Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(71,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 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("770.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
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: | \( x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} - 350 x^{3} + 510 x^{2} - 175 x + 25 \) |
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 | 141.1 | ||
Root | \(-0.674672 + 2.07643i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.141 |
Dual form | 770.2.n.j.71.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | −1.76631 | + | 1.28330i | −1.01978 | + | 0.740915i | −0.966238 | − | 0.257650i | \(-0.917052\pi\) |
−0.0535440 | + | 0.998565i | \(0.517052\pi\) | |||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0.309017 | + | 0.951057i | 0.138197 | + | 0.425325i | ||||
\(6\) | −0.674672 | − | 2.07643i | −0.275434 | − | 0.847698i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | 0.545950 | − | 1.68026i | 0.181983 | − | 0.560088i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.35838 | − | 2.33197i | 0.711077 | − | 0.703114i | ||||
\(12\) | 2.18328 | 0.630260 | ||||||||
\(13\) | 0.782625 | − | 2.40867i | 0.217061 | − | 0.668046i | −0.781940 | − | 0.623354i | \(-0.785769\pi\) |
0.999001 | − | 0.0446916i | \(-0.0142305\pi\) | |||||||
\(14\) | 0.809017 | − | 0.587785i | 0.216219 | − | 0.157092i | ||||
\(15\) | −1.76631 | − | 1.28330i | −0.456060 | − | 0.331347i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −1.77318 | − | 5.45728i | −0.430059 | − | 1.32359i | −0.898066 | − | 0.439861i | \(-0.855028\pi\) |
0.468007 | − | 0.883725i | \(-0.344972\pi\) | |||||||
\(18\) | 1.42932 | + | 1.03846i | 0.336893 | + | 0.244767i | ||||
\(19\) | 1.81268 | − | 1.31699i | 0.415858 | − | 0.302139i | −0.360111 | − | 0.932909i | \(-0.617261\pi\) |
0.775969 | + | 0.630771i | \(0.217261\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | 2.18328 | 0.476432 | ||||||||
\(22\) | 1.48905 | + | 2.96357i | 0.317467 | + | 0.631834i | ||||
\(23\) | −2.51489 | −0.524390 | −0.262195 | − | 0.965015i | \(-0.584446\pi\) | ||||
−0.262195 | + | 0.965015i | \(0.584446\pi\) | |||||||
\(24\) | −0.674672 | + | 2.07643i | −0.137717 | + | 0.423849i | ||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | 2.04894 | + | 1.48864i | 0.401830 | + | 0.291947i | ||||
\(27\) | −0.832051 | − | 2.56079i | −0.160128 | − | 0.492824i | ||||
\(28\) | 0.309017 | + | 0.951057i | 0.0583987 | + | 0.179733i | ||||
\(29\) | 6.97373 | + | 5.06671i | 1.29499 | + | 0.940864i | 0.999893 | − | 0.0146039i | \(-0.00464873\pi\) |
0.295095 | + | 0.955468i | \(0.404649\pi\) | |||||||
\(30\) | 1.76631 | − | 1.28330i | 0.322483 | − | 0.234298i | ||||
\(31\) | 0.568867 | − | 1.75079i | 0.102171 | − | 0.314451i | −0.886885 | − | 0.461991i | \(-0.847135\pi\) |
0.989056 | + | 0.147539i | \(0.0471353\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.17301 | + | 7.14549i | −0.204195 | + | 1.24387i | ||||
\(34\) | 5.73813 | 0.984080 | ||||||||
\(35\) | 0.309017 | − | 0.951057i | 0.0522334 | − | 0.160758i | ||||
\(36\) | −1.42932 | + | 1.03846i | −0.238219 | + | 0.173077i | ||||
\(37\) | 3.74676 | + | 2.72218i | 0.615963 | + | 0.447523i | 0.851509 | − | 0.524340i | \(-0.175688\pi\) |
−0.235546 | + | 0.971863i | \(0.575688\pi\) | |||||||
\(38\) | 0.692383 | + | 2.13094i | 0.112319 | + | 0.345684i | ||||
\(39\) | 1.70869 | + | 5.25882i | 0.273610 | + | 0.842085i | ||||
\(40\) | 0.809017 | + | 0.587785i | 0.127917 | + | 0.0929370i | ||||
\(41\) | 8.53702 | − | 6.20251i | 1.33326 | − | 0.968669i | 0.333595 | − | 0.942716i | \(-0.391738\pi\) |
0.999663 | − | 0.0259525i | \(-0.00826185\pi\) | |||||||
\(42\) | −0.674672 | + | 2.07643i | −0.104104 | + | 0.320400i | ||||
\(43\) | −2.18804 | −0.333672 | −0.166836 | − | 0.985985i | \(-0.553355\pi\) | ||||
−0.166836 | + | 0.985985i | \(0.553355\pi\) | |||||||
\(44\) | −3.27866 | + | 0.500382i | −0.494277 | + | 0.0754355i | ||||
\(45\) | 1.76673 | 0.263369 | ||||||||
\(46\) | 0.777143 | − | 2.39180i | 0.114583 | − | 0.352652i | ||||
\(47\) | −2.60894 | + | 1.89550i | −0.380552 | + | 0.276487i | −0.761573 | − | 0.648079i | \(-0.775573\pi\) |
0.381021 | + | 0.924566i | \(0.375573\pi\) | |||||||
\(48\) | −1.76631 | − | 1.28330i | −0.254946 | − | 0.185229i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −0.309017 | − | 0.951057i | −0.0437016 | − | 0.134500i | ||||
\(51\) | 10.1353 | + | 7.36375i | 1.41923 | + | 1.03113i | ||||
\(52\) | −2.04894 | + | 1.48864i | −0.284137 | + | 0.206438i | ||||
\(53\) | −1.24146 | + | 3.82083i | −0.170528 | + | 0.524832i | −0.999401 | − | 0.0346052i | \(-0.988983\pi\) |
0.828873 | + | 0.559437i | \(0.188983\pi\) | |||||||
\(54\) | 2.69257 | 0.366413 | ||||||||
\(55\) | 2.94661 | + | 1.52233i | 0.397321 | + | 0.205271i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.51167 | + | 4.65244i | −0.200226 | + | 0.616231i | ||||
\(58\) | −6.97373 | + | 5.06671i | −0.915695 | + | 0.665291i | ||||
\(59\) | −1.62940 | − | 1.18383i | −0.212130 | − | 0.154121i | 0.476647 | − | 0.879095i | \(-0.341852\pi\) |
−0.688777 | + | 0.724974i | \(0.741852\pi\) | |||||||
\(60\) | 0.674672 | + | 2.07643i | 0.0870998 | + | 0.268066i | ||||
\(61\) | −0.0828892 | − | 0.255107i | −0.0106129 | − | 0.0326631i | 0.945610 | − | 0.325303i | \(-0.105466\pi\) |
−0.956223 | + | 0.292640i | \(0.905466\pi\) | |||||||
\(62\) | 1.48931 | + | 1.08205i | 0.189143 | + | 0.137420i | ||||
\(63\) | −1.42932 | + | 1.03846i | −0.180077 | + | 0.130834i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 2.53263 | 0.314134 | ||||||||
\(66\) | −6.43329 | − | 3.32368i | −0.791883 | − | 0.409117i | ||||
\(67\) | 3.86233 | 0.471859 | 0.235929 | − | 0.971770i | \(-0.424187\pi\) | ||||
0.235929 | + | 0.971770i | \(0.424187\pi\) | |||||||
\(68\) | −1.77318 | + | 5.45728i | −0.215029 | + | 0.661793i | ||||
\(69\) | 4.44208 | − | 3.22736i | 0.534764 | − | 0.388529i | ||||
\(70\) | 0.809017 | + | 0.587785i | 0.0966960 | + | 0.0702538i | ||||
\(71\) | −2.95270 | − | 9.08747i | −0.350421 | − | 1.07848i | −0.958617 | − | 0.284698i | \(-0.908107\pi\) |
0.608196 | − | 0.793787i | \(-0.291893\pi\) | |||||||
\(72\) | −0.545950 | − | 1.68026i | −0.0643409 | − | 0.198021i | ||||
\(73\) | 9.24371 | + | 6.71595i | 1.08189 | + | 0.786042i | 0.978012 | − | 0.208548i | \(-0.0668737\pi\) |
0.103882 | + | 0.994590i | \(0.466874\pi\) | |||||||
\(74\) | −3.74676 | + | 2.72218i | −0.435552 | + | 0.316447i | ||||
\(75\) | 0.674672 | − | 2.07643i | 0.0779044 | − | 0.239765i | ||||
\(76\) | −2.24060 | −0.257014 | ||||||||
\(77\) | −3.27866 | + | 0.500382i | −0.373638 | + | 0.0570239i | ||||
\(78\) | −5.52945 | −0.626087 | ||||||||
\(79\) | −3.63201 | + | 11.1782i | −0.408633 | + | 1.25764i | 0.509190 | + | 0.860654i | \(0.329945\pi\) |
−0.917823 | + | 0.396990i | \(0.870055\pi\) | |||||||
\(80\) | −0.809017 | + | 0.587785i | −0.0904508 | + | 0.0657164i | ||||
\(81\) | 9.04388 | + | 6.57077i | 1.00488 | + | 0.730085i | ||||
\(82\) | 3.26085 | + | 10.0359i | 0.360101 | + | 1.10828i | ||||
\(83\) | −2.27081 | − | 6.98885i | −0.249254 | − | 0.767126i | −0.994908 | − | 0.100792i | \(-0.967862\pi\) |
0.745653 | − | 0.666334i | \(-0.232138\pi\) | |||||||
\(84\) | −1.76631 | − | 1.28330i | −0.192721 | − | 0.140020i | ||||
\(85\) | 4.64224 | − | 3.37279i | 0.503522 | − | 0.365830i | ||||
\(86\) | 0.676140 | − | 2.08095i | 0.0729101 | − | 0.224394i | ||||
\(87\) | −18.8199 | −2.01771 | ||||||||
\(88\) | 0.537270 | − | 3.27282i | 0.0572732 | − | 0.348884i | ||||
\(89\) | −2.65397 | −0.281321 | −0.140660 | − | 0.990058i | \(-0.544923\pi\) | ||||
−0.140660 | + | 0.990058i | \(0.544923\pi\) | |||||||
\(90\) | −0.545950 | + | 1.68026i | −0.0575482 | + | 0.177115i | ||||
\(91\) | −2.04894 | + | 1.48864i | −0.214787 | + | 0.156052i | ||||
\(92\) | 2.03459 | + | 1.47821i | 0.212120 | + | 0.154114i | ||||
\(93\) | 1.24200 | + | 3.82248i | 0.128789 | + | 0.396372i | ||||
\(94\) | −0.996525 | − | 3.06699i | −0.102784 | − | 0.316336i | ||||
\(95\) | 1.81268 | + | 1.31699i | 0.185977 | + | 0.135120i | ||||
\(96\) | 1.76631 | − | 1.28330i | 0.180274 | − | 0.130977i | ||||
\(97\) | 5.10018 | − | 15.6967i | 0.517845 | − | 1.59376i | −0.260200 | − | 0.965555i | \(-0.583789\pi\) |
0.778045 | − | 0.628208i | \(-0.216211\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −2.63076 | − | 5.23583i | −0.264401 | − | 0.526220i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.95905 | − | 15.2624i | 0.493444 | − | 1.51866i | −0.325925 | − | 0.945396i | \(-0.605676\pi\) |
0.819368 | − | 0.573267i | \(-0.194324\pi\) | |||||||
\(102\) | −10.1353 | + | 7.36375i | −1.00355 | + | 0.729120i | ||||
\(103\) | 10.4387 | + | 7.58413i | 1.02855 | + | 0.747287i | 0.968018 | − | 0.250879i | \(-0.0807197\pi\) |
0.0605337 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(104\) | −0.782625 | − | 2.40867i | −0.0767427 | − | 0.236190i | ||||
\(105\) | 0.674672 | + | 2.07643i | 0.0658413 | + | 0.202639i | ||||
\(106\) | −3.25019 | − | 2.36140i | −0.315687 | − | 0.229360i | ||||
\(107\) | 5.45736 | − | 3.96501i | 0.527583 | − | 0.383312i | −0.291870 | − | 0.956458i | \(-0.594277\pi\) |
0.819453 | + | 0.573146i | \(0.194277\pi\) | |||||||
\(108\) | −0.832051 | + | 2.56079i | −0.0800642 | + | 0.246412i | ||||
\(109\) | 18.6864 | 1.78983 | 0.894916 | − | 0.446235i | \(-0.147235\pi\) | ||||
0.894916 | + | 0.446235i | \(0.147235\pi\) | |||||||
\(110\) | −2.35838 | + | 2.33197i | −0.224862 | + | 0.222344i | ||||
\(111\) | −10.1113 | −0.959725 | ||||||||
\(112\) | 0.309017 | − | 0.951057i | 0.0291994 | − | 0.0898664i | ||||
\(113\) | −6.11968 | + | 4.44620i | −0.575691 | + | 0.418264i | −0.837168 | − | 0.546946i | \(-0.815790\pi\) |
0.261477 | + | 0.965210i | \(0.415790\pi\) | |||||||
\(114\) | −3.95760 | − | 2.87537i | −0.370664 | − | 0.269303i | ||||
\(115\) | −0.777143 | − | 2.39180i | −0.0724689 | − | 0.223036i | ||||
\(116\) | −2.66373 | − | 8.19811i | −0.247321 | − | 0.761175i | ||||
