Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (of order \(6\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 30.6 | ||
Root | \(-1.12906 - 0.851598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.30 |
Dual form | 637.2.u.i.361.6 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34104 | − | 1.35160i | 1.65536 | − | 0.955724i | 0.680549 | − | 0.732702i | \(-0.261741\pi\) |
0.974813 | − | 0.223022i | \(-0.0715921\pi\) | |||||||
\(3\) | 0.345949 | 0.199734 | 0.0998669 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998669 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(4\) | 2.65363 | − | 4.59623i | 1.32682 | − | 2.29811i | ||||
\(5\) | 2.82162 | + | 1.62906i | 1.26187 | + | 0.728539i | 0.973435 | − | 0.228962i | \(-0.0735332\pi\) |
0.288431 | + | 0.957501i | \(0.406867\pi\) | |||||||
\(6\) | 0.809880 | − | 0.467584i | 0.330632 | − | 0.190890i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 8.94020i | − | 3.16084i | ||||||
\(9\) | −2.88032 | −0.960106 | ||||||||
\(10\) | 8.80735 | 2.78513 | ||||||||
\(11\) | 1.84603i | 0.556598i | 0.960494 | + | 0.278299i | \(0.0897707\pi\) | ||||
−0.960494 | + | 0.278299i | \(0.910229\pi\) | |||||||
\(12\) | 0.918023 | − | 1.59006i | 0.265010 | − | 0.459011i | ||||
\(13\) | −3.60550 | + | 0.0186461i | −0.999987 | + | 0.00517151i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.976136 | + | 0.563573i | 0.252037 | + | 0.145514i | ||||
\(16\) | −6.77628 | − | 11.7369i | −1.69407 | − | 2.93422i | ||||
\(17\) | −1.07657 | + | 1.86467i | −0.261107 | + | 0.452250i | −0.966536 | − | 0.256530i | \(-0.917421\pi\) |
0.705430 | + | 0.708780i | \(0.250754\pi\) | |||||||
\(18\) | −6.74293 | + | 3.89303i | −1.58932 | + | 0.917597i | ||||
\(19\) | 2.40096i | 0.550817i | 0.961327 | + | 0.275408i | \(0.0888131\pi\) | ||||
−0.961327 | + | 0.275408i | \(0.911187\pi\) | |||||||
\(20\) | 14.9751 | − | 8.64587i | 3.34853 | − | 1.93328i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.49509 | + | 4.32162i | 0.531954 | + | 0.921372i | ||||
\(23\) | 0.906314 | + | 1.56978i | 0.188979 | + | 0.327322i | 0.944910 | − | 0.327329i | \(-0.106149\pi\) |
−0.755931 | + | 0.654652i | \(0.772815\pi\) | |||||||
\(24\) | − | 3.09285i | − | 0.631326i | ||||||
\(25\) | 2.80769 | + | 4.86305i | 0.561537 | + | 0.972611i | ||||
\(26\) | −8.41541 | + | 4.91684i | −1.65040 | + | 0.964272i | ||||
\(27\) | −2.03429 | −0.391500 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.36703 | − | 2.36777i | 0.253851 | − | 0.439683i | −0.710732 | − | 0.703463i | \(-0.751636\pi\) |
0.964583 | + | 0.263780i | \(0.0849693\pi\) | |||||||
\(30\) | 3.04689 | 0.556284 | ||||||||
\(31\) | −1.50893 | + | 0.871180i | −0.271011 | + | 0.156468i | −0.629347 | − | 0.777124i | \(-0.716678\pi\) |
0.358336 | + | 0.933593i | \(0.383344\pi\) | |||||||
\(32\) | −16.2422 | − | 9.37743i | −2.87124 | − | 1.65771i | ||||
\(33\) | 0.638632i | 0.111172i | ||||||||
\(34\) | 5.82036i | 0.998183i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.64331 | + | 13.2386i | −1.27389 | + | 2.20643i | ||||
\(37\) | 5.14042 | − | 2.96783i | 0.845081 | − | 0.487908i | −0.0139073 | − | 0.999903i | \(-0.504427\pi\) |
0.858988 | + | 0.511996i | \(0.171094\pi\) | |||||||
\(38\) | 3.24513 | + | 5.62072i | 0.526429 | + | 0.911802i | ||||
\(39\) | −1.24732 | + | 0.00645062i | −0.199731 | + | 0.00103293i | ||||
\(40\) | 14.5641 | − | 25.2258i | 2.30279 | − | 3.98855i | ||||
\(41\) | −3.65577 | − | 2.11066i | −0.570935 | − | 0.329629i | 0.186588 | − | 0.982438i | \(-0.440257\pi\) |
−0.757523 | + | 0.652809i | \(0.773590\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.34111 | − | 7.51903i | −0.662014 | − | 1.14664i | −0.980086 | − | 0.198575i | \(-0.936369\pi\) |
0.318072 | − | 0.948067i | \(-0.396965\pi\) | |||||||
\(44\) | 8.48477 | + | 4.89868i | 1.27913 | + | 0.738504i | ||||
\(45\) | −8.12716 | − | 4.69222i | −1.21153 | − | 0.699475i | ||||
\(46\) | 4.24343 | + | 2.44994i | 0.625659 | + | 0.361224i | ||||
\(47\) | −5.09027 | − | 2.93887i | −0.742493 | − | 0.428678i | 0.0804822 | − | 0.996756i | \(-0.474354\pi\) |
−0.822975 | + | 0.568078i | \(0.807687\pi\) | |||||||
\(48\) | −2.34425 | − | 4.06036i | −0.338363 | − | 0.586062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.1458 | + | 7.58972i | 1.85910 | + | 1.07335i | ||||
\(51\) | −0.372438 | + | 0.645082i | −0.0521518 | + | 0.0903296i | ||||
\(52\) | −9.48199 | + | 16.6212i | −1.31491 | + | 2.30495i | ||||
\(53\) | 4.65314 | + | 8.05947i | 0.639158 | + | 1.10705i | 0.985618 | + | 0.168989i | \(0.0540503\pi\) |
−0.346460 | + | 0.938065i | \(0.612616\pi\) | |||||||
\(54\) | −4.76235 | + | 2.74954i | −0.648074 | + | 0.374166i | ||||
\(55\) | −3.00729 | + | 5.20878i | −0.405503 | + | 0.702352i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.830609i | 0.110017i | ||||||||
\(58\) | − | 7.39071i | − | 0.970447i | ||||||
\(59\) | 9.31173 | + | 5.37613i | 1.21228 | + | 0.699912i | 0.963256 | − | 0.268584i | \(-0.0865557\pi\) |
0.249028 | + | 0.968496i | \(0.419889\pi\) | |||||||
\(60\) | 5.18062 | − | 2.99103i | 0.668815 | − | 0.386141i | ||||
\(61\) | −10.1101 | −1.29446 | −0.647231 | − | 0.762294i | \(-0.724073\pi\) | ||||
−0.647231 | + | 0.762294i | \(0.724073\pi\) | |||||||
\(62\) | −2.35497 | + | 4.07893i | −0.299081 | + | 0.518024i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −23.5929 | −2.94911 | ||||||||
\(65\) | −10.2037 | − | 5.82098i | −1.26562 | − | 0.722003i | ||||
\(66\) | 0.863173 | + | 1.49506i | 0.106249 | + | 0.184029i | ||||
\(67\) | − | 0.826916i | − | 0.101024i | −0.998723 | − | 0.0505119i | \(-0.983915\pi\) | ||
0.998723 | − | 0.0505119i | \(-0.0160853\pi\) | |||||||
\(68\) | 5.71365 | + | 9.89633i | 0.692881 | + | 1.20011i | ||||
\(69\) | 0.313538 | + | 0.543065i | 0.0377456 | + | 0.0653773i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.03884 | + | 1.17712i | −0.241965 | + | 0.139699i | −0.616080 | − | 0.787684i | \(-0.711280\pi\) |
0.374114 | + | 0.927383i | \(0.377947\pi\) | |||||||
\(72\) | 25.7506i | 3.03474i | ||||||||
\(73\) | 2.76680 | − | 1.59741i | 0.323829 | − | 0.186963i | −0.329269 | − | 0.944236i | \(-0.606802\pi\) |
0.653098 | + | 0.757273i | \(0.273469\pi\) | |||||||
\(74\) | 8.02261 | − | 13.8956i | 0.932610 | − | 1.61533i | ||||
\(75\) | 0.971316 | + | 1.68237i | 0.112158 | + | 0.194263i | ||||
\(76\) | 11.0353 | + | 6.37126i | 1.26584 | + | 0.730833i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.91130 | + | 1.70098i | −0.329640 | + | 0.192598i | ||||
\(79\) | −0.400955 | + | 0.694475i | −0.0451110 | + | 0.0781345i | −0.887699 | − | 0.460424i | \(-0.847697\pi\) |
0.842588 | + | 0.538558i | \(0.181031\pi\) | |||||||
\(80\) | − | 44.1559i | − | 4.93678i | ||||||
\(81\) | 7.93720 | 0.881911 | ||||||||
\(82\) | −11.4110 | −1.26014 | ||||||||
\(83\) | − | 9.97031i | − | 1.09438i | −0.837007 | − | 0.547192i | \(-0.815697\pi\) | ||
0.837007 | − | 0.547192i | \(-0.184303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.07534 | + | 3.50760i | −0.658963 | + | 0.380452i | ||||
\(86\) | −20.3254 | − | 11.7349i | −2.19175 | − | 1.26541i | ||||
\(87\) | 0.472923 | − | 0.819127i | 0.0507027 | − | 0.0878196i | ||||
\(88\) | 16.5039 | 1.75932 | ||||||||
\(89\) | 13.0886 | − | 7.55674i | 1.38739 | − | 0.801012i | 0.394373 | − | 0.918950i | \(-0.370962\pi\) |
0.993021 | + | 0.117938i | \(0.0376284\pi\) | |||||||
\(90\) | −25.3680 | −2.67402 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.62010 | 1.00296 | ||||||||
\(93\) | −0.522012 | + | 0.301384i | −0.0541301 | + | 0.0312520i | ||||
\(94\) | −15.8887 | −1.63879 | ||||||||
\(95\) | −3.91130 | + | 6.77458i | −0.401291 | + | 0.695057i | ||||
\(96\) | −5.61897 | − | 3.24411i | −0.573484 | − | 0.331101i | ||||
\(97\) | −7.99489 | + | 4.61585i | −0.811758 | + | 0.468669i | −0.847566 | − | 0.530690i | \(-0.821933\pi\) |
0.0358079 | + | 0.999359i | \(0.488600\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.31715i | − | 0.534394i | ||||||
\(100\) | 29.8023 | 2.98023 | ||||||||
\(101\) | 14.8234 | 1.47498 | 0.737491 | − | 0.675357i | \(-0.236011\pi\) | ||||
0.737491 | + | 0.675357i | \(0.236011\pi\) | |||||||
\(102\) | 2.01355i | 0.199371i | ||||||||
\(103\) | 2.14143 | − | 3.70907i | 0.211001 | − | 0.365465i | −0.741027 | − | 0.671475i | \(-0.765661\pi\) |
0.952028 | + | 0.306010i | \(0.0989942\pi\) | |||||||
\(104\) | 0.166700 | + | 32.2339i | 0.0163463 | + | 3.16079i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.7863 | + | 12.5783i | 2.11608 | + | 1.22172i | ||||
\(107\) | 9.56289 | + | 16.5634i | 0.924479 | + | 1.60124i | 0.792397 | + | 0.610006i | \(0.208833\pi\) |
0.132082 | + | 0.991239i | \(0.457834\pi\) | |||||||
\(108\) | −5.39827 | + | 9.35007i | −0.519448 | + | 0.899711i | ||||
\(109\) | 3.69925 | − | 2.13577i | 0.354324 | − | 0.204569i | −0.312264 | − | 0.949995i | \(-0.601087\pi\) |
0.666588 | + | 0.745426i | \(0.267754\pi\) | |||||||
\(110\) | 16.2586i | 1.55020i | ||||||||
\(111\) | 1.77833 | − | 1.02672i | 0.168791 | − | 0.0974516i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.37488 | − | 2.38137i | −0.129338 | − | 0.224020i | 0.794082 | − | 0.607810i | \(-0.207952\pi\) |
−0.923420 | + | 0.383790i | \(0.874619\pi\) | |||||||
\(114\) | 1.12265 | + | 1.94448i | 0.105146 | + | 0.182118i | ||||
\(115\) | 5.90576i | 0.550715i | ||||||||
