.744149i | \(0.732855\pi\) | |||||||
\(230\) | −1.66693 | + | 5.13027i | −0.109914 | + | 0.338280i | ||||
\(231\) | −10.1190 | − | 7.35190i | −0.665783 | − | 0.483720i | ||||
\(232\) | 2.76419 | − | 8.50730i | 0.181478 | − | 0.558531i | ||||
\(233\) | 7.05369 | − | 21.7090i | 0.462103 | − | 1.42221i | −0.400488 | − | 0.916302i | \(-0.631159\pi\) |
0.862590 | − | 0.505903i | \(-0.168841\pi\) | |||||||
\(234\) | −2.57921 | − | 1.87391i | −0.168608 | − | 0.122501i | ||||
\(235\) | −0.253967 | + | 0.781630i | −0.0165670 | + | 0.0509879i | ||||
\(236\) | −1.05792 | − | 3.25595i | −0.0688649 | − | 0.211944i | ||||
\(237\) | 7.67224 | − | 5.57421i | 0.498366 | − | 0.362084i | ||||
\(238\) | −3.99790 | − | 12.3043i | −0.259146 | − | 0.797568i | ||||
\(239\) | 16.2270 | + | 11.7896i | 1.04964 | + | 0.762608i | 0.972144 | − | 0.234385i | \(-0.0753077\pi\) |
0.0774954 | + | 0.996993i | \(0.475308\pi\) | |||||||
\(240\) | −1.51612 | − | 1.10153i | −0.0978654 | − | 0.0711034i | ||||
\(241\) | −0.355771 | + | 0.258483i | −0.0229172 | + | 0.0166503i | −0.599185 | − | 0.800611i | \(-0.704509\pi\) |
0.576268 | + | 0.817261i | \(0.304509\pi\) | |||||||
\(242\) | 7.65685 | 0.492201 | ||||||||
\(243\) | 5.26572 | 0.337796 | ||||||||
\(244\) | −7.59261 | + | 5.51636i | −0.486067 | + | 0.353149i | ||||
\(245\) | −1.95440 | + | 6.01501i | −0.124862 | + | 0.384285i | ||||
\(246\) | −4.65534 | − | 14.3277i | −0.296814 | − | 0.913499i | ||||
\(247\) | −40.9503 | −2.60561 | ||||||||
\(248\) | −4.43440 | − | 3.36691i | −0.281585 | − | 0.213799i | ||||
\(249\) | −5.04927 | −0.319984 | ||||||||
\(250\) | 0.309017 | + | 0.951057i | 0.0195440 | + | 0.0601501i | ||||
\(251\) | −1.04593 | + | 3.21903i | −0.0660183 | + | 0.203183i | −0.978624 | − | 0.205657i | \(-0.934067\pi\) |
0.912606 | + | 0.408841i | \(0.134067\pi\) | |||||||
\(252\) | 1.51200 | − | 1.09853i | 0.0952468 | − | 0.0692009i | ||||
\(253\) | −9.86305 | −0.620085 | ||||||||
\(254\) | −1.65028 | −0.103548 | ||||||||
\(255\) | 5.37351 | − | 3.90409i | 0.336502 | − | 0.244483i | ||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 13.9104 | + | 10.1065i | 0.867707 | + | 0.630426i | 0.929971 | − | 0.367633i | \(-0.119832\pi\) |
−0.0622634 | + | 0.998060i | \(0.519832\pi\) | |||||||
\(258\) | 1.63796 | + | 5.04114i | 0.101975 | + | 0.313847i | ||||
\(259\) | 32.4571 | − | 23.5815i | 2.01679 | − | 1.46528i | ||||
\(260\) | 1.92418 | + | 5.92201i | 0.119332 | + | 0.367268i | ||||
\(261\) | −1.41525 | + | 4.35570i | −0.0876020 | + | 0.269611i | ||||
\(262\) | 0.636603 | + | 0.462519i | 0.0393295 | + | 0.0285745i | ||||
\(263\) | −6.48830 | + | 19.9689i | −0.400086 | + | 1.23134i | 0.524844 | + | 0.851199i | \(0.324124\pi\) |
−0.924929 | + | 0.380139i | \(0.875876\pi\) | |||||||
\(264\) | 1.05886 | − | 3.25882i | 0.0651681 | − | 0.200567i | ||||
\(265\) | 3.32979 | + | 2.41923i | 0.204547 | + | 0.148612i | ||||
\(266\) | 7.41828 | − | 22.8311i | 0.454844 | − | 1.39986i | ||||
\(267\) | −5.88125 | − | 18.1006i | −0.359926 | − | 1.10774i | ||||
\(268\) | 0.147409 | − | 0.107099i | 0.00900445 | − | 0.00654211i | ||||
\(269\) | −2.26951 | − | 6.98484i | −0.138375 | − | 0.425873i | 0.857725 | − | 0.514109i | \(-0.171877\pi\) |
−0.996100 | + | 0.0882353i | \(0.971877\pi\) | |||||||
\(270\) | −3.77212 | − | 2.74061i | −0.229564 | − | 0.166788i | ||||
\(271\) | 1.20972 | + | 0.878915i | 0.0734855 | + | 0.0533903i | 0.623921 | − | 0.781487i | \(-0.285539\pi\) |
−0.550436 | + | 0.834877i | \(0.685539\pi\) | |||||||
\(272\) | 2.86735 | − | 2.08325i | 0.173859 | − | 0.126316i | ||||
\(273\) | −42.5958 | −2.57801 | ||||||||
\(274\) | 15.4215 | 0.931647 | ||||||||
\(275\) | −1.47923 | + | 1.07472i | −0.0892008 | + | 0.0648082i | ||||
\(276\) | 3.12387 | − | 9.61429i | 0.188035 | − | 0.578712i | ||||
\(277\) | 2.95768 | + | 9.10281i | 0.177710 | + | 0.546935i | 0.999747 | − | 0.0224994i | \(-0.00716238\pi\) |
−0.822037 | + | 0.569434i | \(0.807162\pi\) | |||||||
\(278\) | 3.56062 | 0.213552 | ||||||||
\(279\) | 2.27040 | + | 1.72385i | 0.135925 | + | 0.103204i | ||||
\(280\) | −3.65028 | −0.218146 | ||||||||
\(281\) | −1.57940 | − | 4.86091i | −0.0942193 | − | 0.289977i | 0.892830 | − | 0.450394i | \(-0.148716\pi\) |
−0.987049 | + | 0.160416i | \(0.948716\pi\) | |||||||
\(282\) | 0.475942 | − | 1.46480i | 0.0283419 | − | 0.0872276i | ||||
\(283\) | −9.24020 | + | 6.71340i | −0.549273 | + | 0.399070i | −0.827517 | − | 0.561440i | \(-0.810247\pi\) |
0.278245 | + | 0.960510i | \(0.410247\pi\) | |||||||
\(284\) | 1.88467 | 0.111834 | ||||||||
\(285\) | 12.3246 | 0.730044 | ||||||||
\(286\) | −9.21082 | + | 6.69205i | −0.544647 | + | 0.395709i | ||||
\(287\) | −23.7398 | − | 17.2479i | −1.40131 | − | 1.01811i | ||||
\(288\) | 0.414214 | + | 0.300944i | 0.0244078 | + | 0.0177333i | ||||
\(289\) | −1.37152 | − | 4.22111i | −0.0806777 | − | 0.248301i | ||||
\(290\) | 7.23674 | − | 5.25780i | 0.424956 | − | 0.308749i | ||||
\(291\) | −3.30567 | − | 10.1738i | −0.193782 | − | 0.596398i | ||||
\(292\) | −4.90628 | + | 15.1000i | −0.287118 | + | 0.883659i | ||||
\(293\) | −2.41296 | − | 1.75312i | −0.140967 | − | 0.102418i | 0.515067 | − | 0.857150i | \(-0.327767\pi\) |
−0.656034 | + | 0.754732i | \(0.727767\pi\) | |||||||
\(294\) | 3.66260 | − | 11.2723i | 0.213607 | − | 0.657415i | ||||
\(295\) | 1.05792 | − | 3.25595i | 0.0615946 | − | 0.189569i | ||||
\(296\) | 8.89167 | + | 6.46017i | 0.516818 | + | 0.375490i | ||||
\(297\) | 2.63444 | − | 8.10797i | 0.152866 | − | 0.470472i | ||||
\(298\) | −5.26622 | − | 16.2078i | −0.305064 | − | 0.938890i | ||||
\(299\) | −27.1741 | + | 19.7431i | −1.57152 | + | 1.14177i | ||||
\(300\) | −0.579108 | − | 1.78231i | −0.0334348 | − | 0.102902i | ||||
\(301\) | 8.35274 | + | 6.06862i | 0.481444 | + | 0.349790i | ||||
\(302\) | −7.02634 | − | 5.10494i | −0.404321 | − | 0.293756i | ||||
\(303\) | 22.8748 | − | 16.6195i | 1.31412 | − | 0.954764i | ||||
\(304\) | 6.57649 | 0.377188 | ||||||||
\(305\) | −9.38499 | −0.537383 | ||||||||
\(306\) | −1.46807 | + | 1.06662i | −0.0839242 | + | 0.0609745i | ||||
\(307\) | 8.11093 | − | 24.9629i | 0.462915 | − | 1.42471i | −0.398671 | − | 0.917094i | \(-0.630528\pi\) |
0.861586 | − | 0.507612i | \(-0.169472\pi\) | |||||||
\(308\) | −2.06246 | − | 6.34761i | −0.117520 | − | 0.361689i | ||||
\(309\) | −9.65685 | −0.549359 | ||||||||
\(310\) | −1.60848 | − | 5.33036i | −0.0913557 | − | 0.302744i | ||||
\(311\) | 10.7504 | 0.609597 | 0.304799 | − | 0.952417i | \(-0.401411\pi\) | ||||
0.304799 | + | 0.952417i | \(0.401411\pi\) | |||||||
\(312\) | −3.60597 | − | 11.0980i | −0.204148 | − | 0.628303i | ||||
\(313\) | 0.460712 | − | 1.41793i | 0.0260410 | − | 0.0801459i | −0.937191 | − | 0.348816i | \(-0.886584\pi\) |
0.963232 | + | 0.268670i | \(0.0865840\pi\) | |||||||
\(314\) | −8.40695 | + | 6.10801i | −0.474432 | + | 0.344695i | ||||
\(315\) | 1.86893 | 0.105302 | ||||||||
\(316\) | 5.06043 | 0.284672 | ||||||||
\(317\) | 11.2847 | − | 8.19881i | 0.633812 | − | 0.460491i | −0.223907 | − | 0.974611i | \(-0.571881\pi\) |
0.857719 | + | 0.514119i | \(0.171881\pi\) | |||||||
\(318\) | −6.24013 | − | 4.53372i | −0.349929 | − | 0.254238i | ||||
\(319\) | 13.2318 | + | 9.61350i | 0.740841 | + | 0.538253i | ||||
\(320\) | −0.309017 | − | 0.951057i | −0.0172746 | − | 0.0531657i | ||||
\(321\) | 22.4336 | − | 16.2990i | 1.25212 | − | 0.909720i | ||||
\(322\) | −6.08475 | − | 18.7269i | −0.339090 | − | 1.04361i | ||||
\(323\) | −7.20278 | + | 22.1679i | −0.400773 | + | 1.23345i | ||||
\(324\) | 8.31172 | + | 6.03882i | 0.461762 | + | 0.335490i | ||||