\(117\) | −3.61993 | − | 2.63003i | −0.334663 | − | 0.243147i | ||||
\(118\) | 1.62940 | − | 1.18383i | 0.149998 | − | 0.108980i | ||||
\(119\) | −1.77318 | + | 5.45728i | −0.162547 | + | 0.500268i | ||||
\(120\) | −2.18328 | −0.199306 | ||||||||
\(121\) | 0.123865 | − | 10.9993i | 0.0112605 | − | 0.999937i | ||||
\(122\) | 0.268235 | 0.0242849 | ||||||||
\(123\) | −7.11937 | + | 21.9112i | −0.641932 | + | 1.97566i | ||||
\(124\) | −1.48931 | + | 1.08205i | −0.133744 | + | 0.0971708i | ||||
\(125\) | −0.809017 | − | 0.587785i | −0.0723607 | − | 0.0525731i | ||||
\(126\) | −0.545950 | − | 1.68026i | −0.0486371 | − | 0.149690i | ||||
\(127\) | −3.31964 | − | 10.2168i | −0.294570 | − | 0.906594i | −0.983365 | − | 0.181638i | \(-0.941860\pi\) |
0.688795 | − | 0.724956i | \(-0.258140\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 3.86476 | − | 2.80791i | 0.340273 | − | 0.247223i | ||||
\(130\) | −0.782625 | + | 2.40867i | −0.0686408 | + | 0.211255i | ||||
\(131\) | −17.0221 | −1.48723 | −0.743613 | − | 0.668610i | \(-0.766890\pi\) | ||||
−0.743613 | + | 0.668610i | \(0.766890\pi\) | |||||||
\(132\) | 5.14900 | − | 5.09135i | 0.448163 | − | 0.443145i | ||||
\(133\) | −2.24060 | −0.194285 | ||||||||
\(134\) | −1.19353 | + | 3.67329i | −0.103105 | + | 0.317324i | ||||
\(135\) | 2.17834 | − | 1.58266i | 0.187481 | − | 0.136213i | ||||
\(136\) | −4.64224 | − | 3.37279i | −0.398069 | − | 0.289214i | ||||
\(137\) | −3.85581 | − | 11.8670i | −0.329424 | − | 1.01386i | −0.969404 | − | 0.245471i | \(-0.921057\pi\) |
0.639980 | − | 0.768392i | \(-0.278943\pi\) | |||||||
\(138\) | 1.69672 | + | 5.22198i | 0.144435 | + | 0.444524i | ||||
\(139\) | −14.0617 | − | 10.2164i | −1.19270 | − | 0.866547i | −0.199153 | − | 0.979968i | \(-0.563819\pi\) |
−0.993547 | + | 0.113421i | \(0.963819\pi\) | |||||||
\(140\) | −0.809017 | + | 0.587785i | −0.0683744 | + | 0.0496769i | ||||
\(141\) | 2.17570 | − | 6.69611i | 0.183227 | − | 0.563914i | ||||
\(142\) | 9.55514 | 0.801849 | ||||||||
\(143\) | −3.77122 | − | 7.50561i | −0.315365 | − | 0.627651i | ||||
\(144\) | 1.76673 | 0.147228 | ||||||||
\(145\) | −2.66373 | + | 8.19811i | −0.221210 | + | 0.680816i | ||||
\(146\) | −9.24371 | + | 6.71595i | −0.765015 | + | 0.555816i | ||||
\(147\) | −1.76631 | − | 1.28330i | −0.145683 | − | 0.105845i | ||||
\(148\) | −1.43113 | − | 4.40458i | −0.117638 | − | 0.362054i | ||||
\(149\) | −0.461073 | − | 1.41904i | −0.0377726 | − | 0.116252i | 0.930392 | − | 0.366565i | \(-0.119466\pi\) |
−0.968165 | + | 0.250313i | \(0.919466\pi\) | |||||||
\(150\) | 1.76631 | + | 1.28330i | 0.144219 | + | 0.104781i | ||||
\(151\) | 6.46853 | − | 4.69966i | 0.526402 | − | 0.382453i | −0.292608 | − | 0.956232i | \(-0.594523\pi\) |
0.819010 | + | 0.573779i | \(0.194523\pi\) | |||||||
\(152\) | 0.692383 | − | 2.13094i | 0.0561597 | − | 0.172842i | ||||
\(153\) | −10.1377 | −0.819587 | ||||||||
\(154\) | 0.537270 | − | 3.27282i | 0.0432945 | − | 0.263731i | ||||
\(155\) | 1.84089 | 0.147864 | ||||||||
\(156\) | 1.70869 | − | 5.25882i | 0.136805 | − | 0.421043i | ||||
\(157\) | −1.65988 | + | 1.20598i | −0.132473 | + | 0.0962473i | −0.652048 | − | 0.758177i | \(-0.726090\pi\) |
0.519575 | + | 0.854425i | \(0.326090\pi\) | |||||||
\(158\) | −9.50873 | − | 6.90850i | −0.756474 | − | 0.549610i | ||||
\(159\) | −2.71047 | − | 8.34197i | −0.214954 | − | 0.661561i | ||||
\(160\) | −0.309017 | − | 0.951057i | −0.0244299 | − | 0.0751876i | ||||
\(161\) | 2.03459 | + | 1.47821i | 0.160348 | + | 0.116500i | ||||
\(162\) | −9.04388 | + | 6.57077i | −0.710555 | + | 0.516248i | ||||
\(163\) | 6.39590 | − | 19.6846i | 0.500966 | − | 1.54181i | −0.306483 | − | 0.951876i | \(-0.599152\pi\) |
0.807449 | − | 0.589938i | \(-0.200848\pi\) | |||||||
\(164\) | −10.5523 | −0.823999 | ||||||||
\(165\) | −7.15825 | + | 1.09248i | −0.557269 | + | 0.0850492i | ||||
\(166\) | 7.34851 | 0.570355 | ||||||||
\(167\) | 0.408057 | − | 1.25587i | 0.0315764 | − | 0.0971823i | −0.934026 | − | 0.357205i | \(-0.883730\pi\) |
0.965603 | + | 0.260022i | \(0.0837299\pi\) | |||||||
\(168\) | 1.76631 | − | 1.28330i | 0.136274 | − | 0.0990089i | ||||
\(169\) | 5.32802 | + | 3.87103i | 0.409847 | + | 0.297772i | ||||
\(170\) | 1.77318 | + | 5.45728i | 0.135997 | + | 0.418554i | ||||
\(171\) | −1.22326 | − | 3.76480i | −0.0935447 | − | 0.287901i | ||||
\(172\) | 1.77016 | + | 1.28609i | 0.134973 | + | 0.0980638i | ||||
\(173\) | −12.7039 | + | 9.22991i | −0.965858 | + | 0.701737i | −0.954504 | − | 0.298199i | \(-0.903614\pi\) |
−0.0113541 | + | 0.999936i | \(0.503614\pi\) | |||||||
\(174\) | 5.81567 | − | 17.8988i | 0.440885 | − | 1.35690i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 2.94661 | + | 1.52233i | 0.222109 | + | 0.114750i | ||||
\(177\) | 4.39724 | 0.330517 | ||||||||
\(178\) | 0.820123 | − | 2.52408i | 0.0614708 | − | 0.189188i | ||||
\(179\) | −3.76595 | + | 2.73612i | −0.281480 | + | 0.204507i | −0.719563 | − | 0.694427i | \(-0.755658\pi\) |
0.438083 | + | 0.898935i | \(0.355658\pi\) | |||||||
\(180\) | −1.42932 | − | 1.03846i | −0.106535 | − | 0.0774022i | ||||
\(181\) | −1.82459 | − | 5.61552i | −0.135621 | − | 0.417398i | 0.860065 | − | 0.510184i | \(-0.170423\pi\) |
−0.995686 | + | 0.0927860i | \(0.970423\pi\) | |||||||
\(182\) | −0.782625 | − | 2.40867i | −0.0580121 | − | 0.178543i | ||||
\(183\) | 0.473787 | + | 0.344227i | 0.0350234 | + | 0.0254460i | ||||
\(184\) | −2.03459 | + | 1.47821i | −0.149992 | + | 0.108975i | ||||
\(185\) | −1.43113 | + | 4.40458i | −0.105219 | + | 0.323831i | ||||
\(186\) | −4.01919 | −0.294701 | ||||||||
\(187\) | −16.9080 | − | 8.73532i | −1.23644 | − | 0.638790i | ||||
\(188\) | 3.22482 | 0.235194 | ||||||||
\(189\) | −0.832051 | + | 2.56079i | −0.0605228 | + | 0.186270i | ||||
\(190\) | −1.81268 | + | 1.31699i | −0.131506 | + | 0.0955446i | ||||
\(191\) | 4.80071 | + | 3.48792i | 0.347367 | + | 0.252377i | 0.747764 | − | 0.663965i | \(-0.231128\pi\) |
−0.400397 | + | 0.916342i | \(0.631128\pi\) | |||||||
\(192\) | 0.674672 | + | 2.07643i | 0.0486903 | + | 0.149853i | ||||
\(193\) | 3.34902 | + | 10.3072i | 0.241068 | + | 0.741931i | 0.996258 | + | 0.0864256i | \(0.0275445\pi\) |
−0.755190 | + | 0.655506i | \(0.772456\pi\) | |||||||
\(194\) | 13.3525 | + | 9.70112i | 0.958650 | + | 0.696500i | ||||
\(195\) | −4.47342 | + | 3.25013i | −0.320348 | + | 0.232747i | ||||
\(196\) | 0.309017 | − | 0.951057i | 0.0220726 | − | 0.0679326i | ||||
\(197\) | 12.0176 | 0.856216 | 0.428108 | − | 0.903728i | \(-0.359180\pi\) | ||||
0.428108 | + | 0.903728i | \(0.359180\pi\) | |||||||
\(198\) | 5.79252 | − | 0.884042i | 0.411656 | − | 0.0628261i | ||||
\(199\) | 18.4014 | 1.30444 | 0.652220 | − | 0.758030i | \(-0.273838\pi\) | ||||
0.652220 | + | 0.758030i | \(0.273838\pi\) | |||||||
\(200\) | −0.309017 | + | 0.951057i | −0.0218508 | + | 0.0672499i | ||||
\(201\) | −6.82209 | + | 4.95654i | −0.481193 | + | 0.349607i | ||||
\(202\) | 12.9830 | + | 9.43267i | 0.913477 | + | 0.663680i | ||||
\(203\) | −2.66373 | − | 8.19811i | −0.186957 | − | 0.575394i | ||||
\(204\) | −3.87135 | − | 11.9148i | −0.271049 | − | 0.834203i | ||||
\(205\) | 8.53702 | + | 6.20251i | 0.596251 | + | 0.433202i | ||||
\(206\) | −10.4387 | + | 7.58413i | −0.727296 | + | 0.528412i | ||||
\(207\) | −1.37300 | + | 4.22567i | −0.0954303 | + | 0.293704i | ||||
\(208\) | 2.53263 | 0.175606 | ||||||||
\(209\) | 1.20381 | − | 7.33308i | 0.0832691 | − | 0.507239i | ||||
\(210\) | −2.18328 | −0.150661 | ||||||||
\(211\) | 6.19337 | − | 19.0612i | 0.426369 | − | 1.31223i | −0.475308 | − | 0.879820i | \(-0.657663\pi\) |
0.901677 | − | 0.432410i | \(-0.142337\pi\) | |||||||
\(212\) | 3.25019 | − | 2.36140i | 0.223224 | − | 0.162182i | ||||
\(213\) | 16.8774 | + | 12.2621i | 1.15642 | + | 0.840187i | ||||
\(214\) | 2.08453 | + | 6.41552i | 0.142495 | + | 0.438556i | ||||
\(215\) | −0.676140 | − | 2.08095i | −0.0461124 | − | 0.141919i | ||||
\(216\) | −2.17834 | − | 1.58266i | −0.148217 | − | 0.107686i | ||||
\(217\) | −1.48931 | + | 1.08205i | −0.101101 | + | 0.0734543i | ||||
\(218\) | −5.77441 | + | 17.7718i | −0.391093 | + | 1.20366i | ||||
\(219\) | −24.9459 | −1.68569 | ||||||||
\(220\) | −1.48905 | − | 2.96357i | −0.100392 | − | 0.199804i | ||||
\(221\) | −14.5325 | −0.977565 | ||||||||
\(222\) | 3.12457 | − | 9.61644i | 0.209708 | − | 0.645413i | ||||
\(223\) | −9.54638 | + | 6.93585i | −0.639273 | + | 0.464459i | −0.859600 | − | 0.510967i | \(-0.829287\pi\) |
0.220328 | + | 0.975426i | \(0.429287\pi\) | |||||||
\(224\) | 0.809017 | + | 0.587785i | 0.0540547 | + | 0.0392731i | ||||
\(225\) | 0.545950 | + | 1.68026i | 0.0363967 | + | 0.112018i | ||||
\(226\) | −2.33751 | − | 7.19411i | −0.155489 | − | 0.478545i | ||||
\(227\) | −0.801025 | − | 0.581979i | −0.0531659 | − | 0.0386273i | 0.560885 | − | 0.827894i | \(-0.310461\pi\) |
−0.614051 | + | 0.789267i | \(0.710461\pi\) | |||||||
\(228\) | 3.95760 | − | 2.87537i | 0.262099 | − | 0.190426i | ||||
\(229\) | 5.67228 | − | 17.4575i | 0.374835 | − | 1.15362i | −0.568755 | − | 0.822507i | \(-0.692575\pi\) |
0.943590 | − | 0.331116i | \(-0.107425\pi\) | |||||||
\(230\) | 2.51489 | 0.165827 | ||||||||
\(231\) | 5.14900 | − | 5.09135i | 0.338780 | − | 0.334986i | ||||
\(232\) | 8.62000 | 0.565931 | ||||||||
\(233\) | −5.36608 | + | 16.5151i | −0.351543 | + | 1.08194i | 0.606443 | + | 0.795127i | \(0.292596\pi\) |
−0.957987 | + | 0.286813i | \(0.907404\pi\) | |||||||
\(234\) | 3.61993 | − | 2.63003i | 0.236642 | − | 0.171931i | ||||
\(235\) | −2.60894 | − | 1.89550i | −0.170188 | − | 0.123649i | ||||
\(236\) | 0.622375 | + | 1.91547i | 0.0405131 | + | 0.124687i | ||||
\(237\) | −7.92972 | − | 24.4052i | −0.515090 | − | 1.58529i | ||||
\(238\) | −4.64224 | − | 3.37279i | −0.300912 | − | 0.218625i | ||||
\(239\) | −7.21735 | + | 5.24371i | −0.466851 | + | 0.339187i | −0.796213 | − | 0.605017i | \(-0.793166\pi\) |
0.329362 | + | 0.944204i | \(0.393166\pi\) | |||||||
\(240\) | 0.674672 | − | 2.07643i | 0.0435499 | − | 0.134033i | ||||