\(116\) | −7.25520 | − | 12.5664i | −0.673629 | − | 1.16676i | ||||
\(117\) | 10.3850 | − | 0.0537068i | 0.960094 | − | 0.00496520i | ||||
\(118\) | 29.0655 | 2.67569 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.03845 | − | 8.72685i | 0.459945 | − | 0.796649i | ||||
\(121\) | 7.59218 | 0.690198 | ||||||||
\(122\) | −23.6680 | + | 13.6648i | −2.14280 | + | 1.23715i | ||||
\(123\) | −1.26471 | − | 0.730180i | −0.114035 | − | 0.0658381i | ||||
\(124\) | 9.24717i | 0.830420i | ||||||||
\(125\) | 2.00495i | 0.179329i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.86719 | + | 8.43022i | −0.431893 | + | 0.748061i | −0.997036 | − | 0.0769320i | \(-0.975488\pi\) |
0.565143 | + | 0.824993i | \(0.308821\pi\) | |||||||
\(128\) | −22.7475 | + | 13.1333i | −2.01061 | + | 1.16083i | ||||
\(129\) | −1.50181 | − | 2.60120i | −0.132227 | − | 0.229023i | ||||
\(130\) | −31.7549 | + | 0.164223i | −2.78509 | + | 0.0144033i | ||||
\(131\) | −9.33073 | + | 16.1613i | −0.815230 | + | 1.41202i | 0.0939330 | + | 0.995579i | \(0.470056\pi\) |
−0.909163 | + | 0.416441i | \(0.863277\pi\) | |||||||
\(132\) | 2.93530 | + | 1.69470i | 0.255485 | + | 0.147504i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.11766 | − | 1.93584i | −0.0965509 | − | 0.167231i | ||||
\(135\) | −5.73999 | − | 3.31399i | −0.494020 | − | 0.285223i | ||||
\(136\) | 16.6706 | + | 9.62475i | 1.42949 | + | 0.825315i | ||||
\(137\) | 7.29328 | + | 4.21078i | 0.623107 | + | 0.359751i | 0.778078 | − | 0.628168i | \(-0.216195\pi\) |
−0.154971 | + | 0.987919i | \(0.549528\pi\) | |||||||
\(138\) | 1.46801 | + | 0.847556i | 0.124965 | + | 0.0721488i | ||||
\(139\) | −8.81809 | − | 15.2734i | −0.747941 | − | 1.29547i | −0.948808 | − | 0.315853i | \(-0.897709\pi\) |
0.200867 | − | 0.979619i | \(-0.435624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.76098 | − | 1.01670i | −0.148301 | − | 0.0856216i | ||||
\(142\) | −3.18199 | + | 5.51138i | −0.267027 | + | 0.462504i | ||||
\(143\) | −0.0344213 | − | 6.65586i | −0.00287845 | − | 0.556591i | ||||
\(144\) | 19.5179 | + | 33.8059i | 1.62649 | + | 2.81716i | ||||
\(145\) | 7.71448 | − | 4.45396i | 0.640653 | − | 0.369881i | ||||
\(146\) | 4.31811 | − | 7.47919i | 0.357370 | − | 0.618982i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 31.5021i | − | 2.58946i | ||||||
\(149\) | − | 4.02104i | − | 0.329416i | −0.986342 | − | 0.164708i | \(-0.947332\pi\) | ||
0.986342 | − | 0.164708i | \(-0.0526683\pi\) | |||||||
\(150\) | 4.54777 | + | 2.62566i | 0.371324 | + | 0.214384i | ||||
\(151\) | −16.3687 | + | 9.45048i | −1.33207 | + | 0.769069i | −0.985616 | − | 0.168999i | \(-0.945947\pi\) |
−0.346451 | + | 0.938068i | \(0.612613\pi\) | |||||||
\(152\) | 21.4650 | 1.74104 | ||||||||
\(153\) | 3.10086 | − | 5.37086i | 0.250690 | − | 0.434208i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.67682 | −0.455973 | ||||||||
\(156\) | −3.28029 | + | 5.75009i | −0.262633 | + | 0.460376i | ||||
\(157\) | −5.78677 | − | 10.0230i | −0.461835 | − | 0.799922i | 0.537218 | − | 0.843444i | \(-0.319475\pi\) |
−0.999052 | + | 0.0435222i | \(0.986142\pi\) | |||||||
\(158\) | 2.16772i | 0.172455i | ||||||||
\(159\) | 1.60975 | + | 2.78817i | 0.127661 | + | 0.221116i | ||||
\(160\) | −30.5528 | − | 52.9190i | −2.41541 | − | 4.18362i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 18.5813 | − | 10.7279i | 1.45988 | − | 0.842863i | ||||
\(163\) | − | 4.40542i | − | 0.345059i | −0.985004 | − | 0.172529i | \(-0.944806\pi\) | ||
0.985004 | − | 0.172529i | \(-0.0551940\pi\) | |||||||
\(164\) | −19.4021 | + | 11.2018i | −1.51505 | + | 0.874716i | ||||
\(165\) | −1.04037 | + | 1.80197i | −0.0809927 | + | 0.140284i | ||||
\(166\) | −13.4759 | − | 23.3409i | −1.04593 | − | 1.81160i | ||||
\(167\) | 7.81076 | + | 4.50954i | 0.604415 | + | 0.348959i | 0.770776 | − | 0.637106i | \(-0.219869\pi\) |
−0.166362 | + | 0.986065i | \(0.553202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9993 | − | 0.134457i | 0.999947 | − | 0.0103429i | ||||
\(170\) | −9.48173 | + | 16.4228i | −0.727215 | + | 1.25957i | ||||
\(171\) | − | 6.91552i | − | 0.528843i | ||||||
\(172\) | −46.0789 | −3.51349 | ||||||||
\(173\) | 6.09200 | 0.463166 | 0.231583 | − | 0.972815i | \(-0.425609\pi\) | ||||
0.231583 | + | 0.972815i | \(0.425609\pi\) | |||||||
\(174\) | − | 2.55681i | − | 0.193831i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.6666 | − | 12.5092i | 1.63318 | − | 0.942917i | ||||
\(177\) | 3.22139 | + | 1.85987i | 0.242134 | + | 0.139796i | ||||
\(178\) | 20.4273 | − | 35.3812i | 1.53109 | − | 2.65193i | ||||
\(179\) | −3.87964 | −0.289978 | −0.144989 | − | 0.989433i | \(-0.546315\pi\) | ||||
−0.144989 | + | 0.989433i | \(0.546315\pi\) | |||||||
\(180\) | −43.1330 | + | 24.9029i | −3.21495 | + | 1.85615i | ||||
\(181\) | 6.58392 | 0.489379 | 0.244690 | − | 0.969601i | \(-0.421314\pi\) | ||||
0.244690 | + | 0.969601i | \(0.421314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.49757 | −0.258548 | ||||||||
\(184\) | 14.0342 | − | 8.10262i | 1.03461 | − | 0.597333i | ||||
\(185\) | 19.3391 | 1.42184 | ||||||||
\(186\) | −0.814700 | + | 1.41110i | −0.0597367 | + | 0.103467i | ||||
\(187\) | −3.44224 | − | 1.98738i | −0.251721 | − | 0.145331i | ||||
\(188\) | −27.0155 | + | 15.5974i | −1.97030 | + | 1.13756i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.1460i | 1.53410i | ||||||||
\(191\) | −13.7434 | −0.994435 | −0.497218 | − | 0.867626i | \(-0.665645\pi\) | ||||
−0.497218 | + | 0.867626i | \(0.665645\pi\) | |||||||
\(192\) | −8.16195 | −0.589038 | ||||||||
\(193\) | − | 22.7530i | − | 1.63780i | −0.573937 | − | 0.818899i | \(-0.694585\pi\) | ||
0.573937 | − | 0.818899i | \(-0.305415\pi\) | |||||||
\(194\) | −12.4776 | + | 21.6118i | −0.895836 | + | 1.55163i | ||||
\(195\) | −3.52997 | − | 2.01376i | −0.252786 | − | 0.144208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.5809 | − | 7.26358i | −0.896352 | − | 0.517509i | −0.0203371 | − | 0.999793i | \(-0.506474\pi\) |
−0.876015 | + | 0.482284i | \(0.839807\pi\) | |||||||
\(198\) | −7.18665 | − | 12.4476i | −0.510733 | − | 0.884615i | ||||
\(199\) | −11.9202 | + | 20.6464i | −0.845001 | + | 1.46358i | 0.0406192 | + | 0.999175i | \(0.487067\pi\) |
−0.885620 | + | 0.464410i | \(0.846266\pi\) | |||||||
\(200\) | 43.4767 | − | 25.1013i | 3.07426 | − | 1.77493i | ||||
\(201\) | − | 0.286071i | − | 0.0201779i | ||||||
\(202\) | 34.7021 | − | 20.0353i | 2.44163 | − | 1.40968i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.97663 | + | 3.42363i | 0.138392 | + | 0.239702i | ||||
\(205\) | −6.87678 | − | 11.9109i | −0.480295 | − | 0.831896i | ||||
\(206\) | − | 11.5774i | − | 0.806637i | ||||||
\(207\) | −2.61047 | − | 4.52147i | −0.181440 | − | 0.314264i | ||||
\(208\) | 24.6508 | + | 42.1910i | 1.70922 | + | 2.92542i | ||||
\(209\) | −4.43223 | −0.306584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.15764 | + | 3.73714i | −0.148538 | + | 0.257275i | −0.930687 | − | 0.365816i | \(-0.880790\pi\) |
0.782149 | + | 0.623091i | \(0.214123\pi\) | |||||||
\(212\) | 49.3909 | 3.39218 | ||||||||
\(213\) | −0.705334 | + | 0.407225i | −0.0483287 | + | 0.0279026i | ||||
\(214\) | 44.7741 | + | 25.8504i | 3.06070 | + | 1.76709i | ||||
\(215\) | − | 28.2878i | − | 1.92921i | ||||||
\(216\) | 18.1870i | 1.23747i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.77339 | − | 9.99981i | 0.391024 | − | 0.677273i | ||||
\(219\) | 0.957171 | − | 0.552623i | 0.0646796 | − | 0.0373428i | ||||
\(220\) | 15.9605 | + | 27.6444i | 1.07606 | + | 1.86379i | ||||
\(221\) | 3.84681 | − | 6.74316i | 0.258764 | − | 0.453594i | ||||
\(222\) | 2.77542 | − | 4.80716i | 0.186274 | − | 0.322636i | ||||
\(223\) | 20.2604 | + | 11.6973i | 1.35674 | + | 0.783312i | 0.989182 | − | 0.146691i | \(-0.0468623\pi\) |
0.367553 | + | 0.930003i | \(0.380196\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.08703 | − | 14.0071i | −0.539135 | − | 0.933810i | ||||
\(226\) | −6.43730 | − | 3.71658i | −0.428203 | − | 0.247223i | ||||
\(227\) | −23.1427 | − | 13.3614i | −1.53603 | − | 0.886829i | −0.999065 | − | 0.0432270i | \(-0.986236\pi\) |
−0.536968 | − | 0.843602i | \(-0.680431\pi\) | |||||||
\(228\) | 3.81767 | + | 2.20413i | 0.252831 | + | 0.145972i | ||||
\(229\) | 2.60388 | + | 1.50335i | 0.172069 | + | 0.0993442i | 0.583561 | − | 0.812069i | \(-0.301659\pi\) |
−0.411492 | + | 0.911413i | \(0.634992\pi\) | |||||||
\(230\) | 7.98222 | + | 13.8256i | 0.526332 | + | 0.911634i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.1683 | − | 12.2215i | −1.38977 | − | 0.802383i | ||||
\(233\) | −5.85740 | + | 10.1453i | −0.383731 | + | 0.664641i | −0.991592 | − | 0.129402i | \(-0.958694\pi\) |
0.607861 | + | 0.794043i | \(0.292028\pi\) | |||||||
\(234\) | 24.2391 | − | 14.1621i | 1.58456 | − | 0.925804i | ||||
\(235\) | −9.57521 | − | 16.5847i | −0.624618 | − | 1.08187i | ||||
\(236\) | 49.4199 | − | 28.5326i | 3.21696 | − | 1.85731i | ||||
\(237\) | −0.138710 | + | 0.240253i | −0.00901019 | + | 0.0156061i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.42797i | − | 0.0923677i | −0.998933 | − | 0.0461838i | \(-0.985294\pi\) | ||
0.998933 | − | 0.0461838i | \(-0.0147060\pi\) | |||||||
\(240\) | − | 15.2757i | − | 0.986043i | ||||||
\(241\) | −2.32068 | − | 1.33984i | −0.149488 | − | 0.0863069i | 0.423390 | − | 0.905947i | \(-0.360840\pi\) |