\(325\) | −1.92418 | + | 5.92201i | −0.106734 | + | 0.328494i | ||||
\(326\) | −1.97088 | + | 6.06575i | −0.109157 | + | 0.335951i | ||||
\(327\) | 20.7730 | + | 15.0925i | 1.14875 | + | 0.834617i | ||||
\(328\) | 2.48413 | − | 7.64537i | 0.137163 | − | 0.422145i | ||||
\(329\) | −0.927051 | − | 2.85317i | −0.0511100 | − | 0.157300i | ||||
\(330\) | 2.77212 | − | 2.01406i | 0.152600 | − | 0.110871i | ||||
\(331\) | −5.54708 | − | 17.0721i | −0.304895 | − | 0.938370i | −0.979716 | − | 0.200389i | \(-0.935779\pi\) |
0.674822 | − | 0.737981i | \(-0.264221\pi\) | |||||||
\(332\) | −2.17976 | − | 1.58369i | −0.119630 | − | 0.0869163i | ||||
\(333\) | −4.55250 | − | 3.30758i | −0.249475 | − | 0.181254i | ||||
\(334\) | 5.00000 | − | 3.63271i | 0.273588 | − | 0.198773i | ||||
\(335\) | 0.182208 | 0.00995507 | ||||||||
\(336\) | 6.84074 | 0.373193 | ||||||||
\(337\) | 17.6227 | − | 12.8036i | 0.959968 | − | 0.697458i | 0.00682483 | − | 0.999977i | \(-0.497828\pi\) |
0.953143 | + | 0.302519i | \(0.0978276\pi\) | |||||||
\(338\) | −7.96420 | + | 24.5113i | −0.433195 | + | 1.33324i | ||||
\(339\) | 8.32029 | + | 25.6072i | 0.451896 | + | 1.39079i | ||||
\(340\) | 3.54424 | 0.192214 | ||||||||
\(341\) | 8.36035 | − | 5.80879i | 0.452739 | − | 0.314563i | ||||
\(342\) | −3.36714 | −0.182074 | ||||||||
\(343\) | 0.761901 | + | 2.34489i | 0.0411388 | + | 0.126612i | ||||
\(344\) | −0.874032 | + | 2.68999i | −0.0471246 | + | 0.145035i | ||||
\(345\) | 8.17840 | − | 5.94196i | 0.440310 | − | 0.319904i | ||||
\(346\) | −12.8350 | −0.690014 | ||||||||
\(347\) | −14.8499 | −0.797185 | −0.398592 | − | 0.917128i | \(-0.630501\pi\) | ||||
−0.398592 | + | 0.917128i | \(0.630501\pi\) | |||||||
\(348\) | −13.5619 | + | 9.85328i | −0.726993 | + | 0.528191i | ||||
\(349\) | 0.622096 | + | 0.451979i | 0.0333000 | + | 0.0241939i | 0.604311 | − | 0.796749i | \(-0.293449\pi\) |
−0.571011 | + | 0.820943i | \(0.693449\pi\) | |||||||
\(350\) | −2.95314 | − | 2.14558i | −0.157852 | − | 0.114686i | ||||
\(351\) | −8.97167 | − | 27.6120i | −0.478872 | − | 1.47382i | ||||
\(352\) | 1.47923 | − | 1.07472i | 0.0788432 | − | 0.0572829i | ||||
\(353\) | 0.596527 | + | 1.83592i | 0.0317499 | + | 0.0977163i | 0.965676 | − | 0.259751i | \(-0.0836404\pi\) |
−0.933926 | + | 0.357467i | \(0.883640\pi\) | |||||||
\(354\) | −1.98258 | + | 6.10176i | −0.105373 | + | 0.324305i | ||||
\(355\) | 1.52473 | + | 1.10778i | 0.0809241 | + | 0.0587948i | ||||
\(356\) | 3.13829 | − | 9.65865i | 0.166329 | − | 0.511907i | ||||
\(357\) | −7.49220 | + | 23.0586i | −0.396529 | + | 1.22039i | ||||
\(358\) | −11.4200 | − | 8.29709i | −0.603564 | − | 0.438515i | ||||
\(359\) | −0.376319 | + | 1.15819i | −0.0198614 | + | 0.0611270i | −0.960496 | − | 0.278294i | \(-0.910231\pi\) |
0.940635 | + | 0.339421i | \(0.110231\pi\) | |||||||
\(360\) | 0.158216 | + | 0.486937i | 0.00833869 | + | 0.0256638i | ||||
\(361\) | −19.6189 | + | 14.2539i | −1.03257 | + | 0.750207i | ||||
\(362\) | −0.681859 | − | 2.09855i | −0.0358377 | − | 0.110297i | ||||
\(363\) | −11.6087 | − | 8.43424i | −0.609301 | − | 0.442683i | ||||
\(364\) | −18.3885 | − | 13.3600i | −0.963821 | − | 0.700257i | ||||
\(365\) | −12.8448 | + | 9.33230i | −0.672328 | + | 0.488475i | ||||
\(366\) | 17.5878 | 0.919327 | ||||||||
\(367\) | 23.7507 | 1.23978 | 0.619889 | − | 0.784689i | \(-0.287177\pi\) | ||||
0.619889 | + | 0.784689i | \(0.287177\pi\) | |||||||
\(368\) | 4.36407 | − | 3.17068i | 0.227493 | − | 0.165283i | ||||
\(369\) | −1.27187 | + | 3.91440i | −0.0662107 | + | 0.203776i | ||||
\(370\) | 3.39631 | + | 10.4528i | 0.176566 | + | 0.543414i | ||||
\(371\) | −15.0240 | −0.780007 | ||||||||
\(372\) | 3.01435 | + | 9.98927i | 0.156287 | + | 0.517920i | ||||
\(373\) | 22.2480 | 1.15196 | 0.575980 | − | 0.817464i | \(-0.304621\pi\) | ||||
0.575980 | + | 0.817464i | \(0.304621\pi\) | |||||||
\(374\) | 2.00255 | + | 6.16322i | 0.103549 | + | 0.318692i | ||||
\(375\) | 0.579108 | − | 1.78231i | 0.0299050 | − | 0.0920381i | ||||
\(376\) | 0.664894 | − | 0.483074i | 0.0342893 | − | 0.0249126i | ||||
\(377\) | 55.6991 | 2.86865 | ||||||||
\(378\) | 17.0198 | 0.875404 | ||||||||
\(379\) | −27.8708 | + | 20.2493i | −1.43163 | + | 1.04014i | −0.441916 | + | 0.897056i | \(0.645701\pi\) |
−0.989711 | + | 0.143081i | \(0.954299\pi\) | |||||||
\(380\) | 5.32049 | + | 3.86556i | 0.272936 | + | 0.198299i | ||||
\(381\) | 2.50203 | + | 1.81783i | 0.128183 | + | 0.0931304i | ||||
\(382\) | −5.69275 | − | 17.5205i | −0.291266 | − | 0.896426i | ||||
\(383\) | −17.6436 | + | 12.8188i | −0.901545 | + | 0.655011i | −0.938862 | − | 0.344293i | \(-0.888119\pi\) |
0.0373175 | + | 0.999303i | \(0.488119\pi\) | |||||||
\(384\) | 0.579108 | + | 1.78231i | 0.0295525 | + | 0.0909531i | ||||
\(385\) | 2.06246 | − | 6.34761i | 0.105113 | − | 0.323504i | ||||
\(386\) | 4.13839 | + | 3.00672i | 0.210639 | + | 0.153038i | ||||
\(387\) | 0.447501 | − | 1.37727i | 0.0227478 | − | 0.0700104i | ||||
\(388\) | 1.76393 | − | 5.42882i | 0.0895501 | − | 0.275607i | ||||
\(389\) | 12.0537 | + | 8.75753i | 0.611147 | + | 0.444024i | 0.849818 | − | 0.527076i | \(-0.176712\pi\) |
−0.238671 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(390\) | 3.60597 | − | 11.0980i | 0.182596 | − | 0.561971i | ||||
\(391\) | 5.90799 | + | 18.1829i | 0.298780 | + | 0.919550i | ||||
\(392\) | 5.11667 | − | 3.71748i | 0.258431 | − | 0.187761i | ||||
\(393\) | −0.455691 | − | 1.40247i | −0.0229866 | − | 0.0707454i | ||||
\(394\) | 3.84438 | + | 2.79311i | 0.193677 | + | 0.140715i | ||||
\(395\) | 4.09398 | + | 2.97445i | 0.205990 | + | 0.149661i | ||||
\(396\) | −0.757359 | + | 0.550254i | −0.0380587 | + | 0.0276513i | ||||
\(397\) | −15.9773 | −0.801880 | −0.400940 | − | 0.916104i | \(-0.631316\pi\) | ||||
−0.400940 | + | 0.916104i | \(0.631316\pi\) | |||||||
\(398\) | −8.40847 | −0.421478 | ||||||||
\(399\) | −36.3961 | + | 26.4433i | −1.82209 | + | 1.32382i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −10.4644 | − | 32.2061i | −0.522567 | − | 1.60830i | −0.769078 | − | 0.639155i | \(-0.779284\pi\) |
0.246511 | − | 0.969140i | \(-0.420716\pi\) | |||||||
\(402\) | −0.341463 | −0.0170306 | ||||||||
\(403\) | 11.4063 | − | 32.7391i | 0.568189 | − | 1.63085i | ||||
\(404\) | 15.0877 | 0.750639 | ||||||||
\(405\) | 3.17479 | + | 9.77101i | 0.157757 | + | 0.485525i | ||||
\(406\) | −10.0901 | + | 31.0540i | −0.500761 | + | 1.54119i | ||||
\(407\) | −16.2578 | + | 11.8120i | −0.805867 | + | 0.585497i | ||||
\(408\) | −6.64203 | −0.328829 | ||||||||
\(409\) | 22.3749 | 1.10637 | 0.553183 | − | 0.833060i | \(-0.313413\pi\) | ||||
0.553183 | + | 0.833060i | \(0.313413\pi\) | |||||||
\(410\) | 6.50354 | − | 4.72510i | 0.321187 | − | 0.233356i | ||||
\(411\) | −23.3809 | − | 16.9872i | −1.15330 | − | 0.837918i | ||||
\(412\) | −4.16885 | − | 3.02885i | −0.205385 | − | 0.149221i | ||||
\(413\) | 3.86171 | + | 11.8851i | 0.190023 | + | 0.584829i | ||||
\(414\) | −2.23439 | + | 1.62338i | −0.109814 | + | 0.0797846i | ||||
\(415\) | −0.832595 | − | 2.56246i | −0.0408705 | − | 0.125786i | ||||
\(416\) | 1.92418 | − | 5.92201i | 0.0943406 | − | 0.290351i | ||||
\(417\) | −5.39835 | − | 3.92213i | −0.264358 | − | 0.192067i | ||||
\(418\) | −3.71582 | + | 11.4361i | −0.181747 | + | 0.559358i | ||||
\(419\) | 6.09998 | − | 18.7738i | 0.298003 | − | 0.917160i | −0.684193 | − | 0.729301i | \(-0.739845\pi\) |
0.982196 | − | 0.187859i | \(-0.0601547\pi\) | |||||||
\(420\) | 5.53428 | + | 4.02089i | 0.270045 | + | 0.196199i | ||||