\(241\) | −0.896696 | −0.0577613 | −0.0288806 | − | 0.999583i | \(-0.509194\pi\) | ||||
−0.0288806 | + | 0.999583i | \(0.509194\pi\) | |||||||
\(242\) | 10.4227 | + | 3.51677i | 0.669995 | + | 0.226067i | ||||
\(243\) | −16.3289 | −1.04750 | ||||||||
\(244\) | −0.0828892 | + | 0.255107i | −0.00530644 | + | 0.0163315i | ||||
\(245\) | −0.809017 | + | 0.587785i | −0.0516862 | + | 0.0375522i | ||||
\(246\) | −18.6387 | − | 13.5418i | −1.18836 | − | 0.863396i | ||||
\(247\) | −1.75355 | − | 5.39687i | −0.111576 | − | 0.343395i | ||||
\(248\) | −0.568867 | − | 1.75079i | −0.0361231 | − | 0.111175i | ||||
\(249\) | 12.9798 | + | 9.43036i | 0.822560 | + | 0.597625i | ||||
\(250\) | 0.809017 | − | 0.587785i | 0.0511667 | − | 0.0371748i | ||||
\(251\) | −6.95222 | + | 21.3967i | −0.438820 | + | 1.35055i | 0.450301 | + | 0.892877i | \(0.351317\pi\) |
−0.889121 | + | 0.457672i | \(0.848683\pi\) | |||||||
\(252\) | 1.76673 | 0.111294 | ||||||||
\(253\) | −5.93105 | + | 5.86463i | −0.372882 | + | 0.368706i | ||||
\(254\) | 10.7426 | 0.674049 | ||||||||
\(255\) | −3.87135 | + | 11.9148i | −0.242434 | + | 0.746134i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 20.1808 | + | 14.6622i | 1.25884 | + | 0.914604i | 0.998700 | − | 0.0509660i | \(-0.0162300\pi\) |
0.260144 | + | 0.965570i | \(0.416230\pi\) | |||||||
\(258\) | 1.47621 | + | 4.54330i | 0.0919046 | + | 0.282853i | ||||
\(259\) | −1.43113 | − | 4.40458i | −0.0889263 | − | 0.273687i | ||||
\(260\) | −2.04894 | − | 1.48864i | −0.127070 | − | 0.0923217i | ||||
\(261\) | 12.3207 | − | 8.95152i | 0.762633 | − | 0.554085i | ||||
\(262\) | 5.26012 | − | 16.1890i | 0.324971 | − | 1.00016i | ||||
\(263\) | 6.25594 | 0.385758 | 0.192879 | − | 0.981223i | \(-0.438218\pi\) | ||||
0.192879 | + | 0.981223i | \(0.438218\pi\) | |||||||
\(264\) | 3.25103 | + | 6.47031i | 0.200087 | + | 0.398220i | ||||
\(265\) | −4.01746 | −0.246791 | ||||||||
\(266\) | 0.692383 | − | 2.13094i | 0.0424527 | − | 0.130656i | ||||
\(267\) | 4.68775 | − | 3.40585i | 0.286886 | − | 0.208435i | ||||
\(268\) | −3.12469 | − | 2.27022i | −0.190871 | − | 0.138676i | ||||
\(269\) | −4.03802 | − | 12.4277i | −0.246202 | − | 0.757733i | −0.995436 | − | 0.0954274i | \(-0.969578\pi\) |
0.749234 | − | 0.662305i | \(-0.230422\pi\) | |||||||
\(270\) | 0.832051 | + | 2.56079i | 0.0506370 | + | 0.155845i | ||||
\(271\) | 19.6718 | + | 14.2924i | 1.19498 | + | 0.868200i | 0.993781 | − | 0.111351i | \(-0.0355178\pi\) |
0.201194 | + | 0.979551i | \(0.435518\pi\) | |||||||
\(272\) | 4.64224 | − | 3.37279i | 0.281477 | − | 0.204505i | ||||
\(273\) | 1.70869 | − | 5.25882i | 0.103415 | − | 0.318278i | ||||
\(274\) | 12.4777 | 0.753803 | ||||||||
\(275\) | −0.537270 | + | 3.27282i | −0.0323986 | + | 0.197358i | ||||
\(276\) | −5.49071 | −0.330502 | ||||||||
\(277\) | −4.14375 | + | 12.7531i | −0.248974 | + | 0.766262i | 0.745984 | + | 0.665964i | \(0.231980\pi\) |
−0.994957 | + | 0.100298i | \(0.968020\pi\) | |||||||
\(278\) | 14.0617 | − | 10.2164i | 0.843366 | − | 0.612741i | ||||
\(279\) | −2.63122 | − | 1.91169i | −0.157527 | − | 0.114450i | ||||
\(280\) | −0.309017 | − | 0.951057i | −0.0184673 | − | 0.0568365i | ||||
\(281\) | 3.93682 | + | 12.1163i | 0.234851 | + | 0.722797i | 0.997141 | + | 0.0755613i | \(0.0240749\pi\) |
−0.762290 | + | 0.647235i | \(0.775925\pi\) | |||||||
\(282\) | 5.69605 | + | 4.13842i | 0.339195 | + | 0.246439i | ||||
\(283\) | 11.1236 | − | 8.08177i | 0.661230 | − | 0.480412i | −0.205848 | − | 0.978584i | \(-0.565995\pi\) |
0.867078 | + | 0.498172i | \(0.165995\pi\) | |||||||
\(284\) | −2.95270 | + | 9.08747i | −0.175210 | + | 0.539242i | ||||
\(285\) | −4.89187 | −0.289769 | ||||||||
\(286\) | 8.30363 | − | 1.26728i | 0.491004 | − | 0.0749360i | ||||
\(287\) | −10.5523 | −0.622885 | ||||||||
\(288\) | −0.545950 | + | 1.68026i | −0.0321704 | + | 0.0990104i | ||||
\(289\) | −12.8845 | + | 9.36112i | −0.757910 | + | 0.550654i | ||||
\(290\) | −6.97373 | − | 5.06671i | −0.409511 | − | 0.297527i | ||||
\(291\) | 11.1352 | + | 34.2705i | 0.652754 | + | 2.00897i | ||||
\(292\) | −3.53078 | − | 10.8666i | −0.206623 | − | 0.635921i | ||||
\(293\) | −13.4601 | − | 9.77936i | −0.786350 | − | 0.571316i | 0.120528 | − | 0.992710i | \(-0.461541\pi\) |
−0.906878 | + | 0.421393i | \(0.861541\pi\) | |||||||
\(294\) | 1.76631 | − | 1.28330i | 0.103014 | − | 0.0748437i | ||||
\(295\) | 0.622375 | − | 1.91547i | 0.0362361 | − | 0.111523i | ||||
\(296\) | 4.63124 | 0.269186 | ||||||||
\(297\) | −7.93396 | − | 4.09899i | −0.460375 | − | 0.237847i | ||||
\(298\) | 1.49206 | 0.0864329 | ||||||||
\(299\) | −1.96821 | + | 6.05754i | −0.113825 | + | 0.350317i | ||||
\(300\) | −1.76631 | + | 1.28330i | −0.101978 | + | 0.0740915i | ||||
\(301\) | 1.77016 | + | 1.28609i | 0.102030 | + | 0.0741293i | ||||
\(302\) | 2.47076 | + | 7.60422i | 0.142176 | + | 0.437574i | ||||
\(303\) | 10.8270 | + | 33.3221i | 0.621996 | + | 1.91431i | ||||
\(304\) | 1.81268 | + | 1.31699i | 0.103965 | + | 0.0755346i | ||||
\(305\) | 0.217007 | − | 0.157665i | 0.0124258 | − | 0.00902785i | ||||
\(306\) | 3.13273 | − | 9.64156i | 0.179086 | − | 0.551171i | ||||
\(307\) | 5.56226 | 0.317455 | 0.158728 | − | 0.987322i | \(-0.449261\pi\) | ||||
0.158728 | + | 0.987322i | \(0.449261\pi\) | |||||||
\(308\) | 2.94661 | + | 1.52233i | 0.167899 | + | 0.0867428i | ||||
\(309\) | −28.1707 | −1.60258 | ||||||||
\(310\) | −0.568867 | + | 1.75079i | −0.0323095 | + | 0.0994383i | ||||
\(311\) | −14.4959 | + | 10.5319i | −0.821985 | + | 0.597207i | −0.917280 | − | 0.398242i | \(-0.869620\pi\) |
0.0952956 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(312\) | 4.47342 | + | 3.25013i | 0.253258 | + | 0.184002i | ||||
\(313\) | 1.59291 | + | 4.90249i | 0.0900368 | + | 0.277105i | 0.985928 | − | 0.167168i | \(-0.0534622\pi\) |
−0.895892 | + | 0.444273i | \(0.853462\pi\) | |||||||
\(314\) | −0.634019 | − | 1.95131i | −0.0357798 | − | 0.110119i | ||||
\(315\) | −1.42932 | − | 1.03846i | −0.0805329 | − | 0.0585106i | ||||
\(316\) | 9.50873 | − | 6.90850i | 0.534908 | − | 0.388633i | ||||
\(317\) | 8.79505 | − | 27.0684i | 0.493979 | − | 1.52031i | −0.324563 | − | 0.945864i | \(-0.605217\pi\) |
0.818542 | − | 0.574447i | \(-0.194783\pi\) | |||||||
\(318\) | 8.77126 | 0.491868 | ||||||||
\(319\) | 28.2621 | − | 4.31330i | 1.58237 | − | 0.241498i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.55112 | + | 14.0069i | −0.254019 | + | 0.781789i | ||||
\(322\) | −2.03459 | + | 1.47821i | −0.113383 | + | 0.0823776i | ||||
\(323\) | −10.4014 | − | 7.55706i | −0.578750 | − | 0.420486i | ||||
\(324\) | −3.45446 | − | 10.6317i | −0.191914 | − | 0.590651i | ||||
\(325\) | 0.782625 | + | 2.40867i | 0.0434122 | + | 0.133609i | ||||
\(326\) | 16.7447 | + | 12.1657i | 0.927402 | + | 0.673797i | ||||
\(327\) | −33.0060 | + | 23.9803i | −1.82524 | + | 1.32611i | ||||
\(328\) | 3.26085 | − | 10.0359i | 0.180050 | − | 0.554138i | ||||
\(329\) | 3.22482 | 0.177790 | ||||||||
\(330\) | 1.17301 | − | 7.14549i | 0.0645723 | − | 0.393347i | ||||
\(331\) | −24.8572 | −1.36627 | −0.683136 | − | 0.730291i | \(-0.739385\pi\) | ||||
−0.683136 | + | 0.730291i | \(0.739385\pi\) | |||||||
\(332\) | −2.27081 | + | 6.98885i | −0.124627 | + | 0.383563i | ||||
\(333\) | 6.61952 | − | 4.80936i | 0.362747 | − | 0.263551i | ||||
\(334\) | 1.06831 | + | 0.776171i | 0.0584552 | + | 0.0424702i | ||||
\(335\) | 1.19353 | + | 3.67329i | 0.0652092 | + | 0.200693i | ||||
\(336\) | 0.674672 | + | 2.07643i | 0.0368064 | + | 0.113278i | ||||
\(337\) | 12.6590 | + | 9.19732i | 0.689581 | + | 0.501010i | 0.876522 | − | 0.481361i | \(-0.159858\pi\) |
−0.186942 | + | 0.982371i | \(0.559858\pi\) | |||||||
\(338\) | −5.32802 | + | 3.87103i | −0.289806 | + | 0.210556i | ||||
\(339\) | 5.10345 | − | 15.7068i | 0.277181 | − | 0.853076i | ||||
\(340\) | −5.73813 | −0.311194 | ||||||||
\(341\) | −2.74119 | − | 5.45560i | −0.148444 | − | 0.295437i | ||||
\(342\) | 3.95854 | 0.214053 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | −1.77016 | + | 1.28609i | −0.0954405 | + | 0.0693416i | ||||
\(345\) | 4.44208 | + | 3.22736i | 0.239154 | + | 0.173755i | ||||
\(346\) | −4.85245 | − | 14.9343i | −0.260869 | − | 0.802873i | ||||
\(347\) | 4.53162 | + | 13.9469i | 0.243270 | + | 0.748709i | 0.995916 | + | 0.0902833i | \(0.0287773\pi\) |
−0.752646 | + | 0.658426i | \(0.771223\pi\) | |||||||
\(348\) | 15.2256 | + | 11.0621i | 0.816179 | + | 0.592989i | ||||
\(349\) | −21.8243 | + | 15.8563i | −1.16823 | + | 0.848767i | −0.990796 | − | 0.135367i | \(-0.956779\pi\) |
−0.177431 | + | 0.984133i | \(0.556779\pi\) | |||||||
\(350\) | −0.309017 | + | 0.951057i | −0.0165177 | + | 0.0508361i | ||||
\(351\) | −6.81929 | −0.363987 | ||||||||
\(352\) | −2.35838 | + | 2.33197i | −0.125702 | + | 0.124294i | ||||
\(353\) | 4.77463 | 0.254128 | 0.127064 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(354\) | −1.35882 | + | 4.18202i | −0.0722205 | + | 0.222272i | ||||
\(355\) | 7.73027 | − | 5.61637i | 0.410280 | − | 0.298086i | ||||
\(356\) | 2.14711 | + | 1.55997i | 0.113797 | + | 0.0826780i | ||||
\(357\) | −3.87135 | − | 11.9148i | −0.204894 | − | 0.630598i | ||||
\(358\) | −1.43846 | − | 4.42714i | −0.0760252 | − | 0.233982i | ||||
\(359\) | −27.5860 | − | 20.0424i | −1.45593 | − | 1.05780i | −0.984399 | − | 0.175950i | \(-0.943700\pi\) |
−0.471534 | − | 0.881848i | \(-0.656300\pi\) | |||||||
\(360\) | 1.42932 | − | 1.03846i | 0.0753316 | − | 0.0547316i | ||||
\(361\) | −4.31997 | + | 13.2955i | −0.227367 | + | 0.699763i | ||||
\(362\) | 5.90450 | 0.310334 | ||||||||
\(363\) | 13.8966 | + | 19.5872i | 0.729385 | + | 1.02806i | ||||
\(364\) | 2.53263 | 0.132746 | ||||||||
\(365\) | −3.53078 | + | 10.8666i | −0.184810 | + | 0.568785i | ||||
\(366\) | −0.473787 | + | 0.344227i | −0.0247653 | + | 0.0179930i | ||||
\(367\) | 8.08180 | + | 5.87177i | 0.421866 | + | 0.306504i | 0.778388 | − | 0.627783i | \(-0.216038\pi\) |