−0.572878 | + | 0.819640i | \(0.694173\pi\) | |||||||
\(242\) | 17.7736 | − | 10.2616i | 1.14253 | − | 0.659639i | ||||
\(243\) | 8.84874 | 0.567647 | ||||||||
\(244\) | −26.8284 | + | 46.4682i | −1.71751 | + | 2.97482i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.94764 | −0.251692 | ||||||||
\(247\) | −0.0447686 | − | 8.65665i | −0.00284856 | − | 0.550810i | ||||
\(248\) | 7.78852 | + | 13.4901i | 0.494571 | + | 0.856623i | ||||
\(249\) | − | 3.44922i | − | 0.218586i | ||||||
\(250\) | 2.70989 | + | 4.69367i | 0.171389 | + | 0.296854i | ||||
\(251\) | −5.46696 | − | 9.46906i | −0.345072 | − | 0.597681i | 0.640295 | − | 0.768129i | \(-0.278812\pi\) |
−0.985367 | + | 0.170447i | \(0.945479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.89786 | + | 1.67308i | −0.182187 | + | 0.105186i | ||||
\(254\) | 26.3139i | 1.65108i | ||||||||
\(255\) | −2.10176 | + | 1.21345i | −0.131617 | + | 0.0759892i | ||||
\(256\) | −11.9089 | + | 20.6268i | −0.744307 | + | 1.28918i | ||||
\(257\) | −2.07569 | − | 3.59520i | −0.129478 | − | 0.224262i | 0.793996 | − | 0.607922i | \(-0.207997\pi\) |
−0.923474 | + | 0.383660i | \(0.874663\pi\) | |||||||
\(258\) | −7.03156 | − | 4.05967i | −0.437766 | − | 0.252744i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −53.8315 | + | 31.4519i | −3.33849 | + | 1.95057i | ||||
\(261\) | −3.93749 | + | 6.81993i | −0.243724 | + | 0.422143i | ||||
\(262\) | 50.4456i | 3.11654i | ||||||||
\(263\) | 4.05360 | 0.249955 | 0.124978 | − | 0.992160i | \(-0.460114\pi\) | ||||
0.124978 | + | 0.992160i | \(0.460114\pi\) | |||||||
\(264\) | 5.70949 | 0.351395 | ||||||||
\(265\) | 30.3210i | 1.86260i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.52801 | − | 2.61425i | 0.277110 | − | 0.159989i | ||||
\(268\) | −3.80069 | − | 2.19433i | −0.232164 | − | 0.134040i | ||||
\(269\) | 2.00011 | − | 3.46430i | 0.121949 | − | 0.211222i | −0.798587 | − | 0.601879i | \(-0.794419\pi\) |
0.920536 | + | 0.390657i | \(0.127752\pi\) | |||||||
\(270\) | −17.9167 | −1.09038 | ||||||||
\(271\) | −2.41189 | + | 1.39251i | −0.146512 | + | 0.0845888i | −0.571464 | − | 0.820627i | \(-0.693624\pi\) |
0.424952 | + | 0.905216i | \(0.360291\pi\) | |||||||
\(272\) | 29.1806 | 1.76933 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.7651 | 1.37529 | ||||||||
\(275\) | −8.97733 | + | 5.18306i | −0.541353 | + | 0.312551i | ||||
\(276\) | 3.32807 | 0.200326 | ||||||||
\(277\) | 8.34618 | − | 14.4560i | 0.501474 | − | 0.868578i | −0.498525 | − | 0.866875i | \(-0.666125\pi\) |
0.999999 | − | 0.00170243i | \(-0.000541901\pi\) | |||||||
\(278\) | −41.2870 | − | 23.8370i | −2.47623 | − | 1.42965i | ||||
\(279\) | 4.34619 | − | 2.50928i | 0.260200 | − | 0.150226i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.3731i | − | 0.797774i | −0.917000 | − | 0.398887i | \(-0.869397\pi\) | ||
0.917000 | − | 0.398887i | \(-0.130603\pi\) | |||||||
\(282\) | −5.49668 | −0.327322 | ||||||||
\(283\) | −18.8862 | −1.12267 | −0.561335 | − | 0.827589i | \(-0.689712\pi\) | ||||
−0.561335 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(284\) | 12.4946i | 0.741419i | ||||||||
\(285\) | −1.35311 | + | 2.34366i | −0.0801515 | + | 0.138826i | ||||
\(286\) | −9.07663 | − | 15.5351i | −0.536712 | − | 0.918609i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 46.7827 | + | 27.0100i | 2.75669 | + | 1.59158i | ||||
\(289\) | 6.18199 | + | 10.7075i | 0.363647 | + | 0.629855i | ||||
\(290\) | 12.0399 | − | 20.8537i | 0.707008 | − | 1.22457i | ||||
\(291\) | −2.76583 | + | 1.59685i | −0.162136 | + | 0.0936090i | ||||
\(292\) | − | 16.9558i | − | 0.992262i | ||||||
\(293\) | 2.95999 | − | 1.70895i | 0.172925 | − | 0.0998380i | −0.411040 | − | 0.911617i | \(-0.634834\pi\) |
0.583964 | + | 0.811779i | \(0.301501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5161 | + | 30.3388i | 1.01983 | + | 1.76639i | ||||
\(296\) | −26.5329 | − | 45.9564i | −1.54220 | − | 2.67116i | ||||
\(297\) | − | 3.75536i | − | 0.217908i | ||||||
\(298\) | −5.43483 | − | 9.41340i | −0.314831 | − | 0.545304i | ||||
\(299\) | −3.29699 | − | 5.64295i | −0.190670 | − | 0.326340i | ||||
\(300\) | 10.3101 | 0.595252 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.5465 | + | 44.2479i | −1.47004 | + | 2.54618i | ||||
\(303\) | 5.12814 | 0.294604 | ||||||||
\(304\) | 28.1797 | − | 16.2696i | 1.61622 | − | 0.933123i | ||||
\(305\) | −28.5268 | − | 16.4699i | −1.63344 | − | 0.943066i | ||||
\(306\) | − | 16.7645i | − | 0.958362i | ||||||
\(307\) | − | 16.3679i | − | 0.934165i | −0.884214 | − | 0.467083i | \(-0.845305\pi\) | ||
0.884214 | − | 0.467083i | \(-0.154695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.740826 | − | 1.28315i | 0.0421441 | − | 0.0729958i | ||||
\(310\) | −13.2896 | + | 7.67278i | −0.754801 | + | 0.435785i | ||||
\(311\) | −11.8489 | − | 20.5230i | −0.671891 | − | 1.16375i | −0.977367 | − | 0.211550i | \(-0.932149\pi\) |
0.305476 | − | 0.952200i | \(-0.401184\pi\) | |||||||
\(312\) | 0.0576698 | + | 11.1513i | 0.00326491 | + | 0.631318i | ||||
\(313\) | −2.59013 | + | 4.48623i | −0.146403 | + | 0.253577i | −0.929895 | − | 0.367824i | \(-0.880103\pi\) |
0.783493 | + | 0.621401i | \(0.213436\pi\) | |||||||
\(314\) | −27.0941 | − | 15.6428i | −1.52901 | − | 0.882774i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.12798 | + | 3.68577i | 0.119708 | + | 0.207341i | ||||
\(317\) | −5.25276 | − | 3.03268i | −0.295024 | − | 0.170332i | 0.345181 | − | 0.938536i | \(-0.387817\pi\) |
−0.640206 | + | 0.768204i | \(0.721151\pi\) | |||||||
\(318\) | 7.53697 | + | 4.35147i | 0.422652 | + | 0.244018i | ||||
\(319\) | 4.37096 | + | 2.52358i | 0.244727 | + | 0.141293i | ||||
\(320\) | −66.5702 | − | 38.4343i | −3.72139 | − | 2.14854i | ||||
\(321\) | 3.30827 | + | 5.73010i | 0.184650 | + | 0.319823i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.47700 | − | 2.58480i | −0.249107 | − | 0.143822i | ||||
\(324\) | 21.0624 | − | 36.4812i | 1.17013 | − | 2.02673i | ||||
\(325\) | −10.2138 | − | 17.4814i | −0.566559 | − | 0.969694i | ||||
\(326\) | −5.95435 | − | 10.3132i | −0.329781 | − | 0.571198i | ||||
\(327\) | 1.27975 | − | 0.738866i | 0.0707706 | − | 0.0408594i | ||||
\(328\) | −18.8697 | + | 32.6833i | −1.04190 | + | 1.80463i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.62465i | 0.309627i | ||||||||
\(331\) | 17.2749i | 0.949512i | 0.880118 | + | 0.474756i | \(0.157464\pi\) | ||||
−0.880118 | + | 0.474756i | \(0.842536\pi\) | |||||||
\(332\) | −45.8258 | − | 26.4576i | −2.51502 | − | 1.45205i | ||||
\(333\) | −14.8061 | + | 8.54829i | −0.811367 | + | 0.468443i | ||||
\(334\) | 24.3804 | 1.33403 | ||||||||
\(335\) | 1.34710 | − | 2.33324i | 0.0735998 | − | 0.127479i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.35464 | −0.455106 | −0.227553 | − | 0.973766i | \(-0.573073\pi\) | ||||
−0.227553 | + | 0.973766i | \(0.573073\pi\) | |||||||
\(338\) | 30.2501 | − | 17.8846i | 1.64539 | − | 0.972794i | ||||
\(339\) | −0.475639 | − | 0.823832i | −0.0258332 | − | 0.0447444i | ||||
\(340\) | 37.2315i | 2.01916i | ||||||||
\(341\) | −1.60822 | − | 2.78552i | −0.0870901 | − | 0.150844i | ||||
\(342\) | −9.34700 | − | 16.1895i | −0.505428 | − | 0.875427i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −67.2216 | + | 38.8104i | −3.62435 | + | 2.09252i | ||||
\(345\) | 2.04309i | 0.109997i | ||||||||
\(346\) | 14.2616 | − | 8.23394i | 0.766708 | − | 0.442659i | ||||
\(347\) | −14.4110 | + | 24.9606i | −0.773623 | + | 1.33995i | 0.161942 | + | 0.986800i | \(0.448224\pi\) |
−0.935565 | + | 0.353154i | \(0.885109\pi\) | |||||||
\(348\) | −2.50993 | − | 4.34733i | −0.134546 | − | 0.233041i | ||||
\(349\) | 10.1516 | + | 5.86103i | 0.543403 | + | 0.313734i | 0.746457 | − | 0.665434i | \(-0.231753\pi\) |
−0.203054 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.33464 | − | 0.0379317i | 0.391494 | − | 0.00202464i | ||||
\(352\) | 17.3110 | − | 29.9835i | 0.922679 | − | 1.59813i | ||||
\(353\) | 17.8362i | 0.949326i | 0.880168 | + | 0.474663i | \(0.157430\pi\) | ||||
−0.880168 | + | 0.474663i | \(0.842570\pi\) | |||||||
\(354\) | 10.0552 | 0.534426 | ||||||||
\(355\) | −7.67043 | −0.407104 | ||||||||
\(356\) | − | 80.2113i | − | 4.25119i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.08239 | + | 5.24372i | −0.480019 | + | 0.277139i | ||||
\(359\) | −4.92042 | − | 2.84081i | −0.259690 | − | 0.149932i | 0.364503 | − | 0.931202i | \(-0.381239\pi\) |
−0.624193 | + | 0.781270i | \(0.714572\pi\) | |||||||
\(360\) | −41.9494 | + | 72.6584i | −2.21093 | + | 3.82943i | ||||
\(361\) | 13.2354 | 0.696601 | ||||||||
\(362\) | 15.4132 | − | 8.89882i | 0.810100 | − | 0.467712i | ||||
\(363\) | 2.62651 | 0.137856 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4091 | 0.544838 | ||||||||
\(366\) | −8.18794 | + | 4.72731i | −0.427991 | + | 0.247100i | ||||
\(367\) | 19.6316 | 1.02476 | 0.512381 | − | 0.858758i | \(-0.328764\pi\) | ||||
0.512381 | + | 0.858758i | \(0.328764\pi\) | |||||||
\(368\) | 12.2829 | − | 21.2746i | 0.640289 | − | 1.10901i | ||||
\(369\) | 10.5298 | + | 6.07937i | 0.548158 | + | 0.316479i | ||||
\(370\) | 45.2735 | − | 26.1387i | 2.35366 | − | 1.35888i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.19905i | 0.165863i | ||||||||