\(421\) | −2.49942 | + | 7.69243i | −0.121814 | + | 0.374906i | −0.993307 | − | 0.115502i | \(-0.963152\pi\) |
0.871493 | + | 0.490408i | \(0.163152\pi\) | |||||||
\(422\) | 3.45084 | + | 10.6206i | 0.167984 | + | 0.517003i | ||||
\(423\) | −0.340423 | + | 0.247332i | −0.0165519 | + | 0.0120257i | ||||
\(424\) | −1.27187 | − | 3.91440i | −0.0617673 | − | 0.190100i | ||||
\(425\) | 2.86735 | + | 2.08325i | 0.139087 | + | 0.101053i | ||||
\(426\) | −2.85739 | − | 2.07601i | −0.138441 | − | 0.100583i | ||||
\(427\) | 27.7152 | − | 20.1363i | 1.34123 | − | 0.974462i | ||||
\(428\) | 14.7967 | 0.715225 | ||||||||
\(429\) | 21.3362 | 1.03012 | ||||||||
\(430\) | −2.28825 | + | 1.66251i | −0.110349 | + | 0.0801732i | ||||
\(431\) | −10.1624 | + | 31.2768i | −0.489507 | + | 1.50655i | 0.335838 | + | 0.941920i | \(0.390981\pi\) |
−0.825345 | + | 0.564629i | \(0.809019\pi\) | |||||||
\(432\) | 1.44082 | + | 4.43440i | 0.0693216 | + | 0.213350i | ||||
\(433\) | −7.53399 | −0.362060 | −0.181030 | − | 0.983478i | \(-0.557943\pi\) | ||||
−0.181030 | + | 0.983478i | \(0.557943\pi\) | |||||||
\(434\) | 16.1868 | + | 12.2902i | 0.776992 | + | 0.589947i | ||||
\(435\) | −16.7634 | −0.803744 | ||||||||
\(436\) | 4.23397 | + | 13.0308i | 0.202770 | + | 0.624063i | ||||
\(437\) | −10.9625 | + | 33.7392i | −0.524408 | + | 1.61396i | ||||
\(438\) | 24.0716 | − | 17.4890i | 1.15018 | − | 0.835658i | ||||
\(439\) | −10.2727 | −0.490289 | −0.245144 | − | 0.969487i | \(-0.578835\pi\) | ||||
−0.245144 | + | 0.969487i | \(0.578835\pi\) | |||||||
\(440\) | 1.82843 | 0.0871668 | ||||||||
\(441\) | −2.61972 | + | 1.90334i | −0.124748 | + | 0.0906350i | ||||
\(442\) | 17.8544 | + | 12.9720i | 0.849245 | + | 0.617013i | ||||
\(443\) | 3.71605 | + | 2.69987i | 0.176555 | + | 0.128275i | 0.672553 | − | 0.740049i | \(-0.265198\pi\) |
−0.495998 | + | 0.868324i | \(0.665198\pi\) | |||||||
\(444\) | −6.36480 | − | 19.5888i | −0.302060 | − | 0.929646i | ||||
\(445\) | 8.21614 | − | 5.96937i | 0.389482 | − | 0.282975i | ||||
\(446\) | 0.575236 | + | 1.77039i | 0.0272382 | + | 0.0838306i | ||||
\(447\) | −9.86906 | + | 30.3739i | −0.466791 | + | 1.43663i | ||||
\(448\) | 2.95314 | + | 2.14558i | 0.139523 | + | 0.101369i | ||||
\(449\) | −4.70143 | + | 14.4695i | −0.221874 | + | 0.682858i | 0.776720 | + | 0.629846i | \(0.216882\pi\) |
−0.998594 | + | 0.0530119i | \(0.983118\pi\) | |||||||
\(450\) | −0.158216 | + | 0.486937i | −0.00745835 | + | 0.0229544i | ||||
\(451\) | 11.8913 | + | 8.63950i | 0.559937 | + | 0.406818i | ||||
\(452\) | −4.43978 | + | 13.6642i | −0.208830 | + | 0.642712i | ||||
\(453\) | 5.02957 | + | 15.4794i | 0.236310 | + | 0.727287i | ||||
\(454\) | 2.42746 | − | 1.76366i | 0.113927 | − | 0.0827725i | ||||
\(455\) | −7.02379 | − | 21.6170i | −0.329281 | − | 1.01342i | ||||
\(456\) | −9.97077 | − | 7.24419i | −0.466924 | − | 0.339240i | ||||
\(457\) | −23.0196 | − | 16.7247i | −1.07681 | − | 0.782348i | −0.0996862 | − | 0.995019i | \(-0.531784\pi\) |
−0.977124 | + | 0.212670i | \(0.931784\pi\) | |||||||
\(458\) | 12.2745 | − | 8.91793i | 0.573549 | − | 0.416707i | ||||
\(459\) | −16.5254 | −0.771339 | ||||||||
\(460\) | 5.39428 | 0.251510 | ||||||||
\(461\) | −4.80342 | + | 3.48989i | −0.223718 | + | 0.162540i | −0.693999 | − | 0.719976i | \(-0.744153\pi\) |
0.470281 | + | 0.882517i | \(0.344153\pi\) | |||||||
\(462\) | −3.86512 | + | 11.8956i | −0.179822 | + | 0.553435i | ||||
\(463\) | −12.1633 | − | 37.4347i | −0.565275 | − | 1.73974i | −0.667133 | − | 0.744939i | \(-0.732479\pi\) |
0.101858 | − | 0.994799i | \(-0.467521\pi\) | |||||||
\(464\) | −8.94510 | −0.415266 | ||||||||
\(465\) | −3.43289 | + | 9.85328i | −0.159196 | + | 0.456935i | ||||
\(466\) | −22.8262 | −1.05740 | ||||||||
\(467\) | 6.05473 | + | 18.6345i | 0.280179 | + | 0.862304i | 0.987802 | + | 0.155713i | \(0.0497676\pi\) |
−0.707623 | + | 0.706590i | \(0.750232\pi\) | |||||||
\(468\) | −0.985172 | + | 3.03205i | −0.0455396 | + | 0.140156i | ||||
\(469\) | −0.538085 | + | 0.390942i | −0.0248465 | + | 0.0180520i | ||||
\(470\) | 0.821854 | 0.0379093 | ||||||||
\(471\) | 19.4741 | 0.897320 | ||||||||
\(472\) | −2.76968 | + | 2.01229i | −0.127485 | + | 0.0926231i | ||||
\(473\) | −4.18389 | − | 3.03977i | −0.192375 | − | 0.139769i | ||||
\(474\) | −7.67224 | − | 5.57421i | −0.352398 | − | 0.256032i | ||||
\(475\) | 2.03225 | + | 6.25461i | 0.0932459 | + | 0.286981i | ||||
\(476\) | −10.4666 | + | 7.60446i | −0.479738 | + | 0.348550i | ||||
\(477\) | 0.651190 | + | 2.00416i | 0.0298160 | + | 0.0917641i | ||||
\(478\) | 6.19817 | − | 19.0760i | 0.283498 | − | 0.872517i | ||||
\(479\) | 6.10122 | + | 4.43279i | 0.278772 | + | 0.202540i | 0.718382 | − | 0.695649i | \(-0.244883\pi\) |
−0.439610 | + | 0.898189i | \(0.644883\pi\) | |||||||
\(480\) | −0.579108 | + | 1.78231i | −0.0264325 | + | 0.0813510i | ||||
\(481\) | −21.1481 | + | 65.0871i | −0.964269 | + | 2.96772i | ||||
\(482\) | 0.355771 | + | 0.258483i | 0.0162049 | + | 0.0117736i | ||||
\(483\) | −11.4030 | + | 35.0949i | −0.518855 | + | 1.59687i | ||||
\(484\) | −2.36610 | − | 7.28210i | −0.107550 | − | 0.331005i | ||||
\(485\) | 4.61803 | − | 3.35520i | 0.209694 | − | 0.152352i | ||||
\(486\) | −1.62720 | − | 5.00800i | −0.0738112 | − | 0.227168i | ||||
\(487\) | 0.684560 | + | 0.497362i | 0.0310204 | + | 0.0225376i | 0.603187 | − | 0.797599i | \(-0.293897\pi\) |
−0.572167 | + | 0.820137i | \(0.693897\pi\) | |||||||
\(488\) | 7.59261 | + | 5.51636i | 0.343702 | + | 0.249714i | ||||
\(489\) | 9.66969 | − | 7.02544i | 0.437279 | − | 0.317701i | ||||
\(490\) | 6.32456 | 0.285714 | ||||||||
\(491\) | 3.11584 | 0.140616 | 0.0703081 | − | 0.997525i | \(-0.477602\pi\) | ||||
0.0703081 | + | 0.997525i | \(0.477602\pi\) | |||||||
\(492\) | −12.1878 | + | 8.85499i | −0.549471 | + | 0.399214i | ||||
\(493\) | 9.79696 | − | 30.1519i | 0.441233 | − | 1.35797i | ||||
\(494\) | 12.6543 | + | 38.9461i | 0.569346 | + | 1.75227i | ||||
\(495\) | −0.936148 | −0.0420767 | ||||||||
\(496\) | −1.83182 | + | 5.25780i | −0.0822511 | + | 0.236082i | ||||
\(497\) | −6.87956 | −0.308591 | ||||||||
\(498\) | 1.56031 | + | 4.80214i | 0.0699192 | + | 0.215189i | ||||
\(499\) | 4.20601 | − | 12.9448i | 0.188287 | − | 0.579487i | −0.811703 | − | 0.584071i | \(-0.801459\pi\) |
0.999989 | + | 0.00458356i | \(0.00145900\pi\) | |||||||
\(500\) | 0.809017 | − | 0.587785i | 0.0361803 | − | 0.0262866i | ||||
\(501\) | −11.5822 | −0.517453 | ||||||||
\(502\) | 3.38469 | 0.151066 | ||||||||
\(503\) | −10.9043 | + | 7.92246i | −0.486200 | + | 0.353245i | −0.803721 | − | 0.595006i | \(-0.797150\pi\) |
0.317521 | + | 0.948251i | \(0.397150\pi\) | |||||||
\(504\) | −1.51200 | − | 1.09853i | −0.0673497 | − | 0.0489324i | ||||
\(505\) | 12.2062 | + | 8.86830i | 0.543168 | + | 0.394634i | ||||
\(506\) | 3.04785 | + | 9.38032i | 0.135494 | + | 0.417006i | ||||
\(507\) | 39.0746 | − | 28.3894i | 1.73536 | − | 1.26082i | ||||
\(508\) | 0.509965 | + | 1.56951i | 0.0226260 | + | 0.0696358i | ||||
\(509\) | 10.4265 | − | 32.0896i | 0.462148 | − | 1.42234i | −0.400386 | − | 0.916346i | \(-0.631124\pi\) |
0.862534 | − | 0.505999i | \(-0.168876\pi\) | |||||||
\(510\) | −5.37351 | − | 3.90409i | −0.237943 | − | 0.172876i | ||||
\(511\) | 17.9093 | − | 55.1192i | 0.792261 | − | 2.43833i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | −24.8073 | − | 18.0236i | −1.09527 | − | 0.795760i | ||||
\(514\) | 5.31330 | − | 16.3527i | 0.234360 | − | 0.721285i | ||||
\(515\) | −1.59236 | − | 4.90078i | −0.0701677 | − | 0.215954i | ||||
\(516\) | 4.28825 | − | 3.11559i | 0.188779 | − | 0.137156i | ||||