−0.356522 | + | 0.934287i | \(0.616038\pi\) | |||||||
\(368\) | −0.777143 | − | 2.39180i | −0.0405114 | − | 0.124681i | ||||
\(369\) | −5.76105 | − | 17.7307i | −0.299908 | − | 0.923023i | ||||
\(370\) | −3.74676 | − | 2.72218i | −0.194785 | − | 0.141519i | ||||
\(371\) | 3.25019 | − | 2.36140i | 0.168742 | − | 0.122598i | ||||
\(372\) | 1.24200 | − | 3.82248i | 0.0643946 | − | 0.198186i | ||||
\(373\) | −0.510916 | −0.0264542 | −0.0132271 | − | 0.999913i | \(-0.504210\pi\) | ||||
−0.0132271 | + | 0.999913i | \(0.504210\pi\) | |||||||
\(374\) | 13.5327 | − | 13.3811i | 0.699757 | − | 0.691921i | ||||
\(375\) | 2.18328 | 0.112744 | ||||||||
\(376\) | −0.996525 | + | 3.06699i | −0.0513918 | + | 0.158168i | ||||
\(377\) | 17.6619 | − | 12.8321i | 0.909632 | − | 0.660886i | ||||
\(378\) | −2.17834 | − | 1.58266i | −0.112042 | − | 0.0814030i | ||||
\(379\) | 1.64204 | + | 5.05369i | 0.0843460 | + | 0.259590i | 0.984331 | − | 0.176330i | \(-0.0564227\pi\) |
−0.899985 | + | 0.435921i | \(0.856423\pi\) | |||||||
\(380\) | −0.692383 | − | 2.13094i | −0.0355185 | − | 0.109315i | ||||
\(381\) | 18.9748 | + | 13.7860i | 0.972106 | + | 0.706277i | ||||
\(382\) | −4.80071 | + | 3.48792i | −0.245626 | + | 0.178458i | ||||
\(383\) | 7.26815 | − | 22.3691i | 0.371385 | − | 1.14301i | −0.574500 | − | 0.818505i | \(-0.694803\pi\) |
0.945885 | − | 0.324502i | \(-0.105197\pi\) | |||||||
\(384\) | −2.18328 | −0.111415 | ||||||||
\(385\) | −1.48905 | − | 2.96357i | −0.0758892 | − | 0.151037i | ||||
\(386\) | −10.8377 | −0.551623 | ||||||||
\(387\) | −1.19456 | + | 3.67647i | −0.0607228 | + | 0.186886i | ||||
\(388\) | −13.3525 | + | 9.70112i | −0.677868 | + | 0.492500i | ||||
\(389\) | −7.42999 | − | 5.39820i | −0.376715 | − | 0.273700i | 0.383275 | − | 0.923634i | \(-0.374796\pi\) |
−0.759990 | + | 0.649935i | \(0.774796\pi\) | |||||||
\(390\) | −1.70869 | − | 5.25882i | −0.0865231 | − | 0.266291i | ||||
\(391\) | 4.45934 | + | 13.7244i | 0.225519 | + | 0.694075i | ||||
\(392\) | 0.809017 | + | 0.587785i | 0.0408615 | + | 0.0296876i | ||||
\(393\) | 30.0664 | − | 21.8445i | 1.51665 | − | 1.10191i | ||||
\(394\) | −3.71363 | + | 11.4294i | −0.187090 | + | 0.575804i | ||||
\(395\) | −11.7534 | −0.591380 | ||||||||
\(396\) | −0.949212 | + | 5.78220i | −0.0476997 | + | 0.290566i | ||||
\(397\) | −31.5709 | −1.58450 | −0.792248 | − | 0.610199i | \(-0.791089\pi\) | ||||
−0.792248 | + | 0.610199i | \(0.791089\pi\) | |||||||
\(398\) | −5.68634 | + | 17.5008i | −0.285031 | + | 0.877234i | ||||
\(399\) | 3.95760 | − | 2.87537i | 0.198128 | − | 0.143948i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | −3.30043 | − | 10.1577i | −0.164816 | − | 0.507250i | 0.834207 | − | 0.551451i | \(-0.185926\pi\) |
−0.999023 | + | 0.0442012i | \(0.985926\pi\) | |||||||
\(402\) | −2.60581 | − | 8.01984i | −0.129966 | − | 0.399993i | ||||
\(403\) | −3.77188 | − | 2.74043i | −0.187891 | − | 0.136510i | ||||
\(404\) | −12.9830 | + | 9.43267i | −0.645926 | + | 0.469293i | ||||
\(405\) | −3.45446 | + | 10.6317i | −0.171653 | + | 0.528294i | ||||
\(406\) | 8.62000 | 0.427803 | ||||||||
\(407\) | 15.1843 | − | 2.31739i | 0.752657 | − | 0.114869i | ||||
\(408\) | 12.5280 | 0.620227 | ||||||||
\(409\) | −7.28568 | + | 22.4230i | −0.360254 | + | 1.10875i | 0.592647 | + | 0.805463i | \(0.298083\pi\) |
−0.952900 | + | 0.303284i | \(0.901917\pi\) | |||||||
\(410\) | −8.53702 | + | 6.20251i | −0.421613 | + | 0.306320i | ||||
\(411\) | 22.0395 | + | 16.0126i | 1.08713 | + | 0.789844i | ||||
\(412\) | −3.98721 | − | 12.2714i | −0.196436 | − | 0.604568i | ||||
\(413\) | 0.622375 | + | 1.91547i | 0.0306251 | + | 0.0942542i | ||||
\(414\) | −3.59457 | − | 2.61161i | −0.176663 | − | 0.128354i | ||||
\(415\) | 5.94507 | − | 4.31934i | 0.291832 | − | 0.212028i | ||||
\(416\) | −0.782625 | + | 2.40867i | −0.0383714 | + | 0.118095i | ||||
\(417\) | 37.9482 | 1.85833 | ||||||||
\(418\) | 6.60217 | + | 3.41093i | 0.322923 | + | 0.166834i | ||||
\(419\) | −15.9235 | −0.777915 | −0.388958 | − | 0.921256i | \(-0.627165\pi\) | ||||
−0.388958 | + | 0.921256i | \(0.627165\pi\) | |||||||
\(420\) | 0.674672 | − | 2.07643i | 0.0329206 | − | 0.101319i | ||||
\(421\) | 32.2476 | − | 23.4292i | 1.57165 | − | 1.14187i | 0.646096 | − | 0.763256i | \(-0.276401\pi\) |
0.925554 | − | 0.378615i | \(-0.123599\pi\) | |||||||
\(422\) | 16.2145 | + | 11.7805i | 0.789307 | + | 0.573465i | ||||
\(423\) | 1.76059 | + | 5.41855i | 0.0856029 | + | 0.263459i | ||||
\(424\) | 1.24146 | + | 3.82083i | 0.0602908 | + | 0.185556i | ||||
\(425\) | 4.64224 | + | 3.37279i | 0.225182 | + | 0.163604i | ||||
\(426\) | −16.8774 | + | 12.2621i | −0.817712 | + | 0.594102i | ||||
\(427\) | −0.0828892 | + | 0.255107i | −0.00401129 | + | 0.0123455i | ||||
\(428\) | −6.74567 | −0.326064 | ||||||||
\(429\) | 16.2931 | + | 8.41765i | 0.786640 | + | 0.406408i | ||||
\(430\) | 2.18804 | 0.105516 | ||||||||
\(431\) | −5.43589 | + | 16.7300i | −0.261838 | + | 0.805854i | 0.730567 | + | 0.682841i | \(0.239256\pi\) |
−0.992405 | + | 0.123013i | \(0.960744\pi\) | |||||||
\(432\) | 2.17834 | − | 1.58266i | 0.104805 | − | 0.0761455i | ||||
\(433\) | −16.6207 | − | 12.0756i | −0.798739 | − | 0.580318i | 0.111805 | − | 0.993730i | \(-0.464337\pi\) |
−0.910544 | + | 0.413412i | \(0.864337\pi\) | |||||||
\(434\) | −0.568867 | − | 1.75079i | −0.0273065 | − | 0.0840407i | ||||
\(435\) | −5.81567 | − | 17.8988i | −0.278840 | − | 0.858182i | ||||
\(436\) | −15.1176 | − | 10.9836i | −0.724002 | − | 0.526018i | ||||
\(437\) | −4.55869 | + | 3.31208i | −0.218072 | + | 0.158438i | ||||
\(438\) | 7.70870 | − | 23.7249i | 0.368336 | − | 1.13362i | ||||
\(439\) | 22.4200 | 1.07005 | 0.535023 | − | 0.844837i | \(-0.320303\pi\) | ||||
0.535023 | + | 0.844837i | \(0.320303\pi\) | |||||||
\(440\) | 3.27866 | − | 0.500382i | 0.156304 | − | 0.0238548i | ||||
\(441\) | 1.76673 | 0.0841301 | ||||||||
\(442\) | 4.49080 | − | 13.8213i | 0.213606 | − | 0.657411i | ||||
\(443\) | −6.17697 | + | 4.48783i | −0.293477 | + | 0.213223i | −0.724774 | − | 0.688986i | \(-0.758056\pi\) |
0.431297 | + | 0.902210i | \(0.358056\pi\) | |||||||
\(444\) | 8.18023 | + | 5.94329i | 0.388217 | + | 0.282056i | ||||
\(445\) | −0.820123 | − | 2.52408i | −0.0388775 | − | 0.119653i | ||||
\(446\) | −3.64639 | − | 11.2224i | −0.172662 | − | 0.531398i | ||||
\(447\) | 2.63545 | + | 1.91477i | 0.124653 | + | 0.0905655i | ||||
\(448\) | −0.809017 | + | 0.587785i | −0.0382225 | + | 0.0277702i | ||||
\(449\) | −0.201624 | + | 0.620536i | −0.00951524 | + | 0.0292849i | −0.955701 | − | 0.294338i | \(-0.904901\pi\) |
0.946186 | + | 0.323623i | \(0.104901\pi\) | |||||||
\(450\) | −1.76673 | −0.0832846 | ||||||||
\(451\) | 5.66945 | − | 34.5359i | 0.266964 | − | 1.62623i | ||||
\(452\) | 7.56433 | 0.355796 | ||||||||
\(453\) | −5.39437 | + | 16.6022i | −0.253450 | + | 0.780038i | ||||
\(454\) | 0.801025 | − | 0.581979i | 0.0375940 | − | 0.0273136i | ||||
\(455\) | −2.04894 | − | 1.48864i | −0.0960558 | − | 0.0697886i | ||||
\(456\) | 1.51167 | + | 4.65244i | 0.0707904 | + | 0.217871i | ||||
\(457\) | 9.44637 | + | 29.0729i | 0.441882 | + | 1.35997i | 0.885867 | + | 0.463940i | \(0.153565\pi\) |
−0.443984 | + | 0.896035i | \(0.646435\pi\) | |||||||
\(458\) | 14.8502 | + | 10.7893i | 0.693905 | + | 0.504152i | ||||
\(459\) | −12.4996 | + | 9.08147i | −0.583430 | + | 0.423887i | ||||
\(460\) | −0.777143 | + | 2.39180i | −0.0362345 | + | 0.111518i | ||||
\(461\) | −3.55735 | −0.165682 | −0.0828412 | − | 0.996563i | \(-0.526399\pi\) | ||||
−0.0828412 | + | 0.996563i | \(0.526399\pi\) | |||||||
\(462\) | 3.25103 | + | 6.47031i | 0.151252 | + | 0.301026i | ||||
\(463\) | 6.57677 | 0.305648 | 0.152824 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152824 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(464\) | −2.66373 | + | 8.19811i | −0.123660 | + | 0.380588i | ||||
\(465\) | −3.25159 | + | 2.36242i | −0.150789 | + | 0.109555i | ||||
\(466\) | −14.0486 | − | 10.2069i | −0.650787 | − | 0.472825i | ||||
\(467\) | −5.68391 | − | 17.4933i | −0.263020 | − | 0.809492i | −0.992143 | − | 0.125109i | \(-0.960072\pi\) |
0.729123 | − | 0.684383i | \(-0.239928\pi\) | |||||||
\(468\) | 1.38269 | + | 4.25548i | 0.0639149 | + | 0.196710i | ||||
\(469\) | −3.12469 | − | 2.27022i | −0.144285 | − | 0.104829i | ||||
\(470\) | 2.60894 | − | 1.89550i | 0.120341 | − | 0.0874330i | ||||
\(471\) | 1.38424 | − | 4.26026i | 0.0637826 | − | 0.196303i | ||||
\(472\) | −2.01405 | −0.0927040 | ||||||||
\(473\) | −5.16021 | + | 5.10242i | −0.237267 | + | 0.234610i | ||||
\(474\) | 25.6611 | 1.17865 | ||||||||
\(475\) | −0.692383 | + | 2.13094i | −0.0317687 | + | 0.0977741i | ||||
\(476\) | 4.64224 | − | 3.37279i | 0.212777 | − | 0.154591i | ||||
\(477\) | 5.74222 | + | 4.17197i | 0.262918 | + | 0.191021i | ||||
\(478\) | −2.75678 | − | 8.48450i | −0.126092 | − | 0.388072i | ||||
\(479\) | 10.2288 | + | 31.4810i | 0.467366 | + | 1.43840i | 0.855983 | + | 0.517004i | \(0.172953\pi\) |
−0.388617 | + | 0.921399i | \(0.627047\pi\) | |||||||
\(480\) | 1.76631 | + | 1.28330i | 0.0806209 | + | 0.0585745i | ||||
\(481\) | 9.48914 | − | 6.89427i | 0.432668 | − | 0.314351i | ||||
\(482\) | 0.277094 | − | 0.852808i | 0.0126213 | − | 0.0388444i | ||||
\(483\) | −5.49071 | −0.249836 | ||||||||
\(484\) | −6.56544 | + | 8.82582i | −0.298429 | + | 0.401173i | ||||
\(485\) | 16.5045 | 0.749432 | ||||||||
\(486\) | 5.04591 | − | 15.5297i | 0.228887 | − | 0.704442i | ||||
\(487\) | 12.6192 | − | 9.16836i | 0.571829 | − | 0.415458i | −0.263940 | − | 0.964539i | \(-0.585022\pi\) |
0.835769 | + | 0.549081i | \(0.185022\pi\) | |||||||
\(488\) | −0.217007 | − | 0.157665i | −0.00982343 | − | 0.00713714i | ||||
\(489\) | 13.9641 | + | 42.9770i | 0.631477 | + | 1.94349i | ||||
\(490\) | −0.309017 | − | 0.951057i | −0.0139600 | − | 0.0429644i | ||||
\(491\) | 33.7066 | + | 24.4893i | 1.52116 | + | 1.10519i | 0.960910 | + | 0.276860i | \(0.0892938\pi\) |
0.560247 | + | 0.828326i | \(0.310706\pi\) | |||||||