\(373\) | 32.0645 | 1.66024 | 0.830119 | − | 0.557586i | \(-0.188272\pi\) | ||||
0.830119 | + | 0.557586i | \(0.188272\pi\) | |||||||
\(374\) | −10.7445 | −0.555587 | ||||||||
\(375\) | 0.693612i | 0.0358180i | ||||||||
\(376\) | −26.2741 | + | 45.5081i | −1.35498 | + | 2.34690i | ||||
\(377\) | −4.88468 | + | 8.56248i | −0.251574 | + | 0.440990i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4745 | − | 9.51154i | −0.846237 | − | 0.488575i | 0.0131425 | − | 0.999914i | \(-0.495816\pi\) |
−0.859379 | + | 0.511339i | \(0.829150\pi\) | |||||||
\(380\) | 20.7583 | + | 35.9545i | 1.06488 | + | 1.84443i | ||||
\(381\) | −1.68380 | + | 2.91643i | −0.0862637 | + | 0.149413i | ||||
\(382\) | −32.1737 | + | 18.5755i | −1.64615 | + | 0.950406i | ||||
\(383\) | − | 0.699829i | − | 0.0357596i | −0.999840 | − | 0.0178798i | \(-0.994308\pi\) | ||
0.999840 | − | 0.0178798i | \(-0.00569162\pi\) | |||||||
\(384\) | −7.86948 | + | 4.54345i | −0.401588 | + | 0.231857i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.7529 | − | 53.2657i | −1.56528 | − | 2.71115i | ||||
\(387\) | 12.5038 | + | 21.6572i | 0.635604 | + | 1.10090i | ||||
\(388\) | 48.9951i | 2.48735i | ||||||||
\(389\) | −10.0274 | − | 17.3679i | −0.508407 | − | 0.880587i | −0.999953 | − | 0.00973506i | \(-0.996901\pi\) |
0.491545 | − | 0.870852i | \(-0.336432\pi\) | |||||||
\(390\) | −10.9856 | + | 0.0568128i | −0.556277 | + | 0.00287683i | ||||
\(391\) | −3.90284 | −0.197375 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.22796 | + | 5.59099i | −0.162829 | + | 0.282028i | ||||
\(394\) | −39.2698 | −1.97838 | ||||||||
\(395\) | −2.26269 | + | 1.30636i | −0.113848 | + | 0.0657302i | ||||
\(396\) | −24.4388 | − | 14.1098i | −1.22810 | − | 0.709043i | ||||
\(397\) | 22.2803i | 1.11822i | 0.829095 | + | 0.559108i | \(0.188856\pi\) | ||||
−0.829095 | + | 0.559108i | \(0.811144\pi\) | |||||||
\(398\) | 64.4453i | 3.23035i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 38.0513 | − | 65.9069i | 1.90257 | − | 3.29534i | ||||
\(401\) | 4.16341 | − | 2.40374i | 0.207911 | − | 0.120037i | −0.392429 | − | 0.919782i | \(-0.628365\pi\) |
0.600340 | + | 0.799745i | \(0.295032\pi\) | |||||||
\(402\) | −0.386653 | − | 0.669702i | −0.0192845 | − | 0.0334017i | ||||
\(403\) | 5.42420 | − | 3.16918i | 0.270199 | − | 0.157868i | ||||
\(404\) | 39.3358 | − | 68.1317i | 1.95703 | − | 3.38968i | ||||
\(405\) | 22.3957 | + | 12.9302i | 1.11285 | + | 0.642506i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.47869 | + | 9.48937i | 0.271568 | + | 0.470370i | ||||
\(408\) | 5.76716 | + | 3.32967i | 0.285517 | + | 0.164843i | ||||
\(409\) | 31.8727 | + | 18.4017i | 1.57601 | + | 0.909907i | 0.995409 | + | 0.0957164i | \(0.0305142\pi\) |
0.580597 | + | 0.814191i | \(0.302819\pi\) | |||||||
\(410\) | −32.1976 | − | 18.5893i | −1.59013 | − | 0.918060i | ||||
\(411\) | 2.52310 | + | 1.45672i | 0.124456 | + | 0.0718545i | ||||
\(412\) | −11.3651 | − | 19.6850i | −0.559921 | − | 0.969811i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.2224 | − | 7.05662i | −0.600699 | − | 0.346814i | ||||
\(415\) | 16.2423 | − | 28.1324i | 0.797301 | − | 1.38097i | ||||
\(416\) | 58.7361 | + | 33.5075i | 2.87977 | + | 1.64284i | ||||
\(417\) | −3.05061 | − | 5.28382i | −0.149389 | − | 0.258750i | ||||
\(418\) | −10.3760 | + | 5.99059i | −0.507507 | + | 0.293009i | ||||
\(419\) | 14.6334 | − | 25.3457i | 0.714887 | − | 1.23822i | −0.248116 | − | 0.968730i | \(-0.579812\pi\) |
0.963003 | − | 0.269490i | \(-0.0868552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.53862i | 0.367410i | 0.982981 | + | 0.183705i | \(0.0588091\pi\) | ||||
−0.982981 | + | 0.183705i | \(0.941191\pi\) | |||||||
\(422\) | 11.6650i | 0.567845i | ||||||||
\(423\) | 14.6616 | + | 8.46489i | 0.712872 | + | 0.411577i | ||||
\(424\) | 72.0533 | − | 41.6000i | 3.49922 | − | 2.02027i | ||||
\(425\) | −12.0907 | −0.586484 | ||||||||
\(426\) | −1.10081 | + | 1.90666i | −0.0533343 | + | 0.0923778i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 101.506 | 4.90646 | ||||||||
\(429\) | −0.0119080 | − | 2.30259i | −0.000574925 | − | 0.111170i | ||||
\(430\) | −38.2337 | − | 66.2227i | −1.84379 | − | 3.19354i | ||||
\(431\) | 31.2261i | 1.50411i | 0.659101 | + | 0.752055i | \(0.270937\pi\) | ||||
−0.659101 | + | 0.752055i | \(0.729063\pi\) | |||||||
\(432\) | 13.7849 | + | 23.8762i | 0.663228 | + | 1.14874i | ||||
\(433\) | −2.94202 | − | 5.09573i | −0.141384 | − | 0.244885i | 0.786634 | − | 0.617420i | \(-0.211822\pi\) |
−0.928018 | + | 0.372535i | \(0.878489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.66882 | − | 1.54084i | 0.127960 | − | 0.0738777i | ||||
\(436\) | − | 22.6702i | − | 1.08570i | ||||||
\(437\) | −3.76898 | + | 2.17602i | −0.180295 | + | 0.104093i | ||||
\(438\) | 1.49385 | − | 2.58742i | 0.0713788 | − | 0.123632i | ||||
\(439\) | 4.97821 | + | 8.62251i | 0.237597 | + | 0.411530i | 0.960024 | − | 0.279917i | \(-0.0903069\pi\) |
−0.722427 | + | 0.691447i | \(0.756974\pi\) | |||||||
\(440\) | 46.5676 | + | 26.8858i | 2.22002 | + | 1.28173i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.108527 | − | 20.9853i | −0.00516212 | − | 0.998170i | ||||
\(443\) | 17.9406 | − | 31.0741i | 0.852385 | − | 1.47637i | −0.0266653 | − | 0.999644i | \(-0.508489\pi\) |
0.879050 | − | 0.476729i | \(-0.158178\pi\) | |||||||
\(444\) | − | 10.8981i | − | 0.517202i | ||||||
\(445\) | 49.2416 | 2.33427 | ||||||||
\(446\) | 63.2404 | 2.99452 | ||||||||
\(447\) | − | 1.39108i | − | 0.0657956i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.46001 | − | 1.99764i | 0.163288 | − | 0.0942744i | −0.416129 | − | 0.909306i | \(-0.636614\pi\) |
0.579417 | + | 0.815031i | \(0.303280\pi\) | |||||||
\(450\) | −37.8641 | − | 21.8608i | −1.78493 | − | 1.03053i | ||||
\(451\) | 3.89633 | − | 6.74864i | 0.183471 | − | 0.317781i | ||||
\(452\) | −14.5937 | −0.686432 | ||||||||
\(453\) | −5.66274 | + | 3.26939i | −0.266059 | + | 0.153609i | ||||
\(454\) | −72.2371 | −3.39026 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.42580 | 0.347745 | ||||||||
\(457\) | −35.6995 | + | 20.6111i | −1.66995 | + | 0.964147i | −0.702291 | + | 0.711890i | \(0.747840\pi\) |
−0.967660 | + | 0.252257i | \(0.918827\pi\) | |||||||
\(458\) | 8.12770 | 0.379783 | ||||||||
\(459\) | 2.19006 | − | 3.79329i | 0.102223 | − | 0.177056i | ||||
\(460\) | 27.1443 | + | 15.6717i | 1.26561 | + | 0.730699i | ||||
\(461\) | −21.4139 | + | 12.3633i | −0.997343 | + | 0.575816i | −0.907461 | − | 0.420136i | \(-0.861982\pi\) |
−0.0898818 | + | 0.995952i | \(0.528649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4057i | 1.13423i | 0.823639 | + | 0.567115i | \(0.191940\pi\) | ||||
−0.823639 | + | 0.567115i | \(0.808060\pi\) | |||||||
\(464\) | −37.0536 | −1.72017 | ||||||||
\(465\) | −1.96389 | −0.0910733 | ||||||||
\(466\) | 31.6674i | 1.46696i | ||||||||
\(467\) | 2.22430 | − | 3.85260i | 0.102928 | − | 0.178277i | −0.809962 | − | 0.586483i | \(-0.800512\pi\) |
0.912890 | + | 0.408206i | \(0.133845\pi\) | |||||||
\(468\) | 27.3111 | − | 47.8744i | 1.26246 | − | 2.21299i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −44.8318 | − | 25.8837i | −2.06794 | − | 1.19392i | ||||
\(471\) | −2.00193 | − | 3.46744i | −0.0922441 | − | 0.159771i | ||||
\(472\) | 48.0637 | − | 83.2487i | 2.21231 | − | 3.83183i | ||||
\(473\) | 13.8803 | − | 8.01382i | 0.638219 | − | 0.368476i | ||||
\(474\) | 0.749922i | 0.0344450i | ||||||||
\(475\) | −11.6760 | + | 6.74113i | −0.535730 | + | 0.309304i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4025 | − | 23.2139i | −0.613660 | − | 1.06289i | ||||
\(478\) | −1.93004 | − | 3.34293i | −0.0882780 | − | 0.152902i | ||||
\(479\) | − | 31.6766i | − | 1.44734i | −0.690145 | − | 0.723671i | \(-0.742453\pi\) | ||
0.690145 | − | 0.723671i | \(-0.257547\pi\) | |||||||
\(480\) | −10.5697 | − | 18.3073i | −0.482440 | − | 0.835610i | ||||
\(481\) | −18.4785 | + | 10.7964i | −0.842546 | + | 0.492271i | ||||
\(482\) | −7.24372 | −0.329942 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.1469 | − | 34.8954i | 0.915767 | − | 1.58616i | ||||
\(485\) | −30.0780 | −1.36577 | ||||||||
\(486\) | 20.7152 | − | 11.9599i | 0.939662 | − | 0.542514i | ||||
\(487\) | −23.3096 | − | 13.4578i | −1.05626 | − | 0.609832i | −0.131864 | − | 0.991268i | \(-0.542096\pi\) |
−0.924395 | + | 0.381436i | \(0.875430\pi\) | |||||||
\(488\) | 90.3860i | 4.09158i | ||||||||
\(489\) | − | 1.52405i | − | 0.0689200i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.86358 | − | 8.42396i | 0.219490 | − | 0.380168i | −0.735162 | − | 0.677891i | \(-0.762894\pi\) |
0.954652 | + | 0.297723i | \(0.0962273\pi\) | |||||||
\(492\) | −6.71215 | + | 3.87526i | −0.302607 | + | 0.174710i | ||||
\(493\) | 2.94341 | + | 5.09813i | 0.132564 | + | 0.229608i | ||||
\(494\) | −11.8051 | − | 20.2050i | −0.531137 | − | 0.909067i | ||||
\(495\) | 8.66196 | − | 15.0030i | 0.389326 | − | 0.674333i | ||||
\(496\) | 20.4498 | + | 11.8067i | 0.918225 | + | 0.530137i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.66196 | − | 8.07475i | −0.208907 | − | 0.361838i | ||||
\(499\) | 6.82017 | + | 3.93763i | 0.305313 | + | 0.176272i | 0.644827 | − | 0.764329i | \(-0.276929\pi\) |
−0.339514 | + | 0.940601i | \(0.610263\pi\) | |||||||
\(500\) | 9.21523 | + | 5.32042i | 0.412118 | + | 0.237936i | ||||
