Properties

Label 864.2.bk.a.37.11
Level $864$
Weight $2$
Character 864.37
Analytic conductor $6.899$
Analytic rank $0$
Dimension $368$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(37,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bk (of order \(24\), degree \(8\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 37.11
Character \(\chi\) \(=\) 864.37
Dual form 864.2.bk.a.397.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.930084 - 1.06534i) q^{2} +(-0.269888 + 1.98171i) q^{4} +(-2.36155 + 1.81208i) q^{5} +(0.338610 - 1.26371i) q^{7} +(2.36221 - 1.55563i) q^{8} +O(q^{10})\) \(q+(-0.930084 - 1.06534i) q^{2} +(-0.269888 + 1.98171i) q^{4} +(-2.36155 + 1.81208i) q^{5} +(0.338610 - 1.26371i) q^{7} +(2.36221 - 1.55563i) q^{8} +(4.12692 + 0.830461i) q^{10} +(2.23430 - 0.294152i) q^{11} +(0.513433 - 3.89991i) q^{13} +(-1.66121 + 0.814622i) q^{14} +(-3.85432 - 1.06968i) q^{16} +1.90675i q^{17} +(-3.62937 + 1.50334i) q^{19} +(-2.95366 - 5.16896i) q^{20} +(-2.39146 - 2.10670i) q^{22} +(1.29540 + 4.83449i) q^{23} +(0.999188 - 3.72902i) q^{25} +(-4.63226 + 3.08027i) q^{26} +(2.41291 + 1.01209i) q^{28} +(3.13573 - 4.08657i) q^{29} +(-5.15305 + 8.92535i) q^{31} +(2.44527 + 5.10104i) q^{32} +(2.03133 - 1.77343i) q^{34} +(1.49030 + 3.59790i) q^{35} +(5.79919 + 2.40210i) q^{37} +(4.97718 + 2.46828i) q^{38} +(-2.75954 + 7.95421i) q^{40} +(2.12378 + 7.92607i) q^{41} +(7.51451 - 0.989304i) q^{43} +(-0.0200906 + 4.50712i) q^{44} +(3.94554 - 5.87652i) q^{46} +(-3.53204 + 2.03922i) q^{47} +(4.57987 + 2.64419i) q^{49} +(-4.90200 + 2.40383i) q^{50} +(7.58991 + 2.07002i) q^{52} +(-4.38473 + 10.5857i) q^{53} +(-4.74339 + 4.74339i) q^{55} +(-1.16600 - 3.51189i) q^{56} +(-7.27007 + 0.460235i) q^{58} +(1.38929 - 1.06604i) q^{59} +(-1.65646 + 2.15874i) q^{61} +(14.3013 - 2.81158i) q^{62} +(3.16003 - 7.34944i) q^{64} +(5.85447 + 10.1402i) q^{65} +(9.88539 + 1.30144i) q^{67} +(-3.77861 - 0.514609i) q^{68} +(2.44688 - 4.93402i) q^{70} +(-10.8773 - 10.8773i) q^{71} +(-8.05693 + 8.05693i) q^{73} +(-2.83468 - 8.41225i) q^{74} +(-1.99964 - 7.59808i) q^{76} +(0.384835 - 2.92311i) q^{77} +(-4.83346 + 2.79060i) q^{79} +(11.0405 - 4.45824i) q^{80} +(6.46864 - 9.63445i) q^{82} +(1.05266 + 0.807735i) q^{83} +(-3.45518 - 4.50288i) q^{85} +(-8.04307 - 7.08536i) q^{86} +(4.82029 - 4.17060i) q^{88} +(2.84277 + 2.84277i) q^{89} +(-4.75450 - 1.96938i) q^{91} +(-9.93015 + 1.26232i) q^{92} +(5.45756 + 1.86617i) q^{94} +(5.84678 - 10.1269i) q^{95} +(4.30984 + 7.46486i) q^{97} +(-1.44271 - 7.33843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.930084 1.06534i −0.657669 0.753307i
\(3\) 0 0
\(4\) −0.269888 + 1.98171i −0.134944 + 0.990853i
\(5\) −2.36155 + 1.81208i −1.05612 + 0.810388i −0.982381 0.186890i \(-0.940159\pi\)
−0.0737371 + 0.997278i \(0.523493\pi\)
\(6\) 0 0
\(7\) 0.338610 1.26371i 0.127982 0.477637i −0.871946 0.489602i \(-0.837142\pi\)
0.999928 + 0.0119650i \(0.00380868\pi\)
\(8\) 2.36221 1.55563i 0.835166 0.549998i
\(9\) 0 0
\(10\) 4.12692 + 0.830461i 1.30505 + 0.262615i
\(11\) 2.23430 0.294152i 0.673668 0.0886900i 0.214071 0.976818i \(-0.431327\pi\)
0.459596 + 0.888128i \(0.347994\pi\)
\(12\) 0 0
\(13\) 0.513433 3.89991i 0.142401 1.08164i −0.759748 0.650217i \(-0.774678\pi\)
0.902149 0.431424i \(-0.141989\pi\)