\(517\) | 0.464360 | + | 1.42915i | 0.0204225 | + | 0.0628541i | ||||
\(518\) | −32.4571 | − | 23.5815i | −1.42608 | − | 1.03611i | ||||
\(519\) | 19.4594 | + | 14.1381i | 0.854175 | + | 0.620594i | ||||
\(520\) | 5.03756 | − | 3.66001i | 0.220912 | − | 0.160502i | ||||
\(521\) | 14.5687 | 0.638268 | 0.319134 | − | 0.947710i | \(-0.396608\pi\) | ||||
0.319134 | + | 0.947710i | \(0.396608\pi\) | |||||||
\(522\) | 4.57986 | 0.200455 | ||||||||
\(523\) | 36.9164 | − | 26.8213i | 1.61424 | − | 1.17281i | 0.766897 | − | 0.641771i | \(-0.221800\pi\) |
0.847344 | − | 0.531044i | \(-0.178200\pi\) | |||||||
\(524\) | 0.243161 | − | 0.748371i | 0.0106225 | − | 0.0326928i | ||||
\(525\) | 2.11391 | + | 6.50593i | 0.0922584 | + | 0.283942i | ||||
\(526\) | 20.9966 | 0.915494 | ||||||||
\(527\) | −15.7166 | − | 11.9332i | −0.684626 | − | 0.519817i | ||||
\(528\) | −3.42653 | −0.149121 | ||||||||
\(529\) | 1.88448 | + | 5.79982i | 0.0819338 | + | 0.252166i | ||||
\(530\) | 1.27187 | − | 3.91440i | 0.0552463 | − | 0.170031i | ||||
\(531\) | 1.41806 | − | 1.03028i | 0.0615387 | − | 0.0447105i | ||||
\(532\) | −24.0060 | −1.04079 | ||||||||
\(533\) | 50.0559 | 2.16816 | ||||||||
\(534\) | −15.3973 | + | 11.1868i | −0.666307 | + | 0.484100i | ||||
\(535\) | 11.9708 | + | 8.69728i | 0.517542 | + | 0.376016i | ||||
\(536\) | −0.147409 | − | 0.107099i | −0.00636711 | − | 0.00462597i | ||||
\(537\) | 8.17460 | + | 25.1588i | 0.352760 | + | 1.08568i | ||||
\(538\) | −5.94166 | + | 4.31687i | −0.256163 | + | 0.186114i | ||||
\(539\) | 3.57347 | + | 10.9980i | 0.153920 | + | 0.473718i | ||||
\(540\) | −1.44082 | + | 4.43440i | −0.0620031 | + | 0.190826i | ||||
\(541\) | 1.38515 | + | 1.00637i | 0.0595521 | + | 0.0432671i | 0.617163 | − | 0.786835i | \(-0.288282\pi\) |
−0.557611 | + | 0.830102i | \(0.688282\pi\) | |||||||
\(542\) | 0.462073 | − | 1.42212i | 0.0198477 | − | 0.0610851i | ||||
\(543\) | −1.27783 | + | 3.93274i | −0.0548368 | + | 0.168770i | ||||
\(544\) | −2.86735 | − | 2.08325i | −0.122937 | − | 0.0893188i | ||||
\(545\) | −4.23397 | + | 13.0308i | −0.181363 | + | 0.558179i | ||||
\(546\) | 13.1628 | + | 40.5110i | 0.563316 | + | 1.73371i | ||||
\(547\) | 21.8354 | − | 15.8644i | 0.933615 | − | 0.678311i | −0.0132606 | − | 0.999912i | \(-0.504221\pi\) |
0.946875 | + | 0.321601i | \(0.104221\pi\) | |||||||
\(548\) | −4.76551 | − | 14.6667i | −0.203572 | − | 0.626532i | ||||
\(549\) | −3.88739 | − | 2.82435i | −0.165910 | − | 0.120540i | ||||
\(550\) | 1.47923 | + | 1.07472i | 0.0630745 | + | 0.0458263i | ||||
\(551\) | 47.5923 | − | 34.5779i | 2.02750 | − | 1.47307i | ||||
\(552\) | −10.1091 | −0.430270 | ||||||||
\(553\) | −18.4720 | −0.785510 | ||||||||
\(554\) | 7.74331 | − | 5.62584i | 0.328982 | − | 0.239019i | ||||
\(555\) | 6.36480 | − | 19.5888i | 0.270171 | − | 0.831500i | ||||
\(556\) | −1.10029 | − | 3.38635i | −0.0466628 | − | 0.143613i | ||||
\(557\) | −4.48260 | −0.189934 | −0.0949670 | − | 0.995480i | \(-0.530275\pi\) | ||||
−0.0949670 | + | 0.995480i | \(0.530275\pi\) | |||||||
\(558\) | 0.937884 | − | 2.69197i | 0.0397038 | − | 0.113960i | ||||
\(559\) | −17.6120 | −0.744907 | ||||||||
\(560\) | 1.12800 | + | 3.47162i | 0.0476667 | + | 0.146703i | ||||
\(561\) | 3.75284 | − | 11.5501i | 0.158445 | − | 0.487644i | ||||
\(562\) | −4.13493 | + | 3.00421i | −0.174422 | + | 0.126725i | ||||
\(563\) | 29.0236 | 1.22320 | 0.611599 | − | 0.791168i | \(-0.290527\pi\) | ||||
0.611599 | + | 0.791168i | \(0.290527\pi\) | |||||||
\(564\) | −1.54018 | −0.0648533 | ||||||||
\(565\) | −11.6235 | + | 8.44497i | −0.489004 | + | 0.355282i | ||||
\(566\) | 9.24020 | + | 6.71340i | 0.388394 | + | 0.282185i | ||||
\(567\) | −30.3401 | − | 22.0434i | −1.27416 | − | 0.925735i | ||||
\(568\) | −0.582394 | − | 1.79242i | −0.0244367 | − | 0.0752085i | ||||
\(569\) | −14.1596 | + | 10.2875i | −0.593599 | + | 0.431275i | −0.843601 | − | 0.536970i | \(-0.819569\pi\) |
0.250002 | + | 0.968245i | \(0.419569\pi\) | |||||||
\(570\) | −3.80850 | − | 11.7213i | −0.159520 | − | 0.490953i | ||||
\(571\) | −6.46129 | + | 19.8858i | −0.270397 | + | 0.832195i | 0.720004 | + | 0.693970i | \(0.244140\pi\) |
−0.990401 | + | 0.138225i | \(0.955860\pi\) | |||||||
\(572\) | 9.21082 | + | 6.69205i | 0.385124 | + | 0.279809i | ||||
\(573\) | −10.6684 | + | 32.8339i | −0.445679 | + | 1.37166i | ||||
\(574\) | −9.06778 | + | 27.9078i | −0.378482 | + | 1.16485i | ||||
\(575\) | 4.36407 | + | 3.17068i | 0.181994 | + | 0.132227i | ||||
\(576\) | 0.158216 | − | 0.486937i | 0.00659231 | − | 0.0202891i | ||||
\(577\) | −1.74749 | − | 5.37821i | −0.0727488 | − | 0.223898i | 0.908070 | − | 0.418818i | \(-0.137555\pi\) |
−0.980819 | + | 0.194920i | \(0.937555\pi\) | |||||||
\(578\) | −3.59069 | + | 2.60879i | −0.149353 | + | 0.108511i | ||||
\(579\) | −2.96233 | − | 9.11711i | −0.123110 | − | 0.378894i | ||||
\(580\) | −7.23674 | − | 5.25780i | −0.300489 | − | 0.218318i | ||||
\(581\) | 7.95675 | + | 5.78092i | 0.330102 | + | 0.239833i | ||||
\(582\) | −8.65434 | + | 6.28775i | −0.358734 | + | 0.260636i | ||||
\(583\) | 7.52552 | 0.311675 | ||||||||
\(584\) | 15.8771 | 0.656997 | ||||||||
\(585\) | −2.57921 | + | 1.87391i | −0.106637 | + | 0.0774766i | ||||
\(586\) | −0.921668 | + | 2.83660i | −0.0380738 | + | 0.117179i | ||||
\(587\) | −1.55667 | − | 4.79093i | −0.0642505 | − | 0.197743i | 0.913778 | − | 0.406214i | \(-0.133151\pi\) |
−0.978029 | + | 0.208471i | \(0.933151\pi\) | |||||||
\(588\) | −11.8524 | −0.488786 | ||||||||
\(589\) | −10.5782 | − | 35.0551i | −0.435866 | − | 1.44442i | ||||
\(590\) | −3.42351 | −0.140944 | ||||||||
\(591\) | −2.75187 | − | 8.46939i | −0.113197 | − | 0.348384i | ||||
\(592\) | 3.39631 | − | 10.4528i | 0.139588 | − | 0.429607i | ||||
\(593\) | −11.6704 | + | 8.47903i | −0.479245 | + | 0.348192i | −0.801033 | − | 0.598620i | \(-0.795716\pi\) |
0.321788 | + | 0.946812i | \(0.395716\pi\) | |||||||
\(594\) | −8.52522 | −0.349794 | ||||||||
\(595\) | −12.9375 | −0.530385 | ||||||||
\(596\) | −13.7871 | + | 10.0169i | −0.564743 | + | 0.410310i | ||||
\(597\) | 12.7483 | + | 9.26217i | 0.521752 | + | 0.379075i | ||||
\(598\) | 27.1741 | + | 19.7431i | 1.11123 | + | 0.807356i | ||||
\(599\) | −14.0869 | − | 43.3551i | −0.575577 | − | 1.77144i | −0.634208 | − | 0.773163i | \(-0.718674\pi\) |
0.0586309 | − | 0.998280i | \(-0.481326\pi\) | |||||||
\(600\) | −1.51612 | + | 1.10153i | −0.0618955 | + | 0.0449697i | ||||
\(601\) | −1.82772 | − | 5.62513i | −0.0745541 | − | 0.229454i | 0.906834 | − | 0.421487i | \(-0.138492\pi\) |
−0.981388 | + | 0.192033i | \(0.938492\pi\) | |||||||
\(602\) | 3.19046 | − | 9.81924i | 0.130034 | − | 0.400202i | ||||
\(603\) | 0.0754729 | + | 0.0548343i | 0.00307349 | + | 0.00223302i | ||||
\(604\) | −2.68382 | + | 8.25996i | −0.109203 | + | 0.336093i | ||||
\(605\) | 2.36610 | − | 7.28210i | 0.0961956 | − | 0.296060i | ||||
\(606\) | −22.8748 | − | 16.6195i | −0.929224 | − | 0.675120i | ||||
\(607\) | 8.83223 | − | 27.1828i | 0.358489 | − | 1.10332i | −0.595470 | − | 0.803378i | \(-0.703034\pi\) |
0.953959 | − | 0.299938i | \(-0.0969660\pi\) | |||||||
\(608\) | −2.03225 | − | 6.25461i | −0.0824185 | − | 0.253658i | ||||
\(609\) | 49.5047 | − | 35.9673i | 2.00603 | − | 1.45747i | ||||
\(610\) | 2.90012 | + | 8.92565i | 0.117422 | + | 0.361389i | ||||
\(611\) | 4.14015 | + | 3.00799i | 0.167492 | + | 0.121690i | ||||
\(612\) | 1.46807 | + | 1.06662i | 0.0593434 | + | 0.0431155i | ||||
\(613\) | −37.7359 | + | 27.4167i | −1.52414 | + | 1.10735i | −0.564749 | + | 0.825263i | \(0.691027\pi\) |