\(501\) | 2.70213 | + | 1.56007i | 0.120722 | + | 0.0696989i | ||||
\(502\) | −25.5967 | − | 14.7783i | −1.14244 | − | 0.659586i | ||||
\(503\) | −4.87603 | − | 8.44553i | −0.217411 | − | 0.376568i | 0.736604 | − | 0.676324i | \(-0.236428\pi\) |
−0.954016 | + | 0.299756i | \(0.903095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.8259 | + | 24.1482i | 1.86123 | + | 1.07458i | ||||
\(506\) | −4.52266 | + | 7.83348i | −0.201057 | + | 0.348241i | ||||
\(507\) | 4.49710 | − | 0.0465154i | 0.199723 | − | 0.00206582i | ||||
\(508\) | 25.8315 | + | 44.7414i | 1.14609 | + | 1.98508i | ||||
\(509\) | −19.9407 | + | 11.5128i | −0.883857 | + | 0.510295i | −0.871928 | − | 0.489634i | \(-0.837130\pi\) |
−0.0119288 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(510\) | −3.28019 | + | 5.68146i | −0.145249 | + | 0.251579i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.8512i | 0.523752i | ||||||||
\(513\) | − | 4.88424i | − | 0.215645i | ||||||
\(514\) | −9.71853 | − | 5.61100i | −0.428666 | − | 0.247490i | ||||
\(515\) | 12.0846 | − | 6.97705i | 0.532511 | − | 0.307445i | ||||
\(516\) | −15.9410 | −0.701762 | ||||||||
\(517\) | 5.42524 | − | 9.39679i | 0.238602 | − | 0.413270i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.10752 | 0.0925100 | ||||||||
\(520\) | −52.0407 | + | 91.2233i | −2.28213 | + | 4.00041i | ||||
\(521\) | 0.243241 | + | 0.421305i | 0.0106566 | + | 0.0184577i | 0.871305 | − | 0.490743i | \(-0.163275\pi\) |
−0.860648 | + | 0.509200i | \(0.829941\pi\) | |||||||
\(522\) | 21.2876i | 0.931733i | ||||||||
\(523\) | −17.3135 | − | 29.9878i | −0.757065 | − | 1.31128i | −0.944341 | − | 0.328968i | \(-0.893299\pi\) |
0.187275 | − | 0.982307i | \(-0.440034\pi\) | |||||||
\(524\) | 49.5207 | + | 85.7724i | 2.16332 | + | 3.74698i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.48962 | − | 5.47883i | 0.413767 | − | 0.238888i | ||||
\(527\) | − | 3.75154i | − | 0.163420i | ||||||
\(528\) | 7.49554 | − | 4.32755i | 0.326201 | − | 0.188332i | ||||
\(529\) | 9.85719 | − | 17.0732i | 0.428574 | − | 0.742311i | ||||
\(530\) | 40.9818 | + | 70.9826i | 1.78014 | + | 3.08329i | ||||
\(531\) | −26.8208 | − | 15.4850i | −1.16392 | − | 0.671990i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2202 | + | 7.54182i | 0.572632 | + | 0.326672i | ||||
\(534\) | 7.06682 | − | 12.2401i | 0.305811 | − | 0.529681i | ||||
\(535\) | 62.3141i | 2.69408i | ||||||||
\(536\) | −7.39279 | −0.319320 | ||||||||
\(537\) | −1.34216 | −0.0579185 | ||||||||
\(538\) | − | 10.8134i | − | 0.466198i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −30.4637 | + | 17.5882i | −1.31095 | + | 0.756876i | ||||
\(541\) | 19.5188 | + | 11.2692i | 0.839181 | + | 0.484501i | 0.856986 | − | 0.515340i | \(-0.172334\pi\) |
−0.0178050 | + | 0.999841i | \(0.505668\pi\) | |||||||
\(542\) | −3.76422 | + | 6.51982i | −0.161687 | + | 0.280050i | ||||
\(543\) | 2.27770 | 0.0977456 | ||||||||
\(544\) | 34.9717 | − | 20.1909i | 1.49940 | − | 0.865678i | ||||
\(545\) | 13.9172 | 0.596146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.3716 | 1.68341 | 0.841704 | − | 0.539940i | \(-0.181553\pi\) | ||||
0.841704 | + | 0.539940i | \(0.181553\pi\) | |||||||
\(548\) | 38.7074 | − | 22.3477i | 1.65350 | − | 0.954648i | ||||
\(549\) | 29.1202 | 1.24282 | ||||||||
\(550\) | −14.0108 | + | 24.2675i | −0.597424 | + | 1.03477i | ||||
\(551\) | 5.68490 | + | 3.28218i | 0.242185 | + | 0.139826i | ||||
\(552\) | 4.85510 | − | 2.80310i | 0.206647 | − | 0.119308i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 45.1227i | − | 1.91708i | ||||||
\(555\) | 6.69034 | 0.283989 | ||||||||
\(556\) | −93.6000 | −3.96952 | ||||||||
\(557\) | − | 0.726975i | − | 0.0308029i | −0.999881 | − | 0.0154015i | \(-0.995097\pi\) | ||
0.999881 | − | 0.0154015i | \(-0.00490263\pi\) | |||||||
\(558\) | 6.78306 | − | 11.7486i | 0.287150 | − | 0.497358i | ||||
\(559\) | 15.7921 | + | 27.0289i | 0.667935 | + | 1.14320i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.19084 | − | 0.687532i | −0.0502773 | − | 0.0290276i | ||||
\(562\) | −18.0751 | − | 31.3070i | −0.762452 | − | 1.32061i | ||||
\(563\) | −20.8038 | + | 36.0333i | −0.876777 | + | 1.51862i | −0.0219200 | + | 0.999760i | \(0.506978\pi\) |
−0.854857 | + | 0.518863i | \(0.826355\pi\) | |||||||
\(564\) | −9.34597 | + | 5.39590i | −0.393537 | + | 0.227208i | ||||
\(565\) | − | 8.95907i | − | 0.376911i | ||||||
\(566\) | −44.2134 | + | 25.5266i | −1.85843 | + | 1.07296i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.5237 | + | 18.2276i | 0.441565 | + | 0.764813i | ||||
\(569\) | −12.6944 | − | 21.9873i | −0.532177 | − | 0.921757i | −0.999294 | − | 0.0375618i | \(-0.988041\pi\) |
0.467118 | − | 0.884195i | \(-0.345292\pi\) | |||||||
\(570\) | 7.31546i | 0.306411i | ||||||||
\(571\) | 8.49958 | + | 14.7217i | 0.355697 | + | 0.616084i | 0.987237 | − | 0.159259i | \(-0.0509103\pi\) |
−0.631540 | + | 0.775343i | \(0.717577\pi\) | |||||||
\(572\) | −30.6832 | − | 17.5040i | −1.28293 | − | 0.731879i | ||||
\(573\) | −4.75451 | −0.198622 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.08929 | + | 8.81490i | −0.212238 | + | 0.367607i | ||||
\(576\) | 67.9551 | 2.83146 | ||||||||
\(577\) | −13.8355 | + | 7.98794i | −0.575980 | + | 0.332542i | −0.759534 | − | 0.650467i | \(-0.774573\pi\) |
0.183554 | + | 0.983010i | \(0.441240\pi\) | |||||||
\(578\) | 28.9445 | + | 16.7111i | 1.20393 | + | 0.695092i | ||||
\(579\) | − | 7.87139i | − | 0.327124i | ||||||
\(580\) | − | 47.2767i | − | 1.96306i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.31660 | + | 7.47657i | −0.178929 | + | 0.309914i | ||||
\(583\) | −14.8780 | + | 8.58982i | −0.616184 | + | 0.355754i | ||||
\(584\) | −14.2812 | − | 24.7357i | −0.590959 | − | 1.02357i | ||||
\(585\) | 29.3900 | + | 16.7663i | 1.21513 | + | 0.693200i | ||||
\(586\) | 4.61963 | − | 8.00144i | 0.190835 | − | 0.330536i | ||||
\(587\) | 13.8404 | + | 7.99075i | 0.571254 | + | 0.329814i | 0.757650 | − | 0.652661i | \(-0.226347\pi\) |
−0.186396 | + | 0.982475i | \(0.559681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.09166 | − | 3.62287i | −0.0861855 | − | 0.149278i | ||||
\(590\) | 82.0116 | + | 47.3494i | 3.37637 | + | 1.94935i | ||||
\(591\) | −4.35235 | − | 2.51283i | −0.179032 | − | 0.103364i | ||||
\(592\) | −69.6660 | − | 40.2217i | −2.86325 | − | 1.65310i | ||||
\(593\) | 25.1608 | + | 14.5266i | 1.03323 | + | 0.596536i | 0.917908 | − | 0.396792i | \(-0.129877\pi\) |
0.115322 | + | 0.993328i | \(0.463210\pi\) | |||||||
\(594\) | −5.07574 | − | 8.79143i | −0.208260 | − | 0.360717i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.4816 | − | 10.6704i | −0.757037 | − | 0.437075i | ||||
\(597\) | −4.12379 | + | 7.14261i | −0.168775 | + | 0.292327i | ||||
\(598\) | −15.3454 | − | 8.75416i | −0.627519 | − | 0.357984i | ||||
\(599\) | −1.72777 | − | 2.99259i | −0.0705948 | − | 0.122274i | 0.828567 | − | 0.559889i | \(-0.189156\pi\) |
−0.899162 | + | 0.437616i | \(0.855823\pi\) | |||||||
\(600\) | 15.0407 | − | 8.68376i | 0.614035 | − | 0.354513i | ||||
\(601\) | 7.76518 | − | 13.4497i | 0.316748 | − | 0.548624i | −0.663059 | − | 0.748567i | \(-0.730742\pi\) |
0.979808 | + | 0.199943i | \(0.0640756\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.38178i | 0.0969936i | ||||||||
\(604\) | 100.313i | 4.08166i | ||||||||
\(605\) | 21.4222 | + | 12.3681i | 0.870938 | + | 0.502836i | ||||
\(606\) | 12.0052 | − | 6.93118i | 0.487676 | − | 0.281560i | ||||
\(607\) | −15.4784 | −0.628250 | −0.314125 | − | 0.949382i | \(-0.601711\pi\) | ||||
−0.314125 | + | 0.949382i | \(0.601711\pi\) | |||||||
\(608\) | 22.5148 | − | 38.9967i | 0.913095 | − | 1.58153i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −89.0429 | −3.60524 | ||||||||
\(611\) | 18.4078 | + | 10.5012i | 0.744700 | + | 0.424833i | ||||
\(612\) | −16.4571 | − | 28.5046i | −0.665240 | − | 1.15223i | ||||
\(613\) | 7.13223i | 0.288068i | 0.989573 | + | 0.144034i | \(0.0460075\pi\) | ||||
−0.989573 | + | 0.144034i | \(0.953993\pi\) | |||||||
\(614\) | −22.1228 | − | 38.3178i | −0.892804 | − | 1.54638i | ||||
\(615\) | −2.37902 | − | 4.12058i | −0.0959312 | − | 0.166158i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.30142 | + | 2.48342i | −0.173168 | + | 0.0999789i | −0.584079 | − | 0.811697i | \(-0.698544\pi\) |
0.410911 | + | 0.911676i | \(0.365211\pi\) | |||||||
\(618\) | − | 4.00520i | − | 0.161113i | ||||||
\(619\) | −36.6822 | + | 21.1785i | −1.47438 | + | 0.851235i | −0.999583 | − | 0.0288589i | \(-0.990813\pi\) |
−0.474799 | + | 0.880094i | \(0.657479\pi\) | |||||||
\(620\) | −15.0642 | + | 26.0920i | −0.604993 | + | 1.04788i | ||||
\(621\) | −1.84371 | − | 3.19339i | −0.0739854 | − | 0.128146i | ||||
\(622\) | −55.4776 | − | 32.0300i | −2.22445 | − | 1.28429i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.52791 | + | 14.5959i | 0.341390 | + | 0.584305i | ||||
\(625\) | 10.7722 | − | 18.6581i | 0.430889 | − | 0.746322i | ||||
\(626\) | 14.0032i | 0.559682i | ||||||||
\(627\) | −1.53333 | −0.0612352 | ||||||||
\(628\) | −61.4239 | −2.45108 | ||||||||
\(629\) | 12.7803i | 0.509583i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.42803 | + | 3.13387i | −0.216086 | + | 0.124758i | −0.604137 | − | 0.796881i | \(-0.706482\pi\) |
0.388050 | + | 0.921638i | \(0.373149\pi\) | |||||||