\(492\) | 18.6387 | − | 13.5418i | 0.840299 | − | 0.610513i | ||||
\(493\) | 15.2848 | − | 47.0418i | 0.688393 | − | 2.11865i | ||||
\(494\) | 5.67461 | 0.255313 | ||||||||
\(495\) | 4.16662 | − | 4.11996i | 0.187276 | − | 0.185178i | ||||
\(496\) | 1.84089 | 0.0826585 | ||||||||
\(497\) | −2.95270 | + | 9.08747i | −0.132447 | + | 0.407629i | ||||
\(498\) | −12.9798 | + | 9.43036i | −0.581638 | + | 0.422585i | ||||
\(499\) | 1.98298 | + | 1.44072i | 0.0887703 | + | 0.0644954i | 0.631285 | − | 0.775551i | \(-0.282528\pi\) |
−0.542515 | + | 0.840046i | \(0.682528\pi\) | |||||||
\(500\) | 0.309017 | + | 0.951057i | 0.0138197 | + | 0.0425325i | ||||
\(501\) | 0.890905 | + | 2.74193i | 0.0398027 | + | 0.122500i | ||||
\(502\) | −18.2011 | − | 13.2239i | −0.812357 | − | 0.590212i | ||||
\(503\) | 5.41115 | − | 3.93143i | 0.241271 | − | 0.175294i | −0.460578 | − | 0.887619i | \(-0.652358\pi\) |
0.701849 | + | 0.712325i | \(0.252358\pi\) | |||||||
\(504\) | −0.545950 | + | 1.68026i | −0.0243186 | + | 0.0748448i | ||||
\(505\) | 16.0478 | 0.714118 | ||||||||
\(506\) | −3.74480 | − | 7.45303i | −0.166477 | − | 0.331328i | ||||
\(507\) | −14.3787 | −0.638579 | ||||||||
\(508\) | −3.31964 | + | 10.2168i | −0.147285 | + | 0.453297i | ||||
\(509\) | 11.3879 | − | 8.27379i | 0.504760 | − | 0.366729i | −0.306072 | − | 0.952008i | \(-0.599015\pi\) |
0.810832 | + | 0.585279i | \(0.199015\pi\) | |||||||
\(510\) | −10.1353 | − | 7.36375i | −0.448800 | − | 0.326072i | ||||
\(511\) | −3.53078 | − | 10.8666i | −0.156193 | − | 0.480711i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | −4.88078 | − | 3.54610i | −0.215492 | − | 0.156564i | ||||
\(514\) | −20.1808 | + | 14.6622i | −0.890137 | + | 0.646723i | ||||
\(515\) | −3.98721 | + | 12.2714i | −0.175698 | + | 0.540742i | ||||
\(516\) | −4.77710 | −0.210300 | ||||||||
\(517\) | −1.73260 | + | 10.5543i | −0.0761997 | + | 0.464176i | ||||
\(518\) | 4.63124 | 0.203485 | ||||||||
\(519\) | 10.5943 | − | 32.6058i | 0.465037 | − | 1.43124i | ||||
\(520\) | 2.04894 | − | 1.48864i | 0.0898520 | − | 0.0652813i | ||||
\(521\) | −33.7351 | − | 24.5100i | −1.47796 | − | 1.07380i | −0.978206 | − | 0.207638i | \(-0.933423\pi\) |
−0.499757 | − | 0.866166i | \(-0.666577\pi\) | |||||||
\(522\) | 4.70609 | + | 14.4839i | 0.205980 | + | 0.633941i | ||||
\(523\) | 3.30524 | + | 10.1725i | 0.144528 | + | 0.444812i | 0.996950 | − | 0.0780428i | \(-0.0248671\pi\) |
−0.852422 | + | 0.522855i | \(0.824867\pi\) | |||||||
\(524\) | 13.7712 | + | 10.0053i | 0.601596 | + | 0.437085i | ||||
\(525\) | −1.76631 | + | 1.28330i | −0.0770883 | + | 0.0560079i | ||||
\(526\) | −1.93319 | + | 5.94975i | −0.0842911 | + | 0.259421i | ||||
\(527\) | −10.5633 | −0.460143 | ||||||||
\(528\) | −7.15825 | + | 1.09248i | −0.311523 | + | 0.0475440i | ||||
\(529\) | −16.6753 | −0.725015 | ||||||||
\(530\) | 1.24146 | − | 3.82083i | 0.0539257 | − | 0.165966i | ||||
\(531\) | −2.87871 | + | 2.09151i | −0.124925 | + | 0.0907636i | ||||
\(532\) | 1.81268 | + | 1.31699i | 0.0785898 | + | 0.0570988i | ||||
\(533\) | −8.25853 | − | 25.4171i | −0.357716 | − | 1.10094i | ||||
\(534\) | 1.79056 | + | 5.51078i | 0.0774852 | + | 0.238475i | ||||
\(535\) | 5.45736 | + | 3.96501i | 0.235942 | + | 0.171422i | ||||
\(536\) | 3.12469 | − | 2.27022i | 0.134966 | − | 0.0980586i | ||||
\(537\) | 3.14058 | − | 9.66570i | 0.135526 | − | 0.417106i | ||||
\(538\) | 13.0673 | 0.563371 | ||||||||
\(539\) | 2.94661 | + | 1.52233i | 0.126919 | + | 0.0655714i | ||||
\(540\) | −2.69257 | −0.115870 | ||||||||
\(541\) | 2.98174 | − | 9.17684i | 0.128195 | − | 0.394543i | −0.866275 | − | 0.499568i | \(-0.833492\pi\) |
0.994470 | + | 0.105025i | \(0.0334921\pi\) | |||||||
\(542\) | −19.6718 | + | 14.2924i | −0.844975 | + | 0.613910i | ||||
\(543\) | 10.4292 | + | 7.57727i | 0.447560 | + | 0.325172i | ||||
\(544\) | 1.77318 | + | 5.45728i | 0.0760244 | + | 0.233979i | ||||
\(545\) | 5.77441 | + | 17.7718i | 0.247349 | + | 0.761261i | ||||
\(546\) | 4.47342 | + | 3.25013i | 0.191445 | + | 0.139093i | ||||
\(547\) | −12.0176 | + | 8.73126i | −0.513834 | + | 0.373322i | −0.814276 | − | 0.580478i | \(-0.802866\pi\) |
0.300442 | + | 0.953800i | \(0.402866\pi\) | |||||||
\(548\) | −3.85581 | + | 11.8670i | −0.164712 | + | 0.506931i | ||||
\(549\) | −0.473900 | −0.0202255 | ||||||||
\(550\) | −2.94661 | − | 1.52233i | −0.125644 | − | 0.0649124i | ||||
\(551\) | 19.3140 | 0.822803 | ||||||||
\(552\) | 1.69672 | − | 5.22198i | 0.0722174 | − | 0.222262i | ||||
\(553\) | 9.50873 | − | 6.90850i | 0.404352 | − | 0.293779i | ||||
\(554\) | −10.8485 | − | 7.88188i | −0.460907 | − | 0.334869i | ||||
\(555\) | −3.12457 | − | 9.61644i | −0.132631 | − | 0.408195i | ||||
\(556\) | 5.37110 | + | 16.5305i | 0.227785 | + | 0.701051i | ||||
\(557\) | −32.3080 | − | 23.4732i | −1.36893 | − | 0.994589i | −0.997819 | − | 0.0660025i | \(-0.978975\pi\) |
−0.371115 | − | 0.928587i | \(-0.621025\pi\) | |||||||
\(558\) | 2.63122 | − | 1.91169i | 0.111388 | − | 0.0809283i | ||||
\(559\) | −1.71241 | + | 5.27026i | −0.0724273 | + | 0.222908i | ||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 41.0749 | − | 6.26877i | 1.73419 | − | 0.264668i | ||||
\(562\) | −12.7398 | −0.537396 | ||||||||
\(563\) | 1.25587 | − | 3.86518i | 0.0529287 | − | 0.162898i | −0.921098 | − | 0.389331i | \(-0.872706\pi\) |
0.974027 | + | 0.226433i | \(0.0727064\pi\) | |||||||
\(564\) | −5.69605 | + | 4.13842i | −0.239847 | + | 0.174259i | ||||
\(565\) | −6.11968 | − | 4.44620i | −0.257457 | − | 0.187053i | ||||
\(566\) | 4.24884 | + | 13.0766i | 0.178592 | + | 0.549650i | ||||
\(567\) | −3.45446 | − | 10.6317i | −0.145074 | − | 0.446490i | ||||
\(568\) | −7.73027 | − | 5.61637i | −0.324355 | − | 0.235658i | ||||
\(569\) | −25.8072 | + | 18.7500i | −1.08189 | + | 0.786041i | −0.978012 | − | 0.208548i | \(-0.933126\pi\) |
−0.103881 | + | 0.994590i | \(0.533126\pi\) | |||||||
\(570\) | 1.51167 | − | 4.65244i | 0.0633169 | − | 0.194869i | ||||
\(571\) | 20.3883 | 0.853222 | 0.426611 | − | 0.904435i | \(-0.359707\pi\) | ||||
0.426611 | + | 0.904435i | \(0.359707\pi\) | |||||||
\(572\) | −1.36071 | + | 8.28884i | −0.0568940 | + | 0.346574i | ||||
\(573\) | −12.9556 | −0.541229 | ||||||||
\(574\) | 3.26085 | − | 10.0359i | 0.136105 | − | 0.418889i | ||||
\(575\) | 2.03459 | − | 1.47821i | 0.0848481 | − | 0.0616458i | ||||
\(576\) | −1.42932 | − | 1.03846i | −0.0595549 | − | 0.0432691i | ||||
\(577\) | −8.04835 | − | 24.7703i | −0.335057 | − | 1.03120i | −0.966694 | − | 0.255936i | \(-0.917617\pi\) |
0.631637 | − | 0.775265i | \(-0.282383\pi\) | |||||||
\(578\) | −4.92143 | − | 15.1466i | −0.204705 | − | 0.630016i | ||||
\(579\) | −19.1427 | − | 13.9080i | −0.795545 | − | 0.577997i | ||||
\(580\) | 6.97373 | − | 5.06671i | 0.289568 | − | 0.210384i | ||||
\(581\) | −2.27081 | + | 6.98885i | −0.0942092 | + | 0.289946i | ||||
\(582\) | −36.0341 | −1.49366 | ||||||||
\(583\) | 5.98222 | + | 11.9060i | 0.247758 | + | 0.493096i | ||||
\(584\) | 11.4258 | 0.472805 | ||||||||
\(585\) | 1.38269 | − | 4.25548i | 0.0571672 | − | 0.175943i | ||||
\(586\) | 13.4601 | − | 9.77936i | 0.556033 | − | 0.403982i | ||||
\(587\) | 31.5393 | + | 22.9146i | 1.30177 | + | 0.945788i | 0.999971 | − | 0.00758441i | \(-0.00241422\pi\) |
0.301795 | + | 0.953373i | \(0.402414\pi\) | |||||||
\(588\) | 0.674672 | + | 2.07643i | 0.0278230 | + | 0.0856304i | ||||
\(589\) | −1.27460 | − | 3.92282i | −0.0525191 | − | 0.161637i | ||||
\(590\) | 1.62940 | + | 1.18383i | 0.0670813 | + | 0.0487374i | ||||
\(591\) | −21.2268 | + | 15.4222i | −0.873153 | + | 0.634383i | ||||
\(592\) | −1.43113 | + | 4.40458i | −0.0588192 | + | 0.181027i | ||||
\(593\) | −0.526179 | −0.0216076 | −0.0108038 | − | 0.999942i | \(-0.503439\pi\) | ||||
−0.0108038 | + | 0.999942i | \(0.503439\pi\) | |||||||
\(594\) | 6.35010 | − | 6.27899i | 0.260548 | − | 0.257630i | ||||
\(595\) | −5.73813 | −0.235240 | ||||||||
\(596\) | −0.461073 | + | 1.41904i | −0.0188863 | + | 0.0581260i | ||||
\(597\) | −32.5026 | + | 23.6146i | −1.33024 | + | 0.966479i | ||||
\(598\) | −5.15285 | − | 3.74377i | −0.210716 | − | 0.153094i | ||||
\(599\) | −3.82883 | − | 11.7839i | −0.156442 | − | 0.481478i | 0.841862 | − | 0.539692i | \(-0.181459\pi\) |
−0.998304 | + | 0.0582143i | \(0.981459\pi\) | |||||||
\(600\) | −0.674672 | − | 2.07643i | −0.0275434 | − | 0.0847698i | ||||
\(601\) | −21.7409 | − | 15.7957i | −0.886830 | − | 0.644320i | 0.0482193 | − | 0.998837i | \(-0.484645\pi\) |
−0.935050 | + | 0.354517i | \(0.884645\pi\) | |||||||
\(602\) | −1.77016 | + | 1.28609i | −0.0721462 | + | 0.0524173i | ||||
\(603\) | 2.10864 | − | 6.48973i | 0.0858705 | − | 0.264282i | ||||
\(604\) | −7.99555 | −0.325334 | ||||||||
\(605\) | 10.4992 | − | 3.28117i | 0.426855 | − | 0.133398i | ||||
\(606\) | −35.0369 | −1.42328 | ||||||||
\(607\) | −11.1655 | + | 34.3640i | −0.453196 | + | 1.39479i | 0.420045 | + | 0.907503i | \(0.362014\pi\) |
−0.873241 | + | 0.487289i | \(0.837986\pi\) | |||||||
\(608\) | −1.81268 | + | 1.31699i | −0.0735140 | + | 0.0534110i | ||||
\(609\) | 15.2256 | + | 11.0621i | 0.616974 | + | 0.448258i | ||||
\(610\) | 0.0828892 | + | 0.255107i | 0.00335608 | + | 0.0103290i | ||||
\(611\) | 2.52383 | + | 7.76754i | 0.102103 | + | 0.314241i | ||||
\(612\) | 8.20160 | + | 5.95881i | 0.331530 | + | 0.240871i | ||||
\(613\) | 26.9071 | − | 19.5492i | 1.08677 | − | 0.789583i | 0.107917 | − | 0.994160i | \(-0.465582\pi\) |
0.978850 | + | 0.204577i | \(0.0655819\pi\) | |||||||
\(614\) | −1.71883 | + | 5.29003i | −0.0693665 | + | 0.213488i | ||||
\(615\) | −23.0388 | −0.929012 | ||||||||
\(616\) | −2.35838 | + | 2.33197i | −0.0950216 | + | 0.0939576i | ||||
\(617\) | −27.1415 | −1.09267 | −0.546337 | − | 0.837565i | \(-0.683978\pi\) | ||||
−0.546337 | + | 0.837565i | \(0.683978\pi\) | |||||||
\(618\) | 8.70523 | − | 26.7919i | 0.350176 | − | 1.07773i | ||||
\(619\) | −2.37231 | + | 1.72359i | −0.0953513 | + | 0.0692768i | −0.634439 | − | 0.772973i | \(-0.718769\pi\) |