−0.959389 | + | 0.282088i | \(0.908973\pi\) | |||||||
\(614\) | −26.2475 | −1.05926 | ||||||||
\(615\) | −15.0650 | −0.607480 | ||||||||
\(616\) | −5.39960 | + | 3.92304i | −0.217556 | + | 0.158064i | ||||
\(617\) | −7.33953 | + | 22.5888i | −0.295478 | + | 0.909389i | 0.687582 | + | 0.726107i | \(0.258672\pi\) |
−0.983060 | + | 0.183282i | \(0.941328\pi\) | |||||||
\(618\) | 2.98413 | + | 9.18421i | 0.120039 | + | 0.369443i | ||||
\(619\) | −2.98958 | −0.120161 | −0.0600806 | − | 0.998194i | \(-0.519136\pi\) | ||||
−0.0600806 | + | 0.998194i | \(0.519136\pi\) | |||||||
\(620\) | −4.57243 | + | 3.17693i | −0.183633 | + | 0.127589i | ||||
\(621\) | −25.1514 | −1.00929 | ||||||||
\(622\) | −3.32204 | − | 10.2242i | −0.133202 | − | 0.409953i | ||||
\(623\) | −11.4556 | + | 35.2568i | −0.458960 | + | 1.41253i | ||||
\(624\) | −9.44056 | + | 6.85897i | −0.377925 | + | 0.274578i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.49090 | −0.0595882 | ||||||||
\(627\) | 18.2308 | − | 13.2455i | 0.728069 | − | 0.528973i | ||||
\(628\) | 8.40695 | + | 6.10801i | 0.335474 | + | 0.243736i | ||||
\(629\) | 31.5142 | + | 22.8964i | 1.25655 | + | 0.912941i | ||||
\(630\) | −0.577531 | − | 1.77746i | −0.0230094 | − | 0.0708156i | ||||
\(631\) | −39.0903 | + | 28.4008i | −1.55616 | + | 1.13062i | −0.617090 | + | 0.786892i | \(0.711689\pi\) |
−0.939071 | + | 0.343725i | \(0.888311\pi\) | |||||||
\(632\) | −1.56376 | − | 4.81276i | −0.0622030 | − | 0.191441i | ||||
\(633\) | 6.46699 | − | 19.9034i | 0.257040 | − | 0.791088i | ||||
\(634\) | −11.2847 | − | 8.19881i | −0.448172 | − | 0.325616i | ||||
\(635\) | −0.509965 | + | 1.56951i | −0.0202373 | + | 0.0622841i | ||||
\(636\) | −2.38352 | + | 7.33571i | −0.0945126 | + | 0.290880i | ||||
\(637\) | 31.8604 | + | 23.1479i | 1.26235 | + | 0.917153i | ||||
\(638\) | 5.05412 | − | 15.5550i | 0.200094 | − | 0.615827i | ||||
\(639\) | 0.298184 | + | 0.917715i | 0.0117960 | + | 0.0363042i | ||||
\(640\) | −0.809017 | + | 0.587785i | −0.0319792 | + | 0.0232343i | ||||
\(641\) | −6.53277 | − | 20.1058i | −0.258029 | − | 0.794131i | −0.993218 | − | 0.116269i | \(-0.962907\pi\) |
0.735189 | − | 0.677862i | \(-0.237093\pi\) | |||||||
\(642\) | −22.4336 | − | 16.2990i | −0.885384 | − | 0.643269i | ||||
\(643\) | 17.8984 | + | 13.0040i | 0.705845 | + | 0.512827i | 0.881831 | − | 0.471566i | \(-0.156311\pi\) |
−0.175985 | + | 0.984393i | \(0.556311\pi\) | |||||||
\(644\) | −15.9301 | + | 11.5739i | −0.627733 | + | 0.456075i | ||||
\(645\) | 5.30056 | 0.208709 | ||||||||
\(646\) | 23.3087 | 0.917068 | ||||||||
\(647\) | 21.4238 | − | 15.5653i | 0.842255 | − | 0.611934i | −0.0807448 | − | 0.996735i | \(-0.525730\pi\) |
0.923000 | + | 0.384801i | \(0.125730\pi\) | |||||||
\(648\) | 3.17479 | − | 9.77101i | 0.124718 | − | 0.383842i | ||||
\(649\) | −1.93433 | − | 5.95327i | −0.0759293 | − | 0.233686i | ||||
\(650\) | 6.22677 | 0.244234 | ||||||||
\(651\) | −11.0032 | − | 36.4637i | −0.431250 | − | 1.42912i | ||||
\(652\) | 6.37790 | 0.249778 | ||||||||
\(653\) | 13.9300 | + | 42.8722i | 0.545123 | + | 1.67772i | 0.720697 | + | 0.693251i | \(0.243822\pi\) |
−0.175573 | + | 0.984466i | \(0.556178\pi\) | |||||||
\(654\) | 7.93460 | − | 24.4202i | 0.310267 | − | 0.954905i | ||||
\(655\) | 0.636603 | − | 0.462519i | 0.0248741 | − | 0.0180721i | ||||
\(656\) | −8.03882 | −0.313863 | ||||||||
\(657\) | −8.12899 | −0.317142 | ||||||||
\(658\) | −2.42705 | + | 1.76336i | −0.0946163 | + | 0.0687428i | ||||
\(659\) | 8.55519 | + | 6.21571i | 0.333263 | + | 0.242130i | 0.741814 | − | 0.670606i | \(-0.233966\pi\) |
−0.408551 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(660\) | −2.77212 | − | 2.01406i | −0.107905 | − | 0.0783974i | ||||
\(661\) | −8.27708 | − | 25.4742i | −0.321941 | − | 0.990833i | −0.972802 | − | 0.231636i | \(-0.925592\pi\) |
0.650861 | − | 0.759197i | \(-0.274408\pi\) | |||||||
\(662\) | −14.5224 | + | 10.5512i | −0.564430 | + | 0.410083i | ||||
\(663\) | −12.7804 | − | 39.3342i | −0.496351 | − | 1.52761i | ||||
\(664\) | −0.832595 | + | 2.56246i | −0.0323110 | + | 0.0994429i | ||||
\(665\) | −19.4213 | − | 14.1104i | −0.753126 | − | 0.547178i | ||||
\(666\) | −1.73890 | + | 5.35178i | −0.0673810 | + | 0.207377i | ||||
\(667\) | 14.9108 | − | 45.8908i | 0.577349 | − | 1.77690i | ||||
\(668\) | −5.00000 | − | 3.63271i | −0.193456 | − | 0.140554i | ||||
\(669\) | 1.07801 | − | 3.31778i | 0.0416783 | − | 0.128273i | ||||
\(670\) | −0.0563053 | − | 0.173290i | −0.00217526 | − | 0.00669477i | ||||
\(671\) | −13.8825 | + | 10.0863i | −0.535930 | + | 0.389376i | ||||
\(672\) | −2.11391 | − | 6.50593i | −0.0815457 | − | 0.250972i | ||||
\(673\) | −14.1733 | − | 10.2975i | −0.546341 | − | 0.396940i | 0.280093 | − | 0.959973i | \(-0.409635\pi\) |
−0.826435 | + | 0.563033i | \(0.809635\pi\) | |||||||
\(674\) | −17.6227 | − | 12.8036i | −0.678800 | − | 0.493177i | ||||
\(675\) | −3.77212 | + | 2.74061i | −0.145189 | + | 0.105486i | ||||
\(676\) | 25.7727 | 0.991258 | ||||||||
\(677\) | −8.94187 | −0.343664 | −0.171832 | − | 0.985126i | \(-0.554969\pi\) | ||||
−0.171832 | + | 0.985126i | \(0.554969\pi\) | |||||||
\(678\) | 21.7828 | − | 15.8261i | 0.836564 | − | 0.607799i | ||||
\(679\) | −6.43885 | + | 19.8167i | −0.247100 | + | 0.760497i | ||||
\(680\) | −1.09523 | − | 3.37078i | −0.0420002 | − | 0.129263i | ||||
\(681\) | −5.62306 | −0.215476 | ||||||||
\(682\) | −8.10798 | − | 6.15615i | −0.310470 | − | 0.235731i | ||||
\(683\) | −36.6619 | −1.40283 | −0.701415 | − | 0.712754i | \(-0.747448\pi\) | ||||
−0.701415 | + | 0.712754i | \(0.747448\pi\) | |||||||
\(684\) | 1.04050 | + | 3.20234i | 0.0397846 | + | 0.122444i | ||||
\(685\) | 4.76551 | − | 14.6667i | 0.182081 | − | 0.560387i | ||||
\(686\) | 1.99468 | − | 1.44922i | 0.0761573 | − | 0.0553315i | ||||
\(687\) | −28.4330 | −1.08479 | ||||||||
\(688\) | 2.82843 | 0.107833 | ||||||||
\(689\) | 20.7338 | − | 15.0640i | 0.789896 | − | 0.573893i | ||||
\(690\) | −8.17840 | − | 5.94196i | −0.311346 | − | 0.226206i | ||||
\(691\) | 33.7120 | + | 24.4932i | 1.28247 | + | 0.931766i | 0.999625 | − | 0.0274004i | \(-0.00872292\pi\) |
0.282842 | + | 0.959167i | \(0.408723\pi\) | |||||||
\(692\) | 3.96623 | + | 12.2068i | 0.150774 | + | 0.464033i | ||||
\(693\) | 2.76457 | − | 2.00858i | 0.105018 | − | 0.0762997i | ||||
\(694\) | 4.58887 | + | 14.1231i | 0.174191 | + | 0.536106i | ||||
\(695\) | 1.10029 | − | 3.38635i | 0.0417365 | − | 0.128452i | ||||
\(696\) | 13.5619 | + | 9.85328i | 0.514062 | + | 0.373488i | ||||
\(697\) | 8.80437 | − | 27.0971i | 0.333489 | − | 1.02637i | ||||
\(698\) | 0.237620 | − | 0.731318i | 0.00899403 | − | 0.0276808i | ||||
\(699\) | 34.6074 | + | 25.1437i | 1.30897 | + | 0.951023i | ||||
\(700\) | −1.12800 | + | 3.47162i | −0.0426344 | + | 0.131215i | ||||
\(701\) | 2.27567 | + | 7.00380i | 0.0859510 | + | 0.264530i | 0.984790 | − | 0.173749i | \(-0.0555882\pi\) |
−0.898839 | + | 0.438279i | \(0.855588\pi\) | |||||||
\(702\) | −23.4881 | + | 17.0651i | −0.886503 | + | 0.644082i | ||||
\(703\) | 22.3358 | + | 68.7426i | 0.842412 | + | 2.59268i | ||||
\(704\) | −1.47923 | − | 1.07472i | −0.0557505 | − | 0.0405051i | ||||
\(705\) | −1.24603 | − | 0.905296i | −0.0469283 | − | 0.0340954i | ||||
\(706\) | 1.56173 | − | 1.13466i | 0.0587764 | − | 0.0427036i | ||||
\(707\) | −55.0742 | −2.07128 | ||||||||
\(708\) | 6.41577 | 0.241119 | ||||||||
\(709\) | −5.41887 | + | 3.93704i | −0.203510 | + | 0.147859i | −0.684872 | − | 0.728663i | \(-0.740142\pi\) |
0.481362 | + | 0.876522i | \(0.340142\pi\) | |||||||