\(632\) | 6.20874 | + | 3.58462i | 0.246971 | + | 0.142589i | ||||
\(633\) | −0.746432 | + | 1.29286i | −0.0296680 | + | 0.0513865i | ||||
\(634\) | −16.3959 | −0.651163 | ||||||||
\(635\) | −27.4667 | + | 15.8579i | −1.08998 | + | 0.629302i | ||||
\(636\) | 17.0868 | 0.677534 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.6434 | 0.540149 | ||||||||
\(639\) | 5.87250 | − | 3.39049i | 0.232313 | − | 0.134126i | ||||
\(640\) | −85.5797 | −3.38283 | ||||||||
\(641\) | −15.7818 | + | 27.3350i | −0.623345 | + | 1.07967i | 0.365513 | + | 0.930806i | \(0.380894\pi\) |
−0.988858 | + | 0.148860i | \(0.952440\pi\) | |||||||
\(642\) | 15.4896 | + | 8.94291i | 0.611325 | + | 0.352949i | ||||
\(643\) | −15.8053 | + | 9.12520i | −0.623300 | + | 0.359863i | −0.778153 | − | 0.628075i | \(-0.783843\pi\) |
0.154852 | + | 0.987938i | \(0.450510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 9.78613i | − | 0.385329i | ||||||
\(646\) | −13.9744 | −0.549816 | ||||||||
\(647\) | 23.0273 | 0.905298 | 0.452649 | − | 0.891689i | \(-0.350479\pi\) | ||||
0.452649 | + | 0.891689i | \(0.350479\pi\) | |||||||
\(648\) | − | 70.9601i | − | 2.78758i | ||||||
\(649\) | −9.92448 | + | 17.1897i | −0.389570 | + | 0.674755i | ||||
\(650\) | −47.5387 | − | 27.1197i | −1.86462 | − | 1.06372i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.2483 | − | 11.6904i | −0.792985 | − | 0.457830i | ||||
\(653\) | −14.4062 | − | 24.9523i | −0.563759 | − | 0.976459i | −0.997164 | − | 0.0752597i | \(-0.976021\pi\) |
0.433405 | − | 0.901199i | \(-0.357312\pi\) | |||||||
\(654\) | 1.99730 | − | 3.45943i | 0.0781006 | − | 0.135274i | ||||
\(655\) | −52.6555 | + | 30.4007i | −2.05742 | + | 1.18785i | ||||
\(656\) | 57.2096i | 2.23366i | ||||||||
\(657\) | −7.96926 | + | 4.60105i | −0.310910 | + | 0.179504i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6114 | + | 27.0397i | 0.608134 | + | 1.05332i | 0.991548 | + | 0.129742i | \(0.0414149\pi\) |
−0.383414 | + | 0.923577i | \(0.625252\pi\) | |||||||
\(660\) | 5.52153 | + | 9.56356i | 0.214925 | + | 0.372261i | ||||
\(661\) | − | 26.5582i | − | 1.03299i | −0.856289 | − | 0.516496i | \(-0.827236\pi\) | ||
0.856289 | − | 0.516496i | \(-0.172764\pi\) | |||||||
\(662\) | 23.3487 | + | 40.4411i | 0.907471 | + | 1.57179i | ||||
\(663\) | 1.33080 | − | 2.33279i | 0.0516840 | − | 0.0905981i | ||||
\(664\) | −89.1366 | −3.45917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.1077 | + | 40.0237i | −0.895405 | + | 1.55089i | ||||
\(667\) | 4.95584 | 0.191891 | ||||||||
\(668\) | 41.4538 | − | 23.9334i | 1.60390 | − | 0.926010i | ||||
\(669\) | 7.00906 | + | 4.04668i | 0.270986 | + | 0.156454i | ||||
\(670\) | − | 7.28293i | − | 0.281364i | ||||||
\(671\) | − | 18.6635i | − | 0.720495i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.86930 | + | 17.0941i | −0.380434 | + | 0.658930i | −0.991124 | − | 0.132939i | \(-0.957559\pi\) |
0.610691 | + | 0.791869i | \(0.290892\pi\) | |||||||
\(674\) | −19.5585 | + | 11.2921i | −0.753366 | + | 0.434956i | ||||
\(675\) | −5.71165 | − | 9.89287i | −0.219842 | − | 0.380777i | ||||
\(676\) | 33.8774 | − | 60.1046i | 1.30298 | − | 2.31172i | ||||
\(677\) | −6.57198 | + | 11.3830i | −0.252582 | + | 0.437484i | −0.964236 | − | 0.265046i | \(-0.914613\pi\) |
0.711654 | + | 0.702530i | \(0.247946\pi\) | |||||||
\(678\) | −2.22698 | − | 1.28575i | −0.0855266 | − | 0.0493788i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.3586 | + | 54.3147i | 1.20255 | + | 2.08287i | ||||
\(681\) | −8.00619 | − | 4.62238i | −0.306798 | − | 0.177130i | ||||
\(682\) | −7.52981 | − | 4.34734i | −0.288331 | − | 0.166468i | ||||
\(683\) | 5.85654 | + | 3.38128i | 0.224094 | + | 0.129381i | 0.607845 | − | 0.794056i | \(-0.292034\pi\) |
−0.383750 | + | 0.923437i | \(0.625368\pi\) | |||||||
\(684\) | −31.7853 | − | 18.3513i | −1.21534 | − | 0.701678i | ||||
\(685\) | 13.7192 | + | 23.7624i | 0.524185 | + | 0.907915i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.900810 | + | 0.520083i | 0.0343681 | + | 0.0198424i | ||||
\(688\) | −58.8332 | + | 101.902i | −2.24300 | + | 3.88498i | ||||
\(689\) | −16.9272 | − | 28.9717i | −0.644874 | − | 1.10373i | ||||
\(690\) | 2.76144 | + | 4.78296i | 0.105126 | + | 0.182084i | ||||
\(691\) | 7.94223 | − | 4.58545i | 0.302137 | − | 0.174439i | −0.341266 | − | 0.939967i | \(-0.610856\pi\) |
0.643402 | + | 0.765528i | \(0.277522\pi\) | |||||||
\(692\) | 16.1659 | − | 28.0002i | 0.614537 | − | 1.06441i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 77.9115i | 2.95748i | ||||||||
\(695\) | − | 57.4609i | − | 2.17962i | ||||||
\(696\) | −7.32316 | − | 4.22803i | −0.277584 | − | 0.160263i | ||||
\(697\) | 7.87137 | − | 4.54454i | 0.298150 | − | 0.172137i | ||||
\(698\) | 31.6870 | 1.19937 | ||||||||
\(699\) | −2.02636 | + | 3.50976i | −0.0766440 | + | 0.132751i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.4700 | 1.79292 | 0.896459 | − | 0.443127i | \(-0.146131\pi\) | ||||
0.896459 | + | 0.443127i | \(0.146131\pi\) | |||||||
\(702\) | 17.1194 | − | 10.0023i | 0.646130 | − | 0.377512i | ||||
\(703\) | 7.12562 | + | 12.3419i | 0.268748 | + | 0.465485i | ||||
\(704\) | − | 43.5532i | − | 1.64147i | ||||||
\(705\) | −3.31253 | − | 5.73748i | −0.124757 | − | 0.216086i | ||||
\(706\) | 24.1074 | + | 41.7552i | 0.907294 | + | 1.57148i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.0968 | − | 9.87082i | 0.642535 | − | 0.370968i | ||||
\(709\) | 34.9719i | 1.31340i | 0.754153 | + | 0.656699i | \(0.228048\pi\) | ||||
−0.754153 | + | 0.656699i | \(0.771952\pi\) | |||||||
\(710\) | −17.9567 | + | 10.3673i | −0.673905 | + | 0.389079i | ||||
\(711\) | 1.15488 | − | 2.00031i | 0.0433114 | − | 0.0750175i | ||||
\(712\) | −67.5587 | − | 117.015i | −2.53187 | − | 4.38533i | ||||
\(713\) | −2.73512 | − | 1.57912i | −0.102431 | − | 0.0591387i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7457 | − | 18.8364i | 0.401866 | − | 0.704440i | ||||
\(716\) | −10.2952 | + | 17.8317i | −0.384748 | + | 0.666403i | ||||
\(717\) | − | 0.494005i | − | 0.0184490i | ||||||
\(718\) | −15.3585 | −0.573175 | ||||||||
\(719\) | −8.36101 | −0.311813 | −0.155907 | − | 0.987772i | \(-0.549830\pi\) | ||||
−0.155907 | + | 0.987772i | \(0.549830\pi\) | |||||||
\(720\) | 127.183i | 4.73984i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30.9846 | − | 17.8890i | 1.15313 | − | 0.665758i | ||||
\(723\) | −0.802836 | − | 0.463517i | −0.0298578 | − | 0.0172384i | ||||
\(724\) | 17.4713 | − | 30.2612i | 0.649317 | − | 1.12465i | ||||
\(725\) | 15.3528 | 0.570188 | ||||||||
\(726\) | 6.14875 | − | 3.54998i | 0.228202 | − | 0.131752i | ||||
\(727\) | 27.4014 | 1.01626 | 0.508131 | − | 0.861280i | \(-0.330337\pi\) | ||||
0.508131 | + | 0.861280i | \(0.330337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7504 | −0.768532 | ||||||||
\(730\) | 24.3681 | − | 14.0689i | 0.901905 | − | 0.520715i | ||||
\(731\) | 18.6941 | 0.691425 | ||||||||
\(732\) | −9.28127 | + | 16.0756i | −0.343046 | + | 0.594173i | ||||
\(733\) | 10.5282 | + | 6.07846i | 0.388868 | + | 0.224513i | 0.681670 | − | 0.731660i | \(-0.261254\pi\) |
−0.292802 | + | 0.956173i | \(0.594588\pi\) | |||||||
\(734\) | 45.9583 | − | 26.5340i | 1.69635 | − | 0.979389i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 33.9956i | − | 1.25309i | ||||||
\(737\) | 1.52651 | 0.0562297 | ||||||||
\(738\) | 32.8674 | 1.20987 | ||||||||
\(739\) | 48.4439i | 1.78204i | 0.453966 | + | 0.891019i | \(0.350009\pi\) | ||||
−0.453966 | + | 0.891019i | \(0.649991\pi\) | |||||||
\(740\) | 51.3189 | − | 88.8869i | 1.88652 | − | 3.26755i | ||||
\(741\) | −0.0154876 | − | 2.99476i | −0.000568953 | − | 0.110015i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7143 | − | 8.49532i | −0.539816 | − | 0.311663i | 0.205188 | − | 0.978722i | \(-0.434219\pi\) |
−0.745004 | + | 0.667060i | \(0.767553\pi\) | |||||||
\(744\) | 2.69443 | + | 4.66689i | 0.0987826 | + | 0.171097i | ||||
\(745\) | 6.55052 | − | 11.3458i | 0.239993 | − | 0.415679i | ||||
\(746\) | 75.0642 | − | 43.3384i | 2.74830 | − | 1.58673i | ||||
\(747\) | 28.7177i | 1.05073i | ||||||||
\(748\) | −18.2689 | + | 10.5475i | −0.667977 | + | 0.385657i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.937485 | + | 1.62377i | 0.0342321 | + | 0.0592917i | ||||
\(751\) | 21.5162 | + | 37.2671i | 0.785136 | + | 1.35990i | 0.928918 | + | 0.370287i | \(0.120741\pi\) |
−0.143781 | + | 0.989610i | \(0.545926\pi\) | |||||||
\(752\) | 79.6585i | 2.90485i | ||||||||
\(753\) | −1.89129 | − | 3.27581i | −0.0689225 | − | 0.119377i | ||||
\(754\) | 0.137808 | + | 26.6472i | 0.00501868 | + | 0.970434i | ||||
\(755\) | −61.5817 | −2.24119 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5892 | + | 25.2693i | −0.530255 | + | 0.918428i | 0.469122 | + | 0.883133i | \(0.344570\pi\) |
−0.999377 | + | 0.0352949i | \(0.988763\pi\) | |||||||
\(758\) | −51.4231 | −1.86777 | ||||||||
\(759\) | −1.00251 | + | 0.578801i | −0.0363889 | + | 0.0210091i | ||||
\(760\) | 60.5661 | + | 34.9678i | 2.19696 | + | 1.26842i | ||||
\(761\) | 29.4251i | 1.06666i | 0.845907 | + | 0.533330i | \(0.179059\pi\) | ||||
−0.845907 | + | 0.533330i | \(0.820941\pi\) | |||||||
\(762\) | 9.10328i | 0.329777i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −36.4699 | + | 63.1677i | −1.31943 | + | 2.28533i | ||||