0.539088 | + | 0.842249i | \(0.318769\pi\) | |||||||
\(620\) | −1.48931 | − | 1.08205i | −0.0598122 | − | 0.0434561i | ||||
\(621\) | 2.09251 | + | 6.44010i | 0.0839697 | + | 0.258432i | ||||
\(622\) | −5.53692 | − | 17.0409i | −0.222010 | − | 0.683278i | ||||
\(623\) | 2.14711 | + | 1.55997i | 0.0860221 | + | 0.0624987i | ||||
\(624\) | −4.47342 | + | 3.25013i | −0.179080 | + | 0.130109i | ||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | −5.15478 | −0.206026 | ||||||||
\(627\) | 7.28425 | + | 14.4974i | 0.290905 | + | 0.578969i | ||||
\(628\) | 2.05173 | 0.0818729 | ||||||||
\(629\) | 8.21202 | − | 25.2740i | 0.327435 | − | 1.00774i | ||||
\(630\) | 1.42932 | − | 1.03846i | 0.0569453 | − | 0.0413732i | ||||
\(631\) | 5.74575 | + | 4.17453i | 0.228735 | + | 0.166185i | 0.696250 | − | 0.717800i | \(-0.254851\pi\) |
−0.467515 | + | 0.883985i | \(0.654851\pi\) | |||||||
\(632\) | 3.63201 | + | 11.1782i | 0.144474 | + | 0.444644i | ||||
\(633\) | 13.5219 | + | 41.6161i | 0.537447 | + | 1.65409i | ||||
\(634\) | 23.0257 | + | 16.7292i | 0.914469 | + | 0.664400i | ||||
\(635\) | 8.69092 | − | 6.31432i | 0.344889 | − | 0.250576i | ||||
\(636\) | −2.71047 | + | 8.34197i | −0.107477 | + | 0.330780i | ||||
\(637\) | 2.53263 | 0.100346 | ||||||||
\(638\) | −4.63127 | + | 28.2117i | −0.183354 | + | 1.11691i | ||||
\(639\) | −16.8814 | −0.667817 | ||||||||
\(640\) | −0.309017 | + | 0.951057i | −0.0122150 | + | 0.0375938i | ||||
\(641\) | −1.30237 | + | 0.946231i | −0.0514407 | + | 0.0373739i | −0.613208 | − | 0.789921i | \(-0.710121\pi\) |
0.561768 | + | 0.827295i | \(0.310121\pi\) | |||||||
\(642\) | −11.9150 | − | 8.65674i | −0.470247 | − | 0.341654i | ||||
\(643\) | −5.53544 | − | 17.0363i | −0.218297 | − | 0.671848i | −0.998903 | − | 0.0468249i | \(-0.985090\pi\) |
0.780607 | − | 0.625023i | \(-0.214910\pi\) | |||||||
\(644\) | −0.777143 | − | 2.39180i | −0.0306237 | − | 0.0942501i | ||||
\(645\) | 3.86476 | + | 2.80791i | 0.152175 | + | 0.110561i | ||||
\(646\) | 10.4014 | − | 7.55706i | 0.409238 | − | 0.297329i | ||||
\(647\) | −1.66471 | + | 5.12345i | −0.0654464 | + | 0.201423i | −0.978432 | − | 0.206568i | \(-0.933771\pi\) |
0.912986 | + | 0.407991i | \(0.133771\pi\) | |||||||
\(648\) | 11.1789 | 0.439147 | ||||||||
\(649\) | −6.60338 | + | 1.00779i | −0.259205 | + | 0.0395594i | ||||
\(650\) | −2.53263 | −0.0993379 | ||||||||
\(651\) | 1.24200 | − | 3.82248i | 0.0486777 | − | 0.149815i | ||||
\(652\) | −16.7447 | + | 12.1657i | −0.655773 | + | 0.476447i | ||||
\(653\) | −39.3609 | − | 28.5973i | −1.54031 | − | 1.11910i | −0.950141 | − | 0.311820i | \(-0.899062\pi\) |
−0.590168 | − | 0.807281i | \(-0.700938\pi\) | |||||||
\(654\) | −12.6072 | − | 38.8009i | −0.492980 | − | 1.51724i | ||||
\(655\) | −5.26012 | − | 16.1890i | −0.205530 | − | 0.632555i | ||||
\(656\) | 8.53702 | + | 6.20251i | 0.333315 | + | 0.242167i | ||||
\(657\) | 16.3312 | − | 11.8653i | 0.637139 | − | 0.462909i | ||||
\(658\) | −0.996525 | + | 3.06699i | −0.0388486 | + | 0.119564i | ||||
\(659\) | −29.0793 | −1.13277 | −0.566385 | − | 0.824141i | \(-0.691658\pi\) | ||||
−0.566385 | + | 0.824141i | \(0.691658\pi\) | |||||||
\(660\) | 6.43329 | + | 3.32368i | 0.250415 | + | 0.129374i | ||||
\(661\) | −13.9160 | −0.541270 | −0.270635 | − | 0.962682i | \(-0.587234\pi\) | ||||
−0.270635 | + | 0.962682i | \(0.587234\pi\) | |||||||
\(662\) | 7.68128 | − | 23.6406i | 0.298542 | − | 0.918816i | ||||
\(663\) | 25.6690 | − | 18.6497i | 0.996903 | − | 0.724292i | ||||
\(664\) | −5.94507 | − | 4.31934i | −0.230713 | − | 0.167623i | ||||
\(665\) | −0.692383 | − | 2.13094i | −0.0268495 | − | 0.0826342i | ||||
\(666\) | 2.52843 | + | 7.78171i | 0.0979747 | + | 0.301535i | ||||
\(667\) | −17.5381 | − | 12.7422i | −0.679079 | − | 0.493380i | ||||
\(668\) | −1.06831 | + | 0.776171i | −0.0413341 | + | 0.0300310i | ||||
\(669\) | 7.96111 | − | 24.5018i | 0.307794 | − | 0.947294i | ||||
\(670\) | −3.86233 | −0.149215 | ||||||||
\(671\) | −0.790384 | − | 0.408342i | −0.0305124 | − | 0.0157639i | ||||
\(672\) | −2.18328 | −0.0842220 | ||||||||
\(673\) | −10.0802 | + | 31.0236i | −0.388562 | + | 1.19587i | 0.545301 | + | 0.838240i | \(0.316415\pi\) |
−0.933863 | + | 0.357631i | \(0.883585\pi\) | |||||||
\(674\) | −12.6590 | + | 9.19732i | −0.487607 | + | 0.354267i | ||||
\(675\) | 2.17834 | + | 1.58266i | 0.0838443 | + | 0.0609164i | ||||
\(676\) | −2.03512 | − | 6.26346i | −0.0782739 | − | 0.240902i | ||||
\(677\) | 11.6155 | + | 35.7489i | 0.446421 | + | 1.37394i | 0.880918 | + | 0.473270i | \(0.156926\pi\) |
−0.434496 | + | 0.900674i | \(0.643074\pi\) | |||||||
\(678\) | 13.3610 | + | 9.70733i | 0.513126 | + | 0.372808i | ||||
\(679\) | −13.3525 | + | 9.70112i | −0.512420 | + | 0.372295i | ||||
\(680\) | 1.77318 | − | 5.45728i | 0.0679983 | − | 0.209277i | ||||
\(681\) | 2.16172 | 0.0828372 | ||||||||
\(682\) | 6.03566 | − | 0.921150i | 0.231117 | − | 0.0352726i | ||||
\(683\) | −17.5199 | −0.670380 | −0.335190 | − | 0.942151i | \(-0.608800\pi\) | ||||
−0.335190 | + | 0.942151i | \(0.608800\pi\) | |||||||
\(684\) | −1.22326 | + | 3.76480i | −0.0467724 | + | 0.143951i | ||||
\(685\) | 10.0946 | − | 7.33418i | 0.385696 | − | 0.280225i | ||||
\(686\) | 0.809017 | + | 0.587785i | 0.0308884 | + | 0.0224417i | ||||
\(687\) | 12.3842 | + | 38.1146i | 0.472487 | + | 1.45416i | ||||
\(688\) | −0.676140 | − | 2.08095i | −0.0257776 | − | 0.0793353i | ||||
\(689\) | 8.23154 | + | 5.98056i | 0.313597 | + | 0.227841i | ||||
\(690\) | −4.44208 | + | 3.22736i | −0.169107 | + | 0.122864i | ||||
\(691\) | 2.20747 | − | 6.79389i | 0.0839760 | − | 0.258452i | −0.900248 | − | 0.435377i | \(-0.856615\pi\) |
0.984224 | + | 0.176925i | \(0.0566151\pi\) | |||||||
\(692\) | 15.7029 | 0.596933 | ||||||||
\(693\) | −0.949212 | + | 5.78220i | −0.0360576 | + | 0.219647i | ||||
\(694\) | −14.6646 | −0.556662 | ||||||||
\(695\) | 5.37110 | − | 16.5305i | 0.203737 | − | 0.627039i | ||||
\(696\) | −15.2256 | + | 11.0621i | −0.577126 | + | 0.419307i | ||||
\(697\) | −48.9865 | − | 35.5908i | −1.85550 | − | 1.34810i | ||||
\(698\) | −8.33613 | − | 25.6560i | −0.315527 | − | 0.971093i | ||||
\(699\) | −11.7157 | − | 36.0571i | −0.443127 | − | 1.36381i | ||||
\(700\) | −0.809017 | − | 0.587785i | −0.0305780 | − | 0.0222162i | ||||
\(701\) | 31.3683 | − | 22.7904i | 1.18476 | − | 0.860781i | 0.192063 | − | 0.981383i | \(-0.438482\pi\) |
0.992701 | + | 0.120601i | \(0.0384823\pi\) | |||||||
\(702\) | 2.10728 | − | 6.48553i | 0.0795340 | − | 0.244781i | ||||
\(703\) | 10.3768 | 0.391367 | ||||||||
\(704\) | −1.48905 | − | 2.96357i | −0.0561208 | − | 0.111694i | ||||
\(705\) | 7.04070 | 0.265168 | ||||||||
\(706\) | −1.47544 | + | 4.54094i | −0.0555290 | + | 0.170901i | ||||
\(707\) | −12.9830 | + | 9.43267i | −0.488274 | + | 0.354752i | ||||
\(708\) | −3.55744 | − | 2.58463i | −0.133697 | − | 0.0971364i | ||||
\(709\) | 9.37902 | + | 28.8656i | 0.352236 | + | 1.08407i | 0.957595 | + | 0.288119i | \(0.0930298\pi\) |
−0.605358 | + | 0.795953i | \(0.706970\pi\) | |||||||
\(710\) | 2.95270 | + | 9.08747i | 0.110813 | + | 0.341047i | ||||
\(711\) | 16.7994 | + | 12.2055i | 0.630026 | + | 0.457741i | ||||
\(712\) | −2.14711 | + | 1.55997i | −0.0804663 | + | 0.0584622i | ||||
\(713\) | −1.43064 | + | 4.40304i | −0.0535777 | + | 0.164895i | ||||
\(714\) | 12.5280 | 0.468847 | ||||||||
\(715\) | 5.97289 | − | 5.90601i | 0.223373 | − | 0.220872i | ||||
\(716\) | 4.65497 | 0.173964 | ||||||||
\(717\) | 6.01884 | − | 18.5241i | 0.224778 | − | 0.691794i | ||||
\(718\) | 27.5860 | − | 20.0424i | 1.02950 | − | 0.747976i | ||||
\(719\) | −29.1535 | − | 21.1813i | −1.08724 | − | 0.789928i | −0.108311 | − | 0.994117i | \(-0.534544\pi\) |
−0.978931 | + | 0.204189i | \(0.934544\pi\) | |||||||
\(720\) | 0.545950 | + | 1.68026i | 0.0203464 | + | 0.0626197i | ||||
\(721\) | −3.98721 | − | 12.2714i | −0.148492 | − | 0.457010i | ||||
\(722\) | −11.3098 | − | 8.21707i | −0.420908 | − | 0.305808i | ||||
\(723\) | 1.58385 | − | 1.15073i | 0.0589039 | − | 0.0427962i | ||||
\(724\) | −1.82459 | + | 5.61552i | −0.0678104 | + | 0.208699i | ||||
\(725\) | −8.62000 | −0.320139 | ||||||||
\(726\) | −22.9228 | + | 7.16373i | −0.850746 | + | 0.265871i | ||||
\(727\) | 31.1833 | 1.15653 | 0.578263 | − | 0.815850i | \(-0.303731\pi\) | ||||
0.578263 | + | 0.815850i | \(0.303731\pi\) | |||||||
\(728\) | −0.782625 | + | 2.40867i | −0.0290060 | + | 0.0892714i | ||||
\(729\) | 1.71032 | − | 1.24262i | 0.0633454 | − | 0.0460231i | ||||
\(730\) | −9.24371 | − | 6.71595i | −0.342125 | − | 0.248568i | ||||
\(731\) | 3.87978 | + | 11.9407i | 0.143499 | + | 0.441644i | ||||
\(732\) | −0.180971 | − | 0.556970i | −0.00668887 | − | 0.0205862i | ||||
\(733\) | 21.0611 | + | 15.3018i | 0.777909 | + | 0.565184i | 0.904351 | − | 0.426790i | \(-0.140356\pi\) |
−0.126442 | + | 0.991974i | \(0.540356\pi\) | |||||||
\(734\) | −8.08180 | + | 5.87177i | −0.298305 | + | 0.216731i | ||||
\(735\) | 0.674672 | − | 2.07643i | 0.0248857 | − | 0.0765902i | ||||
\(736\) | 2.51489 | 0.0927000 | ||||||||
\(737\) | 9.10882 | − | 9.00682i | 0.335528 | − | 0.331771i | ||||
\(738\) | 18.6432 | 0.686264 | ||||||||
\(739\) | 6.92632 | − | 21.3170i | 0.254789 | − | 0.784159i | −0.739083 | − | 0.673615i | \(-0.764741\pi\) |
0.993871 | − | 0.110544i | \(-0.0352593\pi\) | |||||||
\(740\) | 3.74676 | − | 2.72218i | 0.137733 | − | 0.100069i | ||||
\(741\) | 10.0231 | + | 7.28224i | 0.368209 | + | 0.267520i | ||||
\(742\) | 1.24146 | + | 3.82083i | 0.0455756 | + | 0.140267i | ||||
\(743\) | −13.6919 | − | 42.1394i | −0.502308 | − | 1.54595i | −0.805249 | − | 0.592936i | \(-0.797969\pi\) |
0.302941 | − | 0.953009i | \(-0.402031\pi\) | |||||||
\(744\) | 3.25159 | + | 2.36242i | 0.119209 | + | 0.0866105i | ||||
\(745\) | 1.20710 | − | 0.877013i | 0.0442249 | − | 0.0321313i | ||||
\(746\) | 0.157882 | − | 0.485910i | 0.00578046 | − | 0.0177904i | ||||
\(747\) | −12.9828 | −0.475018 | ||||||||
\(748\) | 8.54438 | + | 17.0053i | 0.312413 | + | 0.621776i | ||||