\(710\) | 0.582394 | − | 1.79242i | 0.0218569 | − | 0.0672685i | ||||
\(711\) | 0.800639 | + | 2.46411i | 0.0300263 | + | 0.0924115i | ||||
\(712\) | −10.1557 | −0.380601 | ||||||||
\(713\) | −23.9204 | − | 18.1621i | −0.895826 | − | 0.680175i | ||||
\(714\) | 24.2453 | 0.907356 | ||||||||
\(715\) | 3.51822 | + | 10.8280i | 0.131574 | + | 0.404943i | ||||
\(716\) | −4.36204 | + | 13.4250i | −0.163017 | + | 0.501715i | ||||
\(717\) | −30.4100 | + | 22.0941i | −1.13568 | + | 0.825121i | ||||
\(718\) | 1.21779 | 0.0454477 | ||||||||
\(719\) | −30.5639 | −1.13984 | −0.569920 | − | 0.821700i | \(-0.693026\pi\) | ||||
−0.569920 | + | 0.821700i | \(0.693026\pi\) | |||||||
\(720\) | 0.414214 | − | 0.300944i | 0.0154368 | − | 0.0112155i | ||||
\(721\) | 15.2175 | + | 11.0561i | 0.566728 | + | 0.411752i | ||||
\(722\) | 19.6189 | + | 14.2539i | 0.730138 | + | 0.530476i | ||||
\(723\) | −0.254667 | − | 0.783784i | −0.00947116 | − | 0.0291492i | ||||
\(724\) | −1.78513 | + | 1.29697i | −0.0663439 | + | 0.0482016i | ||||
\(725\) | −2.76419 | − | 8.50730i | −0.102659 | − | 0.315953i | ||||
\(726\) | −4.43414 | + | 13.6469i | −0.164567 | + | 0.506484i | ||||
\(727\) | 11.5620 | + | 8.40026i | 0.428809 | + | 0.311548i | 0.781173 | − | 0.624315i | \(-0.214622\pi\) |
−0.352363 | + | 0.935863i | \(0.614622\pi\) | |||||||
\(728\) | −7.02379 | + | 21.6170i | −0.260319 | + | 0.801180i | ||||
\(729\) | 6.47496 | − | 19.9279i | 0.239813 | − | 0.738070i | ||||
\(730\) | 12.8448 | + | 9.33230i | 0.475408 | + | 0.345404i | ||||
\(731\) | −3.09778 | + | 9.53399i | −0.114576 | + | 0.352628i | ||||
\(732\) | −5.43492 | − | 16.7270i | −0.200880 | − | 0.618246i | ||||
\(733\) | 21.4403 | − | 15.5773i | 0.791916 | − | 0.575361i | −0.116615 | − | 0.993177i | \(-0.537204\pi\) |
0.908531 | + | 0.417816i | \(0.137204\pi\) | |||||||
\(734\) | −7.33938 | − | 22.5883i | −0.270902 | − | 0.833749i | ||||
\(735\) | −9.58881 | − | 6.96668i | −0.353689 | − | 0.256970i | ||||
\(736\) | −4.36407 | − | 3.17068i | −0.160862 | − | 0.116873i | ||||
\(737\) | 0.269527 | − | 0.195823i | 0.00992815 | − | 0.00721322i | ||||
\(738\) | 4.11584 | 0.151506 | ||||||||
\(739\) | −45.6940 | −1.68088 | −0.840440 | − | 0.541905i | \(-0.817703\pi\) | ||||
−0.840440 | + | 0.541905i | \(0.817703\pi\) | |||||||
\(740\) | 8.89167 | − | 6.46017i | 0.326864 | − | 0.237481i | ||||
\(741\) | 23.7146 | − | 72.9862i | 0.871179 | − | 2.68121i | ||||
\(742\) | 4.64267 | + | 14.2887i | 0.170438 | + | 0.524553i | ||||
\(743\) | 18.3304 | 0.672478 | 0.336239 | − | 0.941777i | \(-0.390845\pi\) | ||||
0.336239 | + | 0.941777i | \(0.390845\pi\) | |||||||
\(744\) | 8.56888 | − | 5.95367i | 0.314150 | − | 0.218272i | ||||
\(745\) | −17.0418 | −0.624365 | ||||||||
\(746\) | −6.87502 | − | 21.1591i | −0.251712 | − | 0.774691i | ||||
\(747\) | 0.426286 | − | 1.31197i | 0.0155970 | − | 0.0480025i | ||||
\(748\) | 5.24275 | − | 3.80908i | 0.191694 | − | 0.139274i | ||||
\(749\) | −54.0121 | −1.97356 | ||||||||
\(750\) | −1.87403 | −0.0684300 | ||||||||
\(751\) | 33.3000 | − | 24.1939i | 1.21514 | − | 0.882848i | 0.219449 | − | 0.975624i | \(-0.429574\pi\) |
0.995687 | + | 0.0927764i | \(0.0295742\pi\) | |||||||
\(752\) | −0.664894 | − | 0.483074i | −0.0242462 | − | 0.0176159i | ||||
\(753\) | −5.13161 | − | 3.72833i | −0.187006 | − | 0.135868i | ||||
\(754\) | −17.2120 | − | 52.9730i | −0.626823 | − | 1.92916i | ||||
\(755\) | −7.02634 | + | 5.10494i | −0.255715 | + | 0.185788i | ||||
\(756\) | −5.25941 | − | 16.1868i | −0.191283 | − | 0.588708i | ||||
\(757\) | −2.96843 | + | 9.13588i | −0.107889 | + | 0.332049i | −0.990398 | − | 0.138247i | \(-0.955853\pi\) |
0.882508 | + | 0.470297i | \(0.155853\pi\) | |||||||
\(758\) | 27.8708 | + | 20.2493i | 1.01231 | + | 0.735489i | ||||
\(759\) | 5.71177 | − | 17.5790i | 0.207324 | − | 0.638078i | ||||
\(760\) | 2.03225 | − | 6.25461i | 0.0737174 | − | 0.226879i | ||||
\(761\) | 26.8533 | + | 19.5100i | 0.973430 | + | 0.707238i | 0.956231 | − | 0.292614i | \(-0.0945251\pi\) |
0.0171990 | + | 0.999852i | \(0.494525\pi\) | |||||||
\(762\) | 0.955691 | − | 2.94131i | 0.0346210 | − | 0.106553i | ||||
\(763\) | −15.4552 | − | 47.5662i | −0.559515 | − | 1.72201i | ||||
\(764\) | −14.9038 | + | 10.8283i | −0.539201 | + | 0.391752i | ||||
\(765\) | 0.560754 | + | 1.72582i | 0.0202741 | + | 0.0623973i | ||||
\(766\) | 17.6436 | + | 12.8188i | 0.637489 | + | 0.463163i | ||||
\(767\) | −17.2461 | − | 12.5301i | −0.622722 | − | 0.452434i | ||||
\(768\) | 1.51612 | − | 1.10153i | 0.0547084 | − | 0.0397480i | ||||
\(769\) | 6.43665 | 0.232112 | 0.116056 | − | 0.993243i | \(-0.462975\pi\) | ||||
0.116056 | + | 0.993243i | \(0.462975\pi\) | |||||||
\(770\) | −6.67427 | −0.240524 | ||||||||
\(771\) | −26.0685 | + | 18.9399i | −0.938836 | + | 0.682104i | ||||
\(772\) | 1.58072 | − | 4.86497i | 0.0568915 | − | 0.175094i | ||||
\(773\) | 12.5320 | + | 38.5696i | 0.450745 | + | 1.38725i | 0.876059 | + | 0.482205i | \(0.160164\pi\) |
−0.425314 | + | 0.905046i | \(0.639836\pi\) | |||||||
\(774\) | −1.44814 | −0.0520525 | ||||||||
\(775\) | −5.56653 | − | 0.117415i | −0.199956 | − | 0.00421767i | ||||
\(776\) | −5.70820 | −0.204913 | ||||||||
\(777\) | 23.2333 | + | 71.5048i | 0.833491 | + | 2.56522i | ||||
\(778\) | 4.60410 | − | 14.1700i | 0.165065 | − | 0.508018i | ||||
\(779\) | 42.7705 | − | 31.0746i | 1.53241 | − | 1.11336i | ||||
\(780\) | −11.6692 | −0.417823 | ||||||||
\(781\) | 3.44598 | 0.123307 | ||||||||
\(782\) | 15.4673 | − | 11.2377i | 0.553110 | − | 0.401858i | ||||
\(783\) | 33.7420 | + | 24.5150i | 1.20584 | + | 0.876095i | ||||
\(784\) | −5.11667 | − | 3.71748i | −0.182738 | − | 0.132767i | ||||
\(785\) | 3.21117 | + | 9.88296i | 0.114612 | + | 0.352738i | ||||
\(786\) | −1.19301 | + | 0.866775i | −0.0425534 | + | 0.0309169i | ||||
\(787\) | −14.3376 | − | 44.1265i | −0.511079 | − | 1.57294i | −0.790305 | − | 0.612713i | \(-0.790078\pi\) |
0.279227 | − | 0.960225i | \(-0.409922\pi\) | |||||||
\(788\) | 1.46842 | − | 4.51934i | 0.0523104 | − | 0.160995i | ||||
\(789\) | −31.8334 | − | 23.1283i | −1.13330 | − | 0.823390i | ||||
\(790\) | 1.56376 | − | 4.81276i | 0.0556361 | − | 0.171230i | ||||
\(791\) | 16.2065 | − | 49.8783i | 0.576235 | − | 1.77347i | ||||
\(792\) | 0.757359 | + | 0.550254i | 0.0269116 | + | 0.0195524i | ||||
\(793\) | −18.0584 | + | 55.5780i | −0.641272 | + | 1.97363i | ||||
\(794\) | 4.93727 | + | 15.1954i | 0.175217 | + | 0.539263i | ||||
\(795\) | −6.24013 | + | 4.53372i | −0.221315 | + | 0.160794i | ||||
\(796\) | 2.59836 | + | 7.99693i | 0.0920964 | + | 0.283444i | ||||
\(797\) | −10.2183 | − | 7.42403i | −0.361951 | − | 0.262973i | 0.391914 | − | 0.920002i | \(-0.371813\pi\) |
−0.753865 | + | 0.657029i | \(0.771813\pi\) | |||||||
\(798\) | 36.3961 | + | 26.4433i | 1.28841 | + | 0.936084i | ||||
\(799\) | 2.35655 | − | 1.71213i | 0.0833686 | − | 0.0605709i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 5.19968 | 0.183722 | ||||||||
\(802\) | −27.3961 | + | 19.9045i | −0.967391 | + | 0.702851i | ||||
\(803\) | −8.97077 | + | 27.6092i | −0.316572 | + | 0.974308i | ||||
\(804\) | 0.105518 | + | 0.324751i | 0.00372133 | + | 0.0114531i | ||||
\(805\) | −19.6907 | −0.694004 | ||||||||
\(806\) | −34.6615 | − | 0.731116i | −1.22090 | − | 0.0257525i | ||||
\(807\) | 13.7635 | 0.484497 | ||||||||
\(808\) | −4.66234 | − | 14.3492i | −0.164021 | − | 0.504804i | ||||
\(809\) | 0.765212 | − | 2.35508i | 0.0269034 | − | 0.0828003i | −0.936703 | − | 0.350124i | \(-0.886139\pi\) |
0.963607 | + | 0.267324i | \(0.0861394\pi\) | |||||||