\(765\) | 17.4989 | − | 10.1030i | 0.632675 | − | 0.365275i | ||||
\(766\) | −0.945888 | − | 1.63833i | −0.0341763 | − | 0.0591951i | ||||
\(767\) | −33.6737 | − | 19.2100i | −1.21589 | − | 0.693634i | ||||
\(768\) | −4.11988 | + | 7.13584i | −0.148663 | + | 0.257492i | ||||
\(769\) | −14.8839 | − | 8.59322i | −0.536727 | − | 0.309879i | 0.207024 | − | 0.978336i | \(-0.433622\pi\) |
−0.743751 | + | 0.668456i | \(0.766955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.718083 | − | 1.24376i | −0.0258611 | − | 0.0447928i | ||||
\(772\) | −104.578 | − | 60.3782i | −3.76385 | − | 2.17306i | ||||
\(773\) | 19.0180 | + | 10.9801i | 0.684031 | + | 0.394926i | 0.801372 | − | 0.598166i | \(-0.204104\pi\) |
−0.117341 | + | 0.993092i | \(0.537437\pi\) | |||||||
\(774\) | 58.5437 | + | 33.8002i | 2.10431 | + | 1.21492i | ||||
\(775\) | −8.47319 | − | 4.89200i | −0.304366 | − | 0.175726i | ||||
\(776\) | 41.2666 | + | 71.4759i | 1.48139 | + | 2.56584i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −46.9488 | − | 27.1059i | −1.68320 | − | 0.971794i | ||||
\(779\) | 5.06759 | − | 8.77733i | 0.181565 | − | 0.314480i | ||||
\(780\) | −18.6230 | + | 10.8808i | −0.666809 | + | 0.389594i | ||||
\(781\) | −2.17300 | − | 3.76375i | −0.0777561 | − | 0.134678i | ||||
\(782\) | −9.13669 | + | 5.27507i | −0.326727 | + | 0.188636i | ||||
\(783\) | −2.78094 | + | 4.81673i | −0.0993827 | + | 0.172136i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 37.7081i | − | 1.34586i | ||||||
\(786\) | 17.4516i | 0.622478i | ||||||||
\(787\) | −2.02275 | − | 1.16784i | −0.0721033 | − | 0.0416289i | 0.463515 | − | 0.886089i | \(-0.346588\pi\) |
−0.535618 | + | 0.844460i | \(0.679921\pi\) | |||||||
\(788\) | −66.7702 | + | 38.5498i | −2.37859 | + | 1.37328i | ||||
\(789\) | 1.40234 | 0.0499246 | ||||||||
\(790\) | −3.53135 | + | 6.11648i | −0.125640 | + | 0.217615i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −47.5364 | −1.68913 | ||||||||
\(793\) | 36.4519 | − | 0.188514i | 1.29444 | − | 0.00669432i | ||||
\(794\) | 30.1140 | + | 52.1590i | 1.06871 | + | 1.85105i | ||||
\(795\) | 10.4895i | 0.372025i | ||||||||
\(796\) | 63.2637 | + | 109.576i | 2.24232 | + | 3.88382i | ||||
\(797\) | −13.9020 | − | 24.0790i | −0.492434 | − | 0.852921i | 0.507528 | − | 0.861635i | \(-0.330560\pi\) |
−0.999962 | + | 0.00871411i | \(0.997226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9601 | − | 6.32780i | 0.387739 | − | 0.223861i | ||||
\(800\) | − | 105.315i | − | 3.72346i | ||||||
\(801\) | −37.6995 | + | 21.7658i | −1.33205 | + | 0.769057i | ||||
\(802\) | 6.49779 | − | 11.2545i | 0.229445 | − | 0.397410i | ||||
\(803\) | 2.94886 | + | 5.10758i | 0.104063 | + | 0.180243i | ||||
\(804\) | −1.31485 | − | 0.759127i | −0.0463711 | − | 0.0267724i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.41479 | − | 14.7505i | 0.296398 | − | 0.519564i | ||||
\(807\) | 0.691937 | − | 1.19847i | 0.0243573 | − | 0.0421882i | ||||
\(808\) | − | 132.524i | − | 4.66218i | ||||||
\(809\) | 15.0203 | 0.528087 | 0.264043 | − | 0.964511i | \(-0.414944\pi\) | ||||
0.264043 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(810\) | 69.9056 | 2.45623 | ||||||||
\(811\) | 43.6933i | 1.53428i | 0.641481 | + | 0.767139i | \(0.278320\pi\) | ||||
−0.641481 | + | 0.767139i | \(0.721680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.834393 | + | 0.481737i | −0.0292634 | + | 0.0168953i | ||||
\(814\) | 25.6516 | + | 14.8100i | 0.899089 | + | 0.519089i | ||||
\(815\) | 7.17670 | − | 12.4304i | 0.251389 | − | 0.435418i | ||||
\(816\) | 10.0950 | 0.353395 | ||||||||
\(817\) | 18.0529 | − | 10.4228i | 0.631590 | − | 0.364648i | ||||
\(818\) | 99.4870 | 3.47848 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −72.9939 | −2.54906 | ||||||||
\(821\) | −15.6492 | + | 9.03506i | −0.546160 | + | 0.315326i | −0.747572 | − | 0.664181i | \(-0.768780\pi\) |
0.201412 | + | 0.979507i | \(0.435447\pi\) | |||||||
\(822\) | 7.87557 | 0.274692 | ||||||||
\(823\) | 2.22775 | − | 3.85857i | 0.0776544 | − | 0.134501i | −0.824583 | − | 0.565741i | \(-0.808590\pi\) |
0.902238 | + | 0.431239i | \(0.141924\pi\) | |||||||
\(824\) | −33.1598 | − | 19.1448i | −1.15518 | − | 0.666941i | ||||
\(825\) | −3.10570 | + | 1.79308i | −0.108127 | + | 0.0624269i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.8352i | − | 0.411549i | −0.978599 | − | 0.205774i | \(-0.934029\pi\) | ||
0.978599 | − | 0.205774i | \(-0.0659713\pi\) | |||||||
\(828\) | −27.7090 | −0.962953 | ||||||||
\(829\) | −3.53894 | −0.122913 | −0.0614563 | − | 0.998110i | \(-0.519574\pi\) | ||||
−0.0614563 | + | 0.998110i | \(0.519574\pi\) | |||||||
\(830\) | − | 87.8120i | − | 3.04800i | ||||||
\(831\) | 2.88736 | − | 5.00105i | 0.100161 | − | 0.173484i | ||||
\(832\) | 85.0643 | − | 0.439917i | 2.94907 | − | 0.0152514i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.2832 | − | 8.24640i | −0.494586 | − | 0.285550i | ||||
\(835\) | 14.6927 | + | 25.4484i | 0.508460 | + | 0.880679i | ||||
\(836\) | −11.7615 | + | 20.3715i | −0.406781 | + | 0.704565i | ||||
\(837\) | 3.06960 | − | 1.77223i | 0.106101 | − | 0.0612573i | ||||
\(838\) | − | 79.1137i | − | 2.73294i | ||||||
\(839\) | 28.9991 | − | 16.7426i | 1.00116 | − | 0.578020i | 0.0925687 | − | 0.995706i | \(-0.470492\pi\) |
0.908591 | + | 0.417686i | \(0.137159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7625 | + | 18.6411i | 0.371119 | + | 0.642797i | ||||
\(842\) | 10.1892 | + | 17.6482i | 0.351143 | + | 0.608197i | ||||
\(843\) | − | 4.62642i | − | 0.159343i | ||||||
\(844\) | 11.4512 | + | 19.8340i | 0.394165 | + | 0.682714i | ||||
\(845\) | 36.8981 | + | 20.7973i | 1.26933 | + | 0.715448i | ||||
\(846\) | 45.7645 | 1.57342 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 63.0620 | − | 109.227i | 2.16556 | − | 3.75086i | ||||
\(849\) | −6.53368 | −0.224235 | ||||||||
\(850\) | −28.3047 | + | 16.3417i | −0.970844 | + | 0.560517i | ||||
\(851\) | 9.31768 | + | 5.37956i | 0.319406 | + | 0.184409i | ||||
\(852\) | 4.32250i | 0.148087i | ||||||||
\(853\) | 22.0871i | 0.756248i | 0.925755 | + | 0.378124i | \(0.123431\pi\) | ||||
−0.925755 | + | 0.378124i | \(0.876569\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.2658 | − | 19.5129i | 0.385282 | − | 0.667329i | ||||
\(856\) | 148.080 | − | 85.4941i | 5.06127 | − | 2.92213i | ||||
\(857\) | 3.44682 | + | 5.97006i | 0.117741 | + | 0.203933i | 0.918872 | − | 0.394555i | \(-0.129101\pi\) |
−0.801131 | + | 0.598489i | \(0.795768\pi\) | |||||||
\(858\) | −3.14005 | − | 5.37435i | −0.107200 | − | 0.183477i | ||||
\(859\) | −18.7417 | + | 32.4616i | −0.639459 | + | 1.10758i | 0.346093 | + | 0.938200i | \(0.387508\pi\) |
−0.985552 | + | 0.169375i | \(0.945825\pi\) | |||||||
\(860\) | −130.017 | − | 75.0654i | −4.43355 | − | 2.55971i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.2052 | + | 73.1015i | 1.43751 | + | 2.48985i | ||||
\(863\) | −15.1769 | − | 8.76241i | −0.516629 | − | 0.298276i | 0.218925 | − | 0.975742i | \(-0.429745\pi\) |
−0.735554 | + | 0.677466i | \(0.763078\pi\) | |||||||
\(864\) | 33.0413 | + | 19.0764i | 1.12409 | + | 0.648993i | ||||
\(865\) | 17.1893 | + | 9.92425i | 0.584454 | + | 0.337435i | ||||
\(866\) | −13.7747 | − | 7.95285i | −0.468085 | − | 0.270249i | ||||
\(867\) | 2.13866 | + | 3.70426i | 0.0726326 | + | 0.125803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.28202 | − | 0.740175i | −0.0434896 | − | 0.0251087i | ||||
\(870\) | 4.16520 | − | 7.21434i | 0.141213 | − | 0.244589i | ||||
\(871\) | 0.0154188 | + | 2.98145i | 0.000522446 | + | 0.101022i | ||||
\(872\) | −19.0942 | − | 33.0721i | −0.646610 | − | 1.11996i | ||||
\(873\) | 23.0278 | − | 13.2951i | 0.779374 | − | 0.449972i | ||||
\(874\) | −5.88221 | + | 10.1883i | −0.198969 | + | 0.344624i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 5.86584i | − | 0.198188i | ||||||
\(877\) | − | 46.7491i | − | 1.57860i | −0.614005 | − | 0.789302i | \(-0.710443\pi\) | ||
0.614005 | − | 0.789302i | \(-0.289557\pi\) | |||||||
\(878\) | 23.3083 | + | 13.4571i | 0.786618 | + | 0.454154i | ||||
\(879\) | 1.02401 | − | 0.591210i | 0.0345389 | − | 0.0199410i | ||||
\(880\) | 81.5131 | 2.74781 | ||||||||
\(881\) | 1.45937 | − | 2.52771i | 0.0491675 | − | 0.0851606i | −0.840394 | − | 0.541976i | \(-0.817677\pi\) |
0.889562 | + | 0.456815i | \(0.151010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.5505 | 0.960801 | 0.480400 | − | 0.877049i | \(-0.340491\pi\) | ||||
0.480400 | + | 0.877049i | \(0.340491\pi\) | |||||||
\(884\) | −20.7851 | − | 35.5747i | −0.699078 | − | 1.19651i | ||||
\(885\) | 6.05968 | + | 10.4957i | 0.203694 | + | 0.352808i | ||||
\(886\) | − | 96.9941i | − | 3.25858i | ||||||
\(887\) | 0.211457 | + | 0.366254i | 0.00710004 | + | 0.0122976i | 0.869554 | − | 0.493839i | \(-0.164407\pi\) |
−0.862454 | + | 0.506136i | \(0.831073\pi\) | |||||||
\(888\) | −9.17905 | − | 15.8986i | −0.308029 | − | 0.533521i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 115.276 | − | 66.5548i | 3.86407 | − | 2.23092i | ||||
\(891\) | 14.6523i | 0.490870i | ||||||||
\(892\) | 107.527 | − | 62.0809i | 3.60028 | − | 2.07862i | ||||
\(893\) | 7.05610 | − | 12.2215i | 0.236123 | − | 0.408978i | ||||
\(894\) | −1.88018 | − | 3.25656i | −0.0628825 | − | 0.108916i | ||||