\(749\) | −6.74567 | −0.246482 | ||||||||
\(750\) | −0.674672 | + | 2.07643i | −0.0246355 | + | 0.0758204i | ||||
\(751\) | −31.8495 | + | 23.1400i | −1.16221 | + | 0.844392i | −0.990055 | − | 0.140678i | \(-0.955072\pi\) |
−0.172151 | + | 0.985071i | \(0.555072\pi\) | |||||||
\(752\) | −2.60894 | − | 1.89550i | −0.0951381 | − | 0.0691219i | ||||
\(753\) | −15.1787 | − | 46.7151i | −0.553142 | − | 1.70239i | ||||
\(754\) | 6.74623 | + | 20.7628i | 0.245683 | + | 0.756135i | ||||
\(755\) | 6.46853 | + | 4.69966i | 0.235414 | + | 0.171038i | ||||
\(756\) | 2.17834 | − | 1.58266i | 0.0792254 | − | 0.0575606i | ||||
\(757\) | −10.3242 | + | 31.7746i | −0.375239 | + | 1.15487i | 0.568079 | + | 0.822974i | \(0.307687\pi\) |
−0.943317 | + | 0.331892i | \(0.892313\pi\) | |||||||
\(758\) | −5.31376 | −0.193004 | ||||||||
\(759\) | 2.95000 | − | 17.9701i | 0.107078 | − | 0.652274i | ||||
\(760\) | 2.24060 | 0.0812751 | ||||||||
\(761\) | 12.0356 | − | 37.0418i | 0.436290 | − | 1.34276i | −0.455469 | − | 0.890252i | \(-0.650528\pi\) |
0.891759 | − | 0.452511i | \(-0.149472\pi\) | |||||||
\(762\) | −18.9748 | + | 13.7860i | −0.687383 | + | 0.499413i | ||||
\(763\) | −15.1176 | − | 10.9836i | −0.547294 | − | 0.397632i | ||||
\(764\) | −1.83371 | − | 5.64357i | −0.0663412 | − | 0.204177i | ||||
\(765\) | −3.13273 | − | 9.64156i | −0.113264 | − | 0.348591i | ||||
\(766\) | 19.0283 | + | 13.8249i | 0.687520 | + | 0.499512i | ||||
\(767\) | −4.12666 | + | 2.99819i | −0.149005 | + | 0.108259i | ||||
\(768\) | 0.674672 | − | 2.07643i | 0.0243451 | − | 0.0749266i | ||||
\(769\) | −0.875099 | −0.0315569 | −0.0157784 | − | 0.999876i | \(-0.505023\pi\) | ||||
−0.0157784 | + | 0.999876i | \(0.505023\pi\) | |||||||
\(770\) | 3.27866 | − | 0.500382i | 0.118155 | − | 0.0180325i | ||||
\(771\) | −54.4617 | −1.96139 | ||||||||
\(772\) | 3.34902 | − | 10.3072i | 0.120534 | − | 0.370966i | ||||
\(773\) | 18.5371 | − | 13.4680i | 0.666731 | − | 0.484409i | −0.202198 | − | 0.979345i | \(-0.564808\pi\) |
0.868929 | + | 0.494936i | \(0.164808\pi\) | |||||||
\(774\) | −3.12740 | − | 2.27219i | −0.112412 | − | 0.0816720i | ||||
\(775\) | 0.568867 | + | 1.75079i | 0.0204343 | + | 0.0628903i | ||||
\(776\) | −5.10018 | − | 15.6967i | −0.183086 | − | 0.563480i | ||||
\(777\) | 8.18023 | + | 5.94329i | 0.293464 | + | 0.213214i | ||||
\(778\) | 7.42999 | − | 5.39820i | 0.266378 | − | 0.193535i | ||||
\(779\) | 7.30626 | − | 22.4864i | 0.261774 | − | 0.805657i | ||||
\(780\) | 5.52945 | 0.197986 | ||||||||
\(781\) | −28.1553 | − | 14.5461i | −1.00747 | − | 0.520500i | ||||
\(782\) | −14.4307 | −0.516042 | ||||||||
\(783\) | 7.17228 | − | 22.0740i | 0.256316 | − | 0.788861i | ||||
\(784\) | −0.809017 | + | 0.587785i | −0.0288935 | + | 0.0209923i | ||||
\(785\) | −1.65988 | − | 1.20598i | −0.0592438 | − | 0.0430431i | ||||
\(786\) | 11.4843 | + | 35.3451i | 0.409632 | + | 1.26072i | ||||
\(787\) | −10.3240 | − | 31.7741i | −0.368012 | − | 1.13262i | −0.948074 | − | 0.318051i | \(-0.896972\pi\) |
0.580062 | − | 0.814572i | \(-0.303028\pi\) | |||||||
\(788\) | −9.72241 | − | 7.06374i | −0.346347 | − | 0.251635i | ||||
\(789\) | −11.0500 | + | 8.02826i | −0.393389 | + | 0.285814i | ||||
\(790\) | 3.63201 | − | 11.1782i | 0.129221 | − | 0.397702i | ||||
\(791\) | 7.56433 | 0.268957 | ||||||||
\(792\) | −5.20587 | − | 2.68955i | −0.184983 | − | 0.0955690i | ||||
\(793\) | −0.679340 | −0.0241241 | ||||||||
\(794\) | 9.75593 | − | 30.0257i | 0.346225 | − | 1.06557i | ||||
\(795\) | 7.09610 | − | 5.15562i | 0.251673 | − | 0.182851i | ||||
\(796\) | −14.8870 | − | 10.8161i | −0.527657 | − | 0.383365i | ||||
\(797\) | −1.06246 | − | 3.26992i | −0.0376343 | − | 0.115827i | 0.930474 | − | 0.366357i | \(-0.119395\pi\) |
−0.968109 | + | 0.250530i | \(0.919395\pi\) | |||||||
\(798\) | 1.51167 | + | 4.65244i | 0.0535125 | + | 0.164695i | ||||
\(799\) | 14.9704 | + | 10.8766i | 0.529615 | + | 0.384788i | ||||
\(800\) | 0.809017 | − | 0.587785i | 0.0286031 | − | 0.0207813i | ||||
\(801\) | −1.44894 | + | 4.45937i | −0.0511957 | + | 0.157564i | ||||
\(802\) | 10.6804 | 0.377138 | ||||||||
\(803\) | 37.4615 | − | 5.71729i | 1.32199 | − | 0.201759i | ||||
\(804\) | 8.43256 | 0.297394 | ||||||||
\(805\) | −0.777143 | + | 2.39180i | −0.0273907 | + | 0.0842999i | ||||
\(806\) | 3.77188 | − | 2.74043i | 0.132859 | − | 0.0965275i | ||||
\(807\) | 23.0810 | + | 16.7693i | 0.812488 | + | 0.590307i | ||||
\(808\) | −4.95905 | − | 15.2624i | −0.174459 | − | 0.536929i | ||||
\(809\) | −10.9180 | − | 33.6022i | −0.383857 | − | 1.18139i | −0.937306 | − | 0.348506i | \(-0.886689\pi\) |
0.553450 | − | 0.832883i | \(-0.313311\pi\) | |||||||
\(810\) | −9.04388 | − | 6.57077i | −0.317770 | − | 0.230873i | ||||
\(811\) | −39.3826 | + | 28.6132i | −1.38291 | + | 1.00474i | −0.386310 | + | 0.922369i | \(0.626251\pi\) |
−0.996601 | + | 0.0823753i | \(0.973749\pi\) | |||||||
\(812\) | −2.66373 | + | 8.19811i | −0.0934785 | + | 0.287697i | ||||
\(813\) | −53.0880 | −1.86188 | ||||||||
\(814\) | −2.48823 | + | 15.1572i | −0.0872124 | + | 0.531260i | ||||
\(815\) | 20.6976 | 0.725004 | ||||||||
\(816\) | −3.87135 | + | 11.9148i | −0.135524 | + | 0.417101i | ||||
\(817\) | −3.96621 | + | 2.88162i | −0.138760 | + | 0.100815i | ||||
\(818\) | −19.0742 | − | 13.8582i | −0.666912 | − | 0.484540i | ||||
\(819\) | 1.38269 | + | 4.25548i | 0.0483151 | + | 0.148699i | ||||
\(820\) | −3.26085 | − | 10.0359i | −0.113874 | − | 0.350468i | ||||
\(821\) | −13.9084 | − | 10.1050i | −0.485406 | − | 0.352668i | 0.318009 | − | 0.948088i | \(-0.396986\pi\) |
−0.803415 | + | 0.595420i | \(0.796986\pi\) | |||||||
\(822\) | −22.0395 | + | 16.0126i | −0.768715 | + | 0.558504i | ||||
\(823\) | −14.1777 | + | 43.6343i | −0.494202 | + | 1.52100i | 0.323995 | + | 0.946059i | \(0.394974\pi\) |
−0.818197 | + | 0.574939i | \(0.805026\pi\) | |||||||
\(824\) | 12.9029 | 0.449494 | ||||||||
\(825\) | −3.25103 | − | 6.47031i | −0.113186 | − | 0.225267i | ||||
\(826\) | −2.01405 | −0.0700777 | ||||||||
\(827\) | −8.64150 | + | 26.5958i | −0.300494 | + | 0.924827i | 0.680826 | + | 0.732445i | \(0.261621\pi\) |
−0.981320 | + | 0.192381i | \(0.938379\pi\) | |||||||
\(828\) | 3.59457 | − | 2.61161i | 0.124920 | − | 0.0907596i | ||||
\(829\) | 15.2755 | + | 11.0983i | 0.530539 | + | 0.385459i | 0.820559 | − | 0.571561i | \(-0.193662\pi\) |
−0.290020 | + | 0.957021i | \(0.593662\pi\) | |||||||
\(830\) | 2.27081 | + | 6.98885i | 0.0788211 | + | 0.242586i | ||||
\(831\) | −9.04698 | − | 27.8437i | −0.313836 | − | 0.965889i | ||||
\(832\) | −2.04894 | − | 1.48864i | −0.0710342 | − | 0.0516094i | ||||
\(833\) | 4.64224 | − | 3.37279i | 0.160844 | − | 0.116860i | ||||
\(834\) | −11.7266 | + | 36.0909i | −0.406060 | + | 1.24973i | ||||
\(835\) | 1.32050 | 0.0456978 | ||||||||
\(836\) | −5.28417 | + | 5.22500i | −0.182757 | + | 0.180710i | ||||
\(837\) | −4.95674 | −0.171330 | ||||||||
\(838\) | 4.92064 | − | 15.1442i | 0.169981 | − | 0.523147i | ||||
\(839\) | 15.9470 | − | 11.5862i | 0.550553 | − | 0.400000i | −0.277436 | − | 0.960744i | \(-0.589485\pi\) |
0.827989 | + | 0.560744i | \(0.189485\pi\) | |||||||
\(840\) | 1.76631 | + | 1.28330i | 0.0609436 | + | 0.0442781i | ||||
\(841\) | 13.9998 | + | 43.0870i | 0.482752 | + | 1.48576i | ||||
\(842\) | 12.3175 | + | 37.9093i | 0.424488 | + | 1.30644i | ||||
\(843\) | −22.5025 | − | 16.3490i | −0.775028 | − | 0.563091i | ||||
\(844\) | −16.2145 | + | 11.7805i | −0.558125 | + | 0.405501i | ||||
\(845\) | −2.03512 | + | 6.26346i | −0.0700103 | + | 0.215470i | ||||
\(846\) | −5.69740 | −0.195881 | ||||||||
\(847\) | −6.56544 | + | 8.82582i | −0.225591 | + | 0.303259i | ||||
\(848\) | −4.01746 | −0.137960 | ||||||||
\(849\) | −9.27643 | + | 28.5499i | −0.318366 | + | 0.979830i | ||||
\(850\) | −4.64224 | + | 3.37279i | −0.159228 | + | 0.115686i | ||||
\(851\) | −9.42267 | − | 6.84597i | −0.323005 | − | 0.234677i | ||||
\(852\) | −6.44658 | − | 19.8405i | −0.220856 | − | 0.679726i | ||||
\(853\) | −9.54664 | − | 29.3815i | −0.326871 | − | 1.00600i | −0.970589 | − | 0.240742i | \(-0.922609\pi\) |
0.643718 | − | 0.765262i | \(-0.277391\pi\) | |||||||
\(854\) | −0.217007 | − | 0.157665i | −0.00742582 | − | 0.00539517i | ||||
\(855\) | 3.20253 | − | 2.32677i | 0.109524 | − | 0.0795739i | ||||
\(856\) | 2.08453 | − | 6.41552i | 0.0712477 | − | 0.219278i | ||||
\(857\) | 24.2847 | 0.829550 | 0.414775 | − | 0.909924i | \(-0.363860\pi\) | ||||
0.414775 | + | 0.909924i | \(0.363860\pi\) | |||||||
\(858\) | −13.0405 | + | 12.8945i | −0.445196 | + | 0.440211i | ||||
\(859\) | 22.0877 | 0.753621 | 0.376811 | − | 0.926290i | \(-0.377021\pi\) | ||||
0.376811 | + | 0.926290i | \(0.377021\pi\) | |||||||
\(860\) | −0.676140 | + | 2.08095i | −0.0230562 | + | 0.0709596i | ||||
\(861\) | 18.6387 | − | 13.5418i | 0.635207 | − | 0.461505i | ||||
\(862\) | −14.2314 | − | 10.3397i | −0.484722 | − | 0.352171i | ||||
\(863\) | −4.35874 | − | 13.4148i | −0.148373 | − | 0.456646i | 0.849056 | − | 0.528303i | \(-0.177171\pi\) |
−0.997429 | + | 0.0716566i | \(0.977171\pi\) | |||||||
\(864\) | 0.832051 | + | 2.56079i | 0.0283070 | + | 0.0871198i | ||||
\(865\) | −12.7039 | − | 9.22991i | −0.431945 | − | 0.313826i | ||||
\(866\) | 16.6207 | − | 12.0756i | 0.564794 | − | 0.410347i | ||||
\(867\) | 10.7449 | − | 33.0694i | 0.364915 | − | 1.12309i | ||||
\(868\) | 1.84089 | 0.0624839 | ||||||||
\(869\) | 17.5015 | + | 34.8321i | 0.593698 | + | 1.18160i | ||||
\(870\) | 18.8199 | 0.638055 | ||||||||
\(871\) | 3.02276 | − | 9.30309i | 0.102422 | − | 0.315223i | ||||
\(872\) | 15.1176 | − | 10.9836i | 0.511947 | − | 0.371951i | ||||
\(873\) | −23.5902 | − | 17.1393i | −0.798408 | − | 0.580077i | ||||
\(874\) | −1.74127 | − | 5.35906i | −0.0588992 | − | 0.181273i | ||||
\(875\) | 0.309017 | + | 0.951057i | 0.0104467 | + | 0.0321516i | ||||
\(876\) | 20.1816 | + | 14.6628i | 0.681875 | + | 0.495411i | ||||
\(877\) | −45.2424 | + | 32.8706i | −1.52773 | + | 1.10996i | −0.570244 | + | 0.821475i | \(0.693151\pi\) |