\(810\) | 8.31172 | − | 6.03882i | 0.292044 | − | 0.212182i | ||||
\(811\) | −17.4043 | −0.611147 | −0.305573 | − | 0.952169i | \(-0.598848\pi\) | ||||
−0.305573 | + | 0.952169i | \(0.598848\pi\) | |||||||
\(812\) | 32.6521 | 1.14587 | ||||||||
\(813\) | −2.26706 | + | 1.64712i | −0.0795093 | + | 0.0577669i | ||||
\(814\) | 16.2578 | + | 11.8120i | 0.569834 | + | 0.414009i | ||||
\(815\) | 5.15983 | + | 3.74884i | 0.180741 | + | 0.131316i | ||||
\(816\) | 2.05250 | + | 6.31694i | 0.0718518 | + | 0.221137i | ||||
\(817\) | −15.0486 | + | 10.9335i | −0.526485 | + | 0.382514i | ||||
\(818\) | −6.91421 | − | 21.2798i | −0.241750 | − | 0.744029i | ||||
\(819\) | 3.59616 | − | 11.0678i | 0.125660 | − | 0.386741i | ||||
\(820\) | −6.50354 | − | 4.72510i | −0.227114 | − | 0.165008i | ||||
\(821\) | 0.600130 | − | 1.84701i | 0.0209447 | − | 0.0644611i | −0.940038 | − | 0.341070i | \(-0.889211\pi\) |
0.960983 | + | 0.276609i | \(0.0892107\pi\) | |||||||
\(822\) | −8.93072 | + | 27.4859i | −0.311494 | + | 0.958681i | ||||
\(823\) | 33.0122 | + | 23.9848i | 1.15073 | + | 0.836057i | 0.988578 | − | 0.150708i | \(-0.0481554\pi\) |
0.162155 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(824\) | −1.59236 | + | 4.90078i | −0.0554725 | + | 0.170727i | ||||
\(825\) | −1.05886 | − | 3.25882i | −0.0368646 | − | 0.113458i | ||||
\(826\) | 10.1101 | − | 7.34542i | 0.351775 | − | 0.255580i | ||||
\(827\) | 7.86323 | + | 24.2005i | 0.273431 | + | 0.841535i | 0.989630 | + | 0.143639i | \(0.0458803\pi\) |
−0.716199 | + | 0.697896i | \(0.754120\pi\) | |||||||
\(828\) | 2.23439 | + | 1.62338i | 0.0776503 | + | 0.0564162i | ||||
\(829\) | −33.7217 | − | 24.5003i | −1.17120 | − | 0.850929i | −0.180051 | − | 0.983657i | \(-0.557626\pi\) |
−0.991152 | + | 0.132728i | \(0.957626\pi\) | |||||||
\(830\) | −2.17976 | + | 1.58369i | −0.0756607 | + | 0.0549707i | ||||
\(831\) | −17.9368 | −0.622222 | ||||||||
\(832\) | −6.22677 | −0.215875 | ||||||||
\(833\) | 18.1347 | − | 13.1757i | 0.628331 | − | 0.456509i | ||||
\(834\) | −2.06198 | + | 6.34614i | −0.0714007 | + | 0.219749i | ||||
\(835\) | −1.90983 | − | 5.87785i | −0.0660924 | − | 0.203411i | ||||
\(836\) | 12.0246 | 0.415881 | ||||||||
\(837\) | 21.3194 | − | 14.8128i | 0.736906 | − | 0.512004i | ||||
\(838\) | −19.7399 | −0.681905 | ||||||||
\(839\) | −9.06758 | − | 27.9071i | −0.313048 | − | 0.963461i | −0.976551 | − | 0.215288i | \(-0.930931\pi\) |
0.663503 | − | 0.748174i | \(-0.269069\pi\) | |||||||
\(840\) | 2.11391 | − | 6.50593i | 0.0729367 | − | 0.224476i | ||||
\(841\) | −41.2718 | + | 29.9858i | −1.42317 | + | 1.03399i | ||||
\(842\) | 8.08830 | 0.278741 | ||||||||
\(843\) | 9.57829 | 0.329894 | ||||||||
\(844\) | 9.03443 | − | 6.56390i | 0.310978 | − | 0.225939i | ||||
\(845\) | 20.8506 | + | 15.1488i | 0.717281 | + | 0.521135i | ||||
\(846\) | 0.340423 | + | 0.247332i | 0.0117040 | + | 0.00850345i | ||||
\(847\) | 8.63692 | + | 26.5817i | 0.296768 | + | 0.913359i | ||||
\(848\) | −3.32979 | + | 2.41923i | −0.114345 | + | 0.0830768i | ||||
\(849\) | −6.61428 | − | 20.3567i | −0.227002 | − | 0.698639i | ||||
\(850\) | 1.09523 | − | 3.37078i | 0.0375661 | − | 0.115617i | ||||
\(851\) | 47.9642 | + | 34.8480i | 1.64419 | + | 1.19457i | ||||
\(852\) | −1.09143 | + | 3.35906i | −0.0373916 | + | 0.115080i | ||||
\(853\) | −16.5273 | + | 50.8658i | −0.565884 | + | 1.74161i | 0.0994259 | + | 0.995045i | \(0.468299\pi\) |
−0.665310 | + | 0.746567i | \(0.731701\pi\) | |||||||
\(854\) | −27.7152 | − | 20.1363i | −0.948394 | − | 0.689049i | ||||
\(855\) | −1.04050 | + | 3.20234i | −0.0355844 | + | 0.109518i | ||||
\(856\) | −4.57243 | − | 14.0725i | −0.156282 | − | 0.480988i | ||||
\(857\) | −16.6880 | + | 12.1245i | −0.570051 | + | 0.414166i | −0.835124 | − | 0.550062i | \(-0.814604\pi\) |
0.265073 | + | 0.964228i | \(0.414604\pi\) | |||||||
\(858\) | −6.59326 | − | 20.2920i | −0.225090 | − | 0.692756i | ||||
\(859\) | −35.4410 | − | 25.7494i | −1.20923 | − | 0.878558i | −0.214071 | − | 0.976818i | \(-0.568672\pi\) |
−0.995161 | + | 0.0982600i | \(0.968672\pi\) | |||||||
\(860\) | 2.28825 | + | 1.66251i | 0.0780285 | + | 0.0566910i | ||||
\(861\) | 44.4891 | − | 32.3232i | 1.51618 | − | 1.10157i | ||||
\(862\) | 32.8863 | 1.12011 | ||||||||
\(863\) | −40.1113 | −1.36540 | −0.682701 | − | 0.730697i | \(-0.739195\pi\) | ||||
−0.682701 | + | 0.730697i | \(0.739195\pi\) | |||||||
\(864\) | 3.77212 | − | 2.74061i | 0.128330 | − | 0.0932373i | ||||
\(865\) | −3.96623 | + | 12.2068i | −0.134856 | + | 0.415044i | ||||
\(866\) | 2.32813 | + | 7.16525i | 0.0791131 | + | 0.243485i | ||||
\(867\) | 8.31759 | 0.282480 | ||||||||
\(868\) | 6.68666 | − | 19.1924i | 0.226960 | − | 0.651434i | ||||
\(869\) | 9.25263 | 0.313874 | ||||||||
\(870\) | 5.18018 | + | 15.9429i | 0.175624 | + | 0.540516i | ||||
\(871\) | 0.350600 | − | 1.07904i | 0.0118796 | − | 0.0365618i | ||||
\(872\) | 11.0847 | − | 8.05349i | 0.375375 | − | 0.272726i | ||||
\(873\) | 2.92258 | 0.0989143 | ||||||||
\(874\) | 35.4755 | 1.19998 | ||||||||
\(875\) | −2.95314 | + | 2.14558i | −0.0998343 | + | 0.0725339i | ||||
\(876\) | −24.0716 | − | 17.4890i | −0.813303 | − | 0.590899i | ||||
\(877\) | −4.07387 | − | 2.95984i | −0.137565 | − | 0.0999468i | 0.516875 | − | 0.856061i | \(-0.327095\pi\) |
−0.654440 | + | 0.756114i | \(0.727095\pi\) | |||||||
\(878\) | 3.17444 | + | 9.76991i | 0.107132 | + | 0.329719i | ||||
\(879\) | 4.52196 | − | 3.28540i | 0.152522 | − | 0.110814i | ||||
\(880\) | −0.565015 | − | 1.73894i | −0.0190467 | − | 0.0586196i | ||||
\(881\) | −6.41078 | + | 19.7304i | −0.215985 | + | 0.664733i | 0.783098 | + | 0.621899i | \(0.213639\pi\) |
−0.999082 | + | 0.0428336i | \(0.986361\pi\) | |||||||
\(882\) | 2.61972 | + | 1.90334i | 0.0882104 | + | 0.0640886i | ||||
\(883\) | −12.5728 | + | 38.6952i | −0.423110 | + | 1.30220i | 0.481683 | + | 0.876345i | \(0.340026\pi\) |
−0.904793 | + | 0.425852i | \(0.859974\pi\) | |||||||
\(884\) | 6.81976 | − | 20.9891i | 0.229373 | − | 0.705938i | ||||
\(885\) | 5.19046 | + | 3.77109i | 0.174476 | + | 0.126764i | ||||
\(886\) | 1.41941 | − | 4.36848i | 0.0476859 | − | 0.146762i | ||||
\(887\) | 16.2555 | + | 50.0294i | 0.545807 | + | 1.67982i | 0.719063 | + | 0.694944i | \(0.244571\pi\) |
−0.173256 | + | 0.984877i | \(0.555429\pi\) | |||||||
\(888\) | −16.6633 | + | 12.1066i | −0.559183 | + | 0.406270i | ||||
\(889\) | −1.86152 | − | 5.72916i | −0.0624332 | − | 0.192150i | ||||
\(890\) | −8.21614 | − | 5.96937i | −0.275406 | − | 0.200094i | ||||
\(891\) | 15.1974 | + | 11.0415i | 0.509131 | + | 0.369905i | ||||
\(892\) | 1.50599 | − | 1.09416i | 0.0504242 | − | 0.0366353i | ||||
\(893\) | 5.40492 | 0.180869 | ||||||||
\(894\) | 31.9370 | 1.06813 | ||||||||
\(895\) | −11.4200 | + | 8.29709i | −0.381727 | + | 0.277341i | ||||
\(896\) | 1.12800 | − | 3.47162i | 0.0376838 | − | 0.115979i | ||||
\(897\) | −19.4516 | − | 59.8660i | −0.649471 | − | 1.99887i | ||||
\(898\) | 15.2141 | 0.507702 | ||||||||
\(899\) | 14.3880 | + | 47.6806i | 0.479868 | + | 1.59024i | ||||
\(900\) | 0.511996 | 0.0170665 | ||||||||
\(901\) | −4.50780 | − | 13.8736i | −0.150177 | − | 0.462196i | ||||
\(902\) | 4.54205 | − | 13.9790i | 0.151234 | − | 0.465450i | ||||
\(903\) | −15.6533 | + | 11.3728i | −0.520909 | + | 0.378463i | ||||
\(904\) | 14.3674 | 0.477854 | ||||||||
\(905\) | −2.20654 | −0.0733480 | ||||||||
\(906\) | 13.1676 | − | 9.56682i | 0.437464 | − | 0.317836i | ||||
\(907\) | −2.35134 | − | 1.70835i | −0.0780748 | − | 0.0567247i | 0.548063 | − | 0.836437i | \(-0.315365\pi\) |