\(895\) | −10.9469 | − | 6.32018i | −0.365914 | − | 0.211260i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.14059 | − | 1.95217i | −0.0380832 | − | 0.0651812i | ||||
\(898\) | 5.40001 | − | 9.35309i | 0.180201 | − | 0.312117i | ||||
\(899\) | 4.76372i | 0.158879i | ||||||||
\(900\) | −85.8401 | −2.86134 | ||||||||
\(901\) | −20.0377 | −0.667553 | ||||||||
\(902\) | − | 21.0651i | − | 0.701391i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.2899 | + | 12.2917i | −0.708091 | + | 0.408816i | ||||
\(905\) | 18.5773 | + | 10.7256i | 0.617531 | + | 0.356532i | ||||
\(906\) | −8.83779 | + | 15.3075i | −0.293616 | + | 0.508558i | ||||
\(907\) | 22.4284 | 0.744723 | 0.372361 | − | 0.928088i | \(-0.378548\pi\) | ||||
0.372361 | + | 0.928088i | \(0.378548\pi\) | |||||||
\(908\) | −122.824 | + | 70.9127i | −4.07607 | + | 2.35332i | ||||
\(909\) | −42.6961 | −1.41614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5788 | −1.07938 | −0.539692 | − | 0.841863i | \(-0.681459\pi\) | ||||
−0.539692 | + | 0.841863i | \(0.681459\pi\) | |||||||
\(912\) | 9.74874 | − | 5.62844i | 0.322813 | − | 0.186376i | ||||
\(913\) | 18.4055 | 0.609132 | ||||||||
\(914\) | −55.7159 | + | 96.5027i | −1.84292 | + | 3.19203i | ||||
\(915\) | −9.86881 | − | 5.69776i | −0.326253 | − | 0.188362i | ||||
\(916\) | 13.8195 | − | 7.97869i | 0.456609 | − | 0.263623i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 11.8403i | − | 0.390788i | ||||||
\(919\) | −9.87913 | −0.325883 | −0.162941 | − | 0.986636i | \(-0.552098\pi\) | ||||
−0.162941 | + | 0.986636i | \(0.552098\pi\) | |||||||
\(920\) | 52.7987 | 1.74072 | ||||||||
\(921\) | − | 5.66246i | − | 0.186584i | ||||||
\(922\) | −33.4204 | + | 57.8859i | −1.10064 | + | 1.90637i | ||||
\(923\) | 7.32908 | − | 4.28214i | 0.241240 | − | 0.140948i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8654 | + | 16.6654i | 0.949088 | + | 0.547956i | ||||
\(926\) | 32.9867 | + | 57.1346i | 1.08401 | + | 1.87756i | ||||
\(927\) | −6.16800 | + | 10.6833i | −0.202584 | + | 0.350886i | ||||
\(928\) | −44.4071 | + | 25.6385i | −1.45774 | + | 0.841624i | ||||
\(929\) | − | 29.9136i | − | 0.981434i | −0.871319 | − | 0.490717i | \(-0.836735\pi\) | ||
0.871319 | − | 0.490717i | \(-0.163265\pi\) | |||||||
\(930\) | −4.59754 | + | 2.65439i | −0.150759 | + | 0.0870409i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 31.0868 | + | 53.8439i | 1.01828 | + | 1.76371i | ||||
\(933\) | −4.09913 | − | 7.09990i | −0.134199 | − | 0.232440i | ||||
\(934\) | − | 12.0255i | − | 0.393485i | ||||||
\(935\) | −6.47512 | − | 11.2152i | −0.211759 | − | 0.366778i | ||||
\(936\) | −0.480150 | − | 92.8439i | −0.0156942 | − | 3.03470i | ||||
\(937\) | 31.8296 | 1.03983 | 0.519914 | − | 0.854219i | \(-0.325964\pi\) | ||||
0.519914 | + | 0.854219i | \(0.325964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.896052 | + | 1.55201i | −0.0292416 | + | 0.0506479i | ||||
\(940\) | −101.636 | −3.31501 | ||||||||
\(941\) | −36.4497 | + | 21.0443i | −1.18823 | + | 0.686023i | −0.957903 | − | 0.287091i | \(-0.907312\pi\) |
−0.230324 | + | 0.973114i | \(0.573979\pi\) | |||||||
\(942\) | −9.37318 | − | 5.41161i | −0.305395 | − | 0.176320i | ||||
\(943\) | − | 7.65167i | − | 0.249173i | ||||||
\(944\) | − | 145.721i | − | 4.74280i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.6629 | − | 37.5213i | 0.704322 | − | 1.21992i | ||||
\(947\) | −52.2540 | + | 30.1689i | −1.69803 | + | 0.980357i | −0.750397 | + | 0.660988i | \(0.770138\pi\) |
−0.947630 | + | 0.319369i | \(0.896529\pi\) | |||||||
\(948\) | 0.736172 | + | 1.27509i | 0.0239098 | + | 0.0414129i | ||||
\(949\) | −9.94591 | + | 5.81106i | −0.322858 | + | 0.188635i | ||||
\(950\) | −18.2226 | + | 31.5624i | −0.591219 | + | 1.02402i | ||||
\(951\) | −1.81719 | − | 1.04915i | −0.0589264 | − | 0.0340212i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.68770 | − | 15.0475i | −0.281422 | − | 0.487438i | 0.690313 | − | 0.723511i | \(-0.257473\pi\) |
−0.971735 | + | 0.236073i | \(0.924139\pi\) | |||||||
\(954\) | −62.7516 | − | 36.2297i | −2.03166 | − | 1.17298i | ||||
\(955\) | −38.7785 | − | 22.3888i | −1.25484 | − | 0.724484i | ||||
\(956\) | −6.56328 | − | 3.78931i | −0.212272 | − | 0.122555i | ||||
\(957\) | 1.51213 | + | 0.873029i | 0.0488803 | + | 0.0282210i | ||||
\(958\) | −42.8140 | − | 74.1561i | −1.38326 | − | 2.39588i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −23.0299 | − | 13.2963i | −0.743287 | − | 0.429137i | ||||
\(961\) | −13.9821 | + | 24.2177i | −0.451035 | + | 0.781216i | ||||
\(962\) | −28.6665 | + | 50.2501i | −0.924244 | + | 1.62013i | ||||
\(963\) | −27.5442 | − | 47.7079i | −0.887598 | − | 1.53737i | ||||
\(964\) | −12.3165 | + | 7.11091i | −0.396686 | + | 0.229027i | ||||
\(965\) | 37.0661 | − | 64.2003i | 1.19320 | − | 2.06668i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.8630i | − | 0.606594i | −0.952896 | − | 0.303297i | \(-0.901913\pi\) | ||
0.952896 | − | 0.303297i | \(-0.0980874\pi\) | |||||||
\(968\) | − | 67.8756i | − | 2.18160i | ||||||
\(969\) | −1.54881 | − | 0.894208i | −0.0497551 | − | 0.0287261i | ||||
\(970\) | −70.4138 | + | 40.6534i | −2.26085 | + | 1.30530i | ||||
\(971\) | 1.56446 | 0.0502060 | 0.0251030 | − | 0.999685i | \(-0.492009\pi\) | ||||
0.0251030 | + | 0.999685i | \(0.492009\pi\) | |||||||
\(972\) | 23.4813 | − | 40.6708i | 0.753164 | − | 1.30452i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −72.7582 | −2.33132 | ||||||||
\(975\) | −3.53345 | − | 6.04768i | −0.113161 | − | 0.193681i | ||||
\(976\) | 68.5087 | + | 118.661i | 2.19291 | + | 3.79823i | ||||
\(977\) | 27.8755i | 0.891817i | 0.895078 | + | 0.445909i | \(0.147119\pi\) | ||||
−0.895078 | + | 0.445909i | \(0.852881\pi\) | |||||||
\(978\) | −2.05990 | − | 3.56786i | −0.0658685 | − | 0.114088i | ||||
\(979\) | 13.9499 | + | 24.1620i | 0.445842 | + | 0.772221i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6550 | + | 6.15169i | −0.340189 | + | 0.196408i | ||||
\(982\) | − | 26.2944i | − | 0.839088i | ||||||
\(983\) | 28.9460 | − | 16.7120i | 0.923233 | − | 0.533029i | 0.0385681 | − | 0.999256i | \(-0.487720\pi\) |
0.884665 | + | 0.466227i | \(0.154387\pi\) | |||||||
\(984\) | −6.52795 | + | 11.3067i | −0.208104 | + | 0.360446i | ||||
\(985\) | −23.6657 | − | 40.9901i | −0.754051 | − | 1.30605i | ||||
\(986\) | 13.7813 | + | 7.95661i | 0.438885 | + | 0.253390i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −39.9068 | − | 22.7658i | −1.26960 | − | 0.724277i | ||||
\(989\) | 7.86882 | − | 13.6292i | 0.250214 | − | 0.433383i | ||||
\(990\) | − | 46.8300i | − | 1.48835i | ||||||
\(991\) | −18.9110 | −0.600726 | −0.300363 | − | 0.953825i | \(-0.597108\pi\) | ||||
−0.300363 | + | 0.953825i | \(0.597108\pi\) | |||||||
\(992\) | 32.6777 | 1.03752 | ||||||||
\(993\) | 5.97622i | 0.189650i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.2685 | + | 38.8375i | −2.13256 | + | 1.23123i | ||||
\(996\) | −15.8534 | − | 9.15297i | −0.502335 | − | 0.290023i | ||||
\(997\) | 21.7888 | − | 37.7393i | 0.690057 | − | 1.19521i | −0.281762 | − | 0.959484i | \(-0.590919\pi\) |
0.971819 | − | 0.235730i | \(-0.0757480\pi\) | |||||||
\(998\) | 21.2884 | 0.673871 | ||||||||
\(999\) | −10.4571 | + | 6.03742i | −0.330849 | + | 0.191016i |
(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 | 637.2.u.i.30.6 | 12 | ||
7.2 | even | 3 | 637.2.q.h.589.1 | 12 | |||
7.3 | odd | 6 | 637.2.k.h.459.6 | 12 | |||
7.4 | even | 3 | 637.2.k.g.459.6 | 12 | |||
7.5 | odd | 6 | 91.2.q.a.43.1 | yes | 12 | ||
7.6 | odd | 2 | 637.2.u.h.30.6 | 12 | |||
13.10 | even | 6 | 637.2.k.g.569.1 | 12 | |||
21.5 | even | 6 | 819.2.ct.a.316.6 | 12 | |||
28.19 | even | 6 | 1456.2.cc.c.225.4 | 12 | |||
91.10 | odd | 6 | 637.2.u.h.361.6 | 12 | |||
91.19 | even | 12 | 1183.2.a.p.1.6 | 6 | |||
91.23 | even | 6 | 637.2.q.h.491.1 | 12 | |||
91.33 | even | 12 | 1183.2.a.m.1.1 | 6 | |||
91.58 | odd | 12 | 8281.2.a.ch.1.6 | 6 | |||
91.61 | odd | 6 | 1183.2.c.i.337.12 | 12 | |||
91.62 | odd | 6 | 637.2.k.h.569.1 | 12 | |||
91.72 | odd | 12 | 8281.2.a.by.1.1 | 6 | |||
91.75 | odd | 6 | 91.2.q.a.36.1 | ✓ | 12 | ||
91.82 | odd | 6 | 1183.2.c.i.337.1 | 12 | |||
91.88 | even | 6 | inner | 637.2.u.i.361.6 | 12 | ||
273.257 | even | 6 | 819.2.ct.a.127.6 | 12 | |||
364.75 | even | 6 | 1456.2.cc.c.673.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.1 | ✓ | 12 | 91.75 | odd | 6 | ||
91.2.q.a.43.1 | yes | 12 | 7.5 | odd | 6 | ||
637.2.k.g.459.6 | 12 | 7.4 | even | 3 | |||
637.2.k.g.569.1 | 12 | 13.10 | even | 6 | |||
637.2.k.h.459.6 | 12 | 7.3 | odd | 6 | |||
637.2.k.h.569.1 | 12 | 91.62 | odd | 6 | |||
637.2.q.h.491.1 | 12 | 91.23 | even | 6 | |||
637.2.q.h.589.1 | 12 | 7.2 | even | 3 | |||
637.2.u.h.30.6 | 12 | 7.6 | odd | 2 | |||
637.2.u.h.361.6 | 12 | 91.10 | odd | 6 | |||
637.2.u.i.30.6 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.i.361.6 | 12 | 91.88 | even | 6 | inner | ||
819.2.ct.a.127.6 | 12 | 273.257 | even | 6 | |||
819.2.ct.a.316.6 | 12 | 21.5 | even | 6 | |||
1183.2.a.m.1.1 | 6 | 91.33 | even | 12 | |||
1183.2.a.p.1.6 | 6 | 91.19 | even | 12 | |||
1183.2.c.i.337.1 | 12 | 91.82 | odd | 6 | |||
1183.2.c.i.337.12 | 12 | 91.61 | odd | 6 | |||
1456.2.cc.c.225.4 | 12 | 28.19 | even | 6 | |||
1456.2.cc.c.673.4 | 12 | 364.75 | even | 6 | |||
8281.2.a.by.1.1 | 6 | 91.72 | odd | 12 | |||
8281.2.a.ch.1.6 | 6 | 91.58 | odd | 12 |