−0.957485 | + | 0.288484i | \(0.906849\pi\) | |||||||
\(878\) | −6.92815 | + | 21.3226i | −0.233814 | + | 0.719604i | ||||
\(879\) | 36.3247 | 1.22520 | ||||||||
\(880\) | −0.537270 | + | 3.27282i | −0.0181114 | + | 0.110327i | ||||
\(881\) | −46.2057 | −1.55671 | −0.778354 | − | 0.627826i | \(-0.783945\pi\) | ||||
−0.778354 | + | 0.627826i | \(0.783945\pi\) | |||||||
\(882\) | −0.545950 | + | 1.68026i | −0.0183831 | + | 0.0565774i | ||||
\(883\) | 11.4320 | − | 8.30582i | 0.384717 | − | 0.279513i | −0.378570 | − | 0.925572i | \(-0.623584\pi\) |
0.763287 | + | 0.646060i | \(0.223584\pi\) | |||||||
\(884\) | 11.7571 | + | 8.54201i | 0.395433 | + | 0.287299i | ||||
\(885\) | 1.35882 | + | 4.18202i | 0.0456763 | + | 0.140577i | ||||
\(886\) | −2.35939 | − | 7.26147i | −0.0792654 | − | 0.243954i | ||||
\(887\) | 30.4359 | + | 22.1129i | 1.02194 | + | 0.742480i | 0.966679 | − | 0.255992i | \(-0.0824022\pi\) |
0.0552571 | + | 0.998472i | \(0.482402\pi\) | |||||||
\(888\) | −8.18023 | + | 5.94329i | −0.274511 | + | 0.199444i | ||||
\(889\) | −3.31964 | + | 10.2168i | −0.111337 | + | 0.342660i | ||||
\(890\) | 2.65397 | 0.0889614 | ||||||||
\(891\) | 36.6517 | − | 5.59370i | 1.22788 | − | 0.187396i | ||||
\(892\) | 11.8000 | 0.395092 | ||||||||
\(893\) | −2.23281 | + | 6.87189i | −0.0747182 | + | 0.229959i | ||||
\(894\) | −2.63545 | + | 1.91477i | −0.0881428 | + | 0.0640395i | ||||
\(895\) | −3.76595 | − | 2.73612i | −0.125882 | − | 0.0914585i | ||||
\(896\) | −0.309017 | − | 0.951057i | −0.0103235 | − | 0.0317726i | ||||
\(897\) | −4.29717 | − | 13.2253i | −0.143478 | − | 0.441581i | ||||
\(898\) | −0.527860 | − | 0.383512i | −0.0176149 | − | 0.0127980i | ||||
\(899\) | 12.8379 | − | 9.32726i | 0.428167 | − | 0.311081i | ||||
\(900\) | 0.545950 | − | 1.68026i | 0.0181983 | − | 0.0560088i | ||||
\(901\) | 23.0527 | 0.767997 | ||||||||
\(902\) | 31.0936 | + | 16.0641i | 1.03530 | + | 0.534877i | ||||
\(903\) | −4.77710 | −0.158972 | ||||||||
\(904\) | −2.33751 | + | 7.19411i | −0.0777444 | + | 0.239273i | ||||
\(905\) | 4.77684 | − | 3.47058i | 0.158788 | − | 0.115366i | ||||
\(906\) | −14.1227 | − | 10.2607i | −0.469194 | − | 0.340889i | ||||
\(907\) | −0.919382 | − | 2.82957i | −0.0305276 | − | 0.0939542i | 0.934632 | − | 0.355617i | \(-0.115729\pi\) |
−0.965159 | + | 0.261663i | \(0.915729\pi\) | |||||||
\(908\) | 0.305964 | + | 0.941661i | 0.0101538 | + | 0.0312501i | ||||
\(909\) | −22.9374 | − | 16.6650i | −0.760786 | − | 0.552743i | ||||
\(910\) | 2.04894 | − | 1.48864i | 0.0679217 | − | 0.0493480i | ||||
\(911\) | −16.6469 | + | 51.2340i | −0.551538 | + | 1.69746i | 0.153377 | + | 0.988168i | \(0.450985\pi\) |
−0.704915 | + | 0.709292i | \(0.749015\pi\) | |||||||
\(912\) | −4.89187 | −0.161986 | ||||||||
\(913\) | −21.6532 | − | 11.1869i | −0.716616 | − | 0.370231i | ||||
\(914\) | −30.5691 | −1.01114 | ||||||||
\(915\) | −0.180971 | + | 0.556970i | −0.00598271 | + | 0.0184129i | ||||
\(916\) | −14.8502 | + | 10.7893i | −0.490665 | + | 0.356489i | ||||
\(917\) | 13.7712 | + | 10.0053i | 0.454764 | + | 0.330405i | ||||
\(918\) | −4.77441 | − | 14.6941i | −0.157579 | − | 0.484979i | ||||
\(919\) | −5.24298 | − | 16.1362i | −0.172950 | − | 0.532286i | 0.826584 | − | 0.562814i | \(-0.190281\pi\) |
−0.999534 | + | 0.0305280i | \(0.990281\pi\) | |||||||
\(920\) | −2.03459 | − | 1.47821i | −0.0670783 | − | 0.0487353i | ||||
\(921\) | −9.82471 | + | 7.13807i | −0.323735 | + | 0.235207i | ||||
\(922\) | 1.09928 | − | 3.38324i | 0.0362029 | − | 0.111421i | ||||
\(923\) | −24.1996 | −0.796540 | ||||||||
\(924\) | −7.15825 | + | 1.09248i | −0.235489 | + | 0.0359399i | ||||
\(925\) | −4.63124 | −0.152274 | ||||||||
\(926\) | −2.03233 | + | 6.25488i | −0.0667866 | + | 0.205548i | ||||
\(927\) | 18.4423 | − | 13.3991i | 0.605725 | − | 0.440085i | ||||
\(928\) | −6.97373 | − | 5.06671i | −0.228924 | − | 0.166323i | ||||
\(929\) | 10.0083 | + | 30.8024i | 0.328362 | + | 1.01060i | 0.969900 | + | 0.243504i | \(0.0782968\pi\) |
−0.641538 | + | 0.767092i | \(0.721703\pi\) | |||||||
\(930\) | −1.24200 | − | 3.82248i | −0.0407267 | − | 0.125344i | ||||
\(931\) | 1.81268 | + | 1.31699i | 0.0594083 | + | 0.0431626i | ||||
\(932\) | 14.0486 | − | 10.2069i | 0.460176 | − | 0.334338i | ||||
\(933\) | 12.0887 | − | 37.2051i | 0.395766 | − | 1.21804i | ||||
\(934\) | 18.3935 | 0.601854 | ||||||||
\(935\) | 3.08292 | − | 18.7798i | 0.100822 | − | 0.614167i | ||||
\(936\) | −4.47448 | −0.146253 | ||||||||
\(937\) | −7.46123 | + | 22.9633i | −0.243748 | + | 0.750178i | 0.752092 | + | 0.659058i | \(0.229045\pi\) |
−0.995840 | + | 0.0911204i | \(0.970955\pi\) | |||||||
\(938\) | 3.12469 | − | 2.27022i | 0.102025 | − | 0.0741253i | ||||
\(939\) | −9.10496 | − | 6.61514i | −0.297129 | − | 0.215877i | ||||
\(940\) | 0.996525 | + | 3.06699i | 0.0325031 | + | 0.100034i | ||||
\(941\) | 12.5475 | + | 38.6173i | 0.409037 | + | 1.25889i | 0.917477 | + | 0.397790i | \(0.130223\pi\) |
−0.508439 | + | 0.861098i | \(0.669777\pi\) | |||||||
\(942\) | 3.62400 | + | 2.63299i | 0.118076 | + | 0.0857874i | ||||
\(943\) | −21.4696 | + | 15.5986i | −0.699148 | + | 0.507960i | ||||
\(944\) | 0.622375 | − | 1.91547i | 0.0202566 | − | 0.0623433i | ||||
\(945\) | −2.69257 | −0.0875894 | ||||||||
\(946\) | −3.25810 | − | 6.48439i | −0.105930 | − | 0.210826i | ||||
\(947\) | 0.111103 | 0.00361036 | 0.00180518 | − | 0.999998i | \(-0.499425\pi\) | ||||
0.00180518 | + | 0.999998i | \(0.499425\pi\) | |||||||
\(948\) | −7.92972 | + | 24.4052i | −0.257545 | + | 0.792643i | ||||
\(949\) | 23.4109 | − | 17.0090i | 0.759949 | − | 0.552135i | ||||
\(950\) | −1.81268 | − | 1.31699i | −0.0588112 | − | 0.0427288i | ||||
\(951\) | 19.2021 | + | 59.0980i | 0.622671 | + | 1.91638i | ||||
\(952\) | 1.77318 | + | 5.45728i | 0.0574690 | + | 0.176872i | ||||
\(953\) | 6.23263 | + | 4.52827i | 0.201895 | + | 0.146685i | 0.684139 | − | 0.729352i | \(-0.260178\pi\) |
−0.482244 | + | 0.876037i | \(0.660178\pi\) | |||||||
\(954\) | −5.74222 | + | 4.17197i | −0.185911 | + | 0.135073i | ||||
\(955\) | −1.83371 | + | 5.64357i | −0.0593374 | + | 0.182622i | ||||
\(956\) | 8.92113 | 0.288530 | ||||||||
\(957\) | −44.3844 | + | 43.8874i | −1.43474 | + | 1.41868i | ||||
\(958\) | −33.1011 | −1.06945 | ||||||||
\(959\) | −3.85581 | + | 11.8670i | −0.124511 | + | 0.383204i | ||||
\(960\) | −1.76631 | + | 1.28330i | −0.0570076 | + | 0.0414184i | ||||
\(961\) | 22.3379 | + | 16.2294i | 0.720576 | + | 0.523529i | ||||
\(962\) | 3.62453 | + | 11.1552i | 0.116860 | + | 0.359657i | ||||
\(963\) | −3.68280 | − | 11.3345i | −0.118677 | − | 0.365249i | ||||
\(964\) | 0.725442 | + | 0.527065i | 0.0233649 | + | 0.0169756i | ||||
\(965\) | −8.76786 | + | 6.37022i | −0.282247 | + | 0.205065i | ||||
\(966\) | 1.69672 | − | 5.22198i | 0.0545912 | − | 0.168014i | ||||
\(967\) | 41.8250 | 1.34500 | 0.672501 | − | 0.740096i | \(-0.265220\pi\) | ||||
0.672501 | + | 0.740096i | \(0.265220\pi\) | |||||||
\(968\) | −6.36502 | − | 8.97143i | −0.204579 | − | 0.288353i | ||||
\(969\) | 28.0701 | 0.901743 | ||||||||
\(970\) | −5.10018 | + | 15.6967i | −0.163757 | + | 0.503992i | ||||
\(971\) | −30.1680 | + | 21.9184i | −0.968138 | + | 0.703394i | −0.955026 | − | 0.296520i | \(-0.904174\pi\) |
−0.0131117 | + | 0.999914i | \(0.504174\pi\) | |||||||
\(972\) | 13.2104 | + | 9.59789i | 0.423722 | + | 0.307852i | ||||
\(973\) | 5.37110 | + | 16.5305i | 0.172190 | + | 0.529945i | ||||
\(974\) | 4.82009 | + | 14.8347i | 0.154446 | + | 0.475335i | ||||
\(975\) | −4.47342 | − | 3.25013i | −0.143264 | − | 0.104087i | ||||
\(976\) | 0.217007 | − | 0.157665i | 0.00694621 | − | 0.00504672i | ||||
\(977\) | 0.745160 | − | 2.29337i | 0.0238398 | − | 0.0733713i | −0.938429 | − | 0.345473i | \(-0.887719\pi\) |
0.962269 | + | 0.272101i | \(0.0877186\pi\) | |||||||
\(978\) | −45.1887 | −1.44498 | ||||||||
\(979\) | −6.25906 | + | 6.18898i | −0.200041 | + | 0.197801i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 10.2018 | − | 31.3980i | 0.325720 | − | 1.00246i | ||||
\(982\) | −33.7066 | + | 24.4893i | −1.07562 | + | 0.781484i | ||||
\(983\) | 32.7154 | + | 23.7691i | 1.04346 | + | 0.758118i | 0.970958 | − | 0.239250i | \(-0.0769016\pi\) |
0.0725021 | + | 0.997368i | \(0.476902\pi\) | |||||||
\(984\) | 7.11937 | + | 21.9112i | 0.226957 | + | 0.698502i | ||||
\(985\) | 3.71363 | + | 11.4294i | 0.118326 | + | 0.364170i | ||||
\(986\) | 40.0161 | + | 29.0734i | 1.27437 | + | 0.925886i | ||||
\(987\) | −5.69605 | + | 4.13842i | −0.181307 | + | 0.131727i | ||||
\(988\) | −1.75355 | + | 5.39687i | −0.0557879 | + | 0.171697i | ||||
\(989\) | 5.50266 | 0.174974 | ||||||||
\(990\) | 2.63076 | + | 5.23583i | 0.0836110 | + | 0.166406i | ||||
\(991\) | 26.7075 | 0.848392 | 0.424196 | − | 0.905570i | \(-0.360557\pi\) | ||||
0.424196 | + | 0.905570i | \(0.360557\pi\) | |||||||
\(992\) | −0.568867 | + | 1.75079i | −0.0180615 | + | 0.0555877i | ||||
\(993\) | 43.9055 | − | 31.8992i | 1.39330 | − | 1.01229i | ||||
\(994\) | −7.73027 | − | 5.61637i | −0.245189 | − | 0.178140i | ||||
\(995\) | 5.68634 | + | 17.5008i | 0.180269 | + | 0.554811i | ||||
\(996\) | −4.95783 | − | 15.2586i | −0.157095 | − | 0.483489i | ||||
\(997\) | 22.1125 | + | 16.0657i | 0.700310 | + | 0.508805i | 0.880033 | − | 0.474912i | \(-0.157520\pi\) |
−0.179723 | + | 0.983717i | \(0.557520\pi\) | |||||||
\(998\) | −1.98298 | + | 1.44072i | −0.0627701 | + | 0.0456051i | ||||
\(999\) | 3.85343 | − | 11.8596i | 0.121917 | − | 0.375223i |
(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 | 770.2.n.j.141.1 | yes | 12 | |
11.4 | even | 5 | 8470.2.a.cw.1.6 | 6 | |||
11.5 | even | 5 | inner | 770.2.n.j.71.1 | ✓ | 12 | |
11.7 | odd | 10 | 8470.2.a.dc.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.j.71.1 | ✓ | 12 | 11.5 | even | 5 | inner | |
770.2.n.j.141.1 | yes | 12 | 1.1 | even | 1 | trivial | |
8470.2.a.cw.1.6 | 6 | 11.4 | even | 5 | |||
8470.2.a.dc.1.6 | 6 | 11.7 | odd | 10 |