−0.626138 | + | 0.779712i | \(0.715365\pi\) | |||||||
\(908\) | −2.42746 | − | 1.76366i | −0.0805583 | − | 0.0585290i | ||||
\(909\) | 2.38710 | + | 7.34674i | 0.0791752 | + | 0.243676i | ||||
\(910\) | −18.3885 | + | 13.3600i | −0.609574 | + | 0.442881i | ||||
\(911\) | 6.30722 | + | 19.4116i | 0.208967 | + | 0.643136i | 0.999527 | + | 0.0307506i | \(0.00978975\pi\) |
−0.790560 | + | 0.612385i | \(0.790210\pi\) | |||||||
\(912\) | −3.80850 | + | 11.7213i | −0.126112 | + | 0.388133i | ||||
\(913\) | −3.98554 | − | 2.89566i | −0.131902 | − | 0.0958324i | ||||
\(914\) | −8.79269 | + | 27.0611i | −0.290836 | + | 0.895103i | ||||
\(915\) | 5.43492 | − | 16.7270i | 0.179673 | − | 0.552976i | ||||
\(916\) | −12.2745 | − | 8.91793i | −0.405560 | − | 0.294657i | ||||
\(917\) | −0.887605 | + | 2.73177i | −0.0293113 | + | 0.0902109i | ||||
\(918\) | 5.10663 | + | 15.7166i | 0.168544 | + | 0.518724i | ||||
\(919\) | 30.4959 | − | 22.1566i | 1.00597 | − | 0.730879i | 0.0426087 | − | 0.999092i | \(-0.486433\pi\) |
0.963360 | + | 0.268213i | \(0.0864331\pi\) | |||||||
\(920\) | −1.66693 | − | 5.13027i | −0.0549569 | − | 0.169140i | ||||
\(921\) | 39.7945 | + | 28.9124i | 1.31127 | + | 0.952695i | ||||
\(922\) | 4.80342 | + | 3.48989i | 0.158192 | + | 0.114933i | ||||
\(923\) | 9.49413 | − | 6.89789i | 0.312503 | − | 0.227047i | ||||
\(924\) | 12.5078 | 0.411477 | ||||||||
\(925\) | 10.9907 | 0.361372 | ||||||||
\(926\) | −31.8439 | + | 23.1359i | −1.04645 | + | 0.760293i | ||||
\(927\) | 0.815282 | − | 2.50918i | 0.0267774 | − | 0.0824123i | ||||
\(928\) | 2.76419 | + | 8.50730i | 0.0907389 | + | 0.279266i | ||||
\(929\) | −53.0190 | −1.73950 | −0.869748 | − | 0.493497i | \(-0.835719\pi\) | ||||
−0.869748 | + | 0.493497i | \(0.835719\pi\) | |||||||
\(930\) | 10.4318 | + | 0.220039i | 0.342074 | + | 0.00721538i | ||||
\(931\) | 41.5934 | 1.36317 | ||||||||
\(932\) | 7.05369 | + | 21.7090i | 0.231051 | + | 0.711103i | ||||
\(933\) | −6.22562 | + | 19.1605i | −0.203818 | + | 0.627286i | ||||
\(934\) | 15.8515 | − | 11.5168i | 0.518676 | − | 0.376840i | ||||
\(935\) | 6.48039 | 0.211931 | ||||||||
\(936\) | 3.18808 | 0.104206 | ||||||||
\(937\) | −20.1962 | + | 14.6734i | −0.659780 | + | 0.479358i | −0.866589 | − | 0.499023i | \(-0.833692\pi\) |
0.206809 | + | 0.978381i | \(0.433692\pi\) | |||||||
\(938\) | 0.538085 | + | 0.390942i | 0.0175691 | + | 0.0127647i | ||||
\(939\) | 2.26038 | + | 1.64226i | 0.0737648 | + | 0.0535932i | ||||
\(940\) | −0.253967 | − | 0.781630i | −0.00828349 | − | 0.0254940i | ||||
\(941\) | 12.1036 | − | 8.79376i | 0.394565 | − | 0.286668i | −0.372758 | − | 0.927928i | \(-0.621588\pi\) |
0.767324 | + | 0.641260i | \(0.221588\pi\) | |||||||
\(942\) | −6.01783 | − | 18.5210i | −0.196072 | − | 0.603446i | ||||
\(943\) | 13.4001 | − | 41.2413i | 0.436368 | − | 1.34300i | ||||
\(944\) | 2.76968 | + | 2.01229i | 0.0901453 | + | 0.0654944i | ||||
\(945\) | 5.25941 | − | 16.1868i | 0.171089 | − | 0.526556i | ||||
\(946\) | −1.59810 | + | 4.91846i | −0.0519588 | + | 0.159913i | ||||
\(947\) | 8.00574 | + | 5.81651i | 0.260152 | + | 0.189011i | 0.710214 | − | 0.703986i | \(-0.248598\pi\) |
−0.450062 | + | 0.892997i | \(0.648598\pi\) | |||||||
\(948\) | −2.93054 | + | 9.01926i | −0.0951794 | + | 0.292932i | ||||
\(949\) | 30.5503 | + | 94.0241i | 0.991704 | + | 3.05215i | ||||
\(950\) | 5.32049 | − | 3.86556i | 0.172620 | − | 0.125415i | ||||
\(951\) | 8.07777 | + | 24.8608i | 0.261940 | + | 0.806167i | ||||
\(952\) | 10.4666 | + | 7.60446i | 0.339226 | + | 0.246462i | ||||
\(953\) | −14.9427 | − | 10.8565i | −0.484040 | − | 0.351676i | 0.318848 | − | 0.947806i | \(-0.396704\pi\) |
−0.802888 | + | 0.596130i | \(0.796704\pi\) | |||||||
\(954\) | 1.70484 | − | 1.23864i | 0.0551962 | − | 0.0401024i | ||||
\(955\) | −18.4221 | −0.596126 | ||||||||
\(956\) | −20.0577 | −0.648713 | ||||||||
\(957\) | −24.7969 | + | 18.0160i | −0.801570 | + | 0.582375i | ||||
\(958\) | 2.33046 | − | 7.17241i | 0.0752937 | − | 0.231730i | ||||
\(959\) | 17.3954 | + | 53.5377i | 0.561728 | + | 1.72882i | ||||
\(960\) | 1.87403 | 0.0604841 | ||||||||
\(961\) | 30.9724 | + | 1.30719i | 0.999111 | + | 0.0421673i | ||||
\(962\) | 68.4366 | 2.20649 | ||||||||
\(963\) | 2.34107 | + | 7.20506i | 0.0754398 | + | 0.232180i | ||||
\(964\) | 0.135893 | − | 0.418234i | 0.00437680 | − | 0.0134704i | ||||
\(965\) | 4.13839 | − | 3.00672i | 0.133220 | − | 0.0967897i | ||||
\(966\) | 36.9009 | 1.18727 | ||||||||
\(967\) | −39.4622 | −1.26902 | −0.634510 | − | 0.772915i | \(-0.718798\pi\) | ||||
−0.634510 | + | 0.772915i | \(0.718798\pi\) | |||||||
\(968\) | −6.19453 | + | 4.50059i | −0.199100 | + | 0.144654i | ||||
\(969\) | −35.3389 | − | 25.6752i | −1.13525 | − | 0.824806i | ||||
\(970\) | −4.61803 | − | 3.35520i | −0.148276 | − | 0.107729i | ||||
\(971\) | −11.4029 | − | 35.0944i | −0.365935 | − | 1.12623i | −0.949393 | − | 0.314089i | \(-0.898301\pi\) |
0.583458 | − | 0.812143i | \(-0.301699\pi\) | |||||||
\(972\) | −4.26006 | + | 3.09511i | −0.136641 | + | 0.0992759i | ||||
\(973\) | 4.01638 | + | 12.3611i | 0.128759 | + | 0.396280i | ||||
\(974\) | 0.261479 | − | 0.804749i | 0.00837832 | − | 0.0257858i | ||||
\(975\) | −9.44056 | − | 6.85897i | −0.302340 | − | 0.219663i | ||||
\(976\) | 2.90012 | − | 8.92565i | 0.0928306 | − | 0.285703i | ||||
\(977\) | −10.8631 | + | 33.4330i | −0.347540 | + | 1.06962i | 0.612670 | + | 0.790339i | \(0.290095\pi\) |
−0.960210 | + | 0.279279i | \(0.909905\pi\) | |||||||
\(978\) | −9.66969 | − | 7.02544i | −0.309203 | − | 0.224649i | ||||
\(979\) | 5.73813 | − | 17.6601i | 0.183391 | − | 0.564420i | ||||
\(980\) | −1.95440 | − | 6.01501i | −0.0624309 | − | 0.192142i | ||||
\(981\) | −5.67531 | + | 4.12336i | −0.181199 | + | 0.131649i | ||||
\(982\) | −0.962849 | − | 2.96334i | −0.0307257 | − | 0.0945641i | ||||
\(983\) | 27.0782 | + | 19.6734i | 0.863659 | + | 0.627485i | 0.928878 | − | 0.370386i | \(-0.120775\pi\) |
−0.0652190 | + | 0.997871i | \(0.520775\pi\) | |||||||
\(984\) | 12.1878 | + | 8.85499i | 0.388534 | + | 0.282287i | ||||
\(985\) | 3.84438 | − | 2.79311i | 0.122492 | − | 0.0889957i | ||||
\(986\) | −31.7036 | −1.00965 | ||||||||
\(987\) | 5.62210 | 0.178953 | ||||||||
\(988\) | 33.1295 | − | 24.0700i | 1.05399 | − | 0.765768i | ||||
\(989\) | −4.71478 | + | 14.5106i | −0.149921 | + | 0.461410i | ||||
\(990\) | 0.289286 | + | 0.890329i | 0.00919410 | + | 0.0282965i | ||||
\(991\) | −11.8203 | −0.375483 | −0.187741 | − | 0.982218i | \(-0.560117\pi\) | ||||
−0.187741 | + | 0.982218i | \(0.560117\pi\) | |||||||
\(992\) | 5.56653 | + | 0.117415i | 0.176737 | + | 0.00372793i | ||||
\(993\) | 33.6402 | 1.06754 | ||||||||
\(994\) | 2.12590 | + | 6.54285i | 0.0674295 | + | 0.207527i | ||||
\(995\) | −2.59836 | + | 7.99693i | −0.0823735 | + | 0.253520i | ||||
\(996\) | 4.08495 | − | 2.96789i | 0.129436 | − | 0.0940411i | ||||
\(997\) | 56.2299 | 1.78082 | 0.890410 | − | 0.455159i | \(-0.150418\pi\) | ||||
0.890410 | + | 0.455159i | \(0.150418\pi\) | |||||||
\(998\) | −13.6109 | −0.430847 | ||||||||
\(999\) | −41.4583 | + | 30.1212i | −1.31168 | + | 0.952993i |
(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 | 310.2.h.e.221.1 | yes | 8 | |
31.8 | even | 5 | inner | 310.2.h.e.101.1 | ✓ | 8 | |
31.15 | odd | 10 | 9610.2.a.bh.1.3 | 4 | |||
31.16 | even | 5 | 9610.2.a.ba.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
310.2.h.e.101.1 | ✓ | 8 | 31.8 | even | 5 | inner | |
310.2.h.e.221.1 | yes | 8 | 1.1 | even | 1 | trivial | |
9610.2.a.ba.1.2 | 4 | 31.16 | even | 5 | |||
9610.2.a.bh.1.3 | 4 | 31.15 | odd | 10 |