\(14\) −1.66121 + 0.814622i −0.443978 + 0.217717i
\(15\) 0 0
\(16\) −3.85432 1.06968i −0.963580 0.267420i
\(17\) 1.90675i 0.462454i 0.972900 + 0.231227i \(0.0742740\pi\)
−0.972900 + 0.231227i \(0.925726\pi\)
\(18\) 0 0
\(19\) −3.62937 + 1.50334i −0.832635 + 0.344889i −0.757945 0.652318i \(-0.773797\pi\)
−0.0746898 + 0.997207i \(0.523797\pi\)
\(20\) −2.95366 5.16896i −0.660458 1.15582i
\(21\) 0 0
\(22\) −2.39146 2.10670i −0.509861 0.449150i
\(23\) 1.29540 + 4.83449i 0.270109 + 1.00806i 0.959048 + 0.283242i \(0.0914100\pi\)
−0.688939 + 0.724819i \(0.741923\pi\)
\(24\) 0 0
\(25\) 0.999188 3.72902i 0.199838 0.745804i
\(26\) −4.63226 + 3.08027i −0.908461 + 0.604090i
\(27\) 0 0
\(28\) 2.41291 + 1.01209i 0.455998 + 0.191266i
\(29\) 3.13573 4.08657i 0.582291 0.758856i −0.405593 0.914054i \(-0.632935\pi\)
0.987883 + 0.155198i \(0.0496015\pi\)
\(30\) 0 0
\(31\) −5.15305 + 8.92535i −0.925516 + 1.60304i −0.134786 + 0.990875i \(0.543035\pi\)
−0.790730 + 0.612166i \(0.790299\pi\)
\(32\) 2.44527 + 5.10104i 0.432267 + 0.901746i
\(33\) 0 0
\(34\) 2.03133 1.77343i 0.348370 0.304141i
\(35\) 1.49030 + 3.59790i 0.251907 + 0.608157i
\(36\) 0 0
\(37\) 5.79919 + 2.40210i 0.953381 + 0.394903i 0.804501 0.593952i \(-0.202433\pi\)
0.148880 + 0.988855i \(0.452433\pi\)
\(38\) 4.97718 + 2.46828i 0.807405 + 0.400408i
\(39\) 0 0
\(40\) −2.75954 + 7.95421i −0.436321 + 1.25767i
\(41\) 2.12378 + 7.92607i 0.331679 + 1.23784i 0.907425 + 0.420215i \(0.138045\pi\)
−0.575745 + 0.817629i \(0.695288\pi\)
\(42\) 0 0
\(43\) 7.51451 0.989304i 1.14595 0.150867i 0.466455 0.884545i \(-0.345531\pi\)
0.679498 + 0.733678i \(0.262198\pi\)
\(44\) −0.0200906 + 4.50712i −0.00302878 + 0.679474i
\(45\) 0 0
\(46\) 3.94554 5.87652i 0.581738 0.866445i
\(47\) −3.53204 + 2.03922i −0.515201 + 0.297451i −0.734969 0.678101i \(-0.762803\pi\)
0.219768 + 0.975552i \(0.429470\pi\)
\(48\) 0 0
\(49\) 4.57987 + 2.64419i 0.654268 + 0.377742i
\(50\) −4.90200 + 2.40383i −0.693247 + 0.339953i
\(51\) 0 0
\(52\) 7.58991 + 2.07002i 1.05253 + 0.287060i
\(53\) −4.38473 + 10.5857i −0.602289 + 1.45406i 0.268929 + 0.963160i \(0.413330\pi\)
−0.871219 + 0.490895i \(0.836670\pi\)
\(54\) 0 0
\(55\) −4.74339 + 4.74339i −0.639599 + 0.639599i
\(56\) −1.16600 3.51189i −0.155813 0.469296i
\(57\) 0 0
\(58\) −7.27007 + 0.460235i −0.954606 + 0.0604318i
\(59\) 1.38929 1.06604i 0.180871 0.138787i −0.514358 0.857576i \(-0.671970\pi\)
0.695229 + 0.718789i \(0.255303\pi\)
\(60\) 0 0
\(61\) −1.65646 + 2.15874i −0.212088 + 0.276399i −0.887268 0.461255i \(-0.847399\pi\)
0.675180 + 0.737653i \(0.264066\pi\)
\(62\) 14.3013 2.81158i 1.81626 0.357071i
\(63\) 0 0
\(64\) 3.16003 7.34944i 0.395003 0.918680i
\(65\) 5.85447 + 10.1402i 0.726157 + 1.25774i
\(66\) 0 0
\(67\) 9.88539 + 1.30144i 1.20769 + 0.158996i 0.707370 0.706843i \(-0.249881\pi\)
0.500323 + 0.865839i \(0.333215\pi\)
\(68\) −3.77861 0.514609i −0.458224 0.0624055i
\(69\) 0 0
\(70\) 2.44688 4.93402i 0.292458 0.589729i
\(71\) −10.8773 10.8773i −1.29090 1.29090i −0.934230 0.356671i \(-0.883912\pi\)
−0.356671 0.934230i \(-0.616088\pi\)
\(72\) 0 0
\(73\) −8.05693 + 8.05693i −0.942992 + 0.942992i −0.998460 0.0554684i \(-0.982335\pi\)
0.0554684 + 0.998460i \(0.482335\pi\)
\(74\) −2.83468 8.41225i −0.329525 0.977905i
\(75\) 0 0
\(76\) −1.99964 7.59808i −0.229375 0.871560i
\(77\) 0.384835 2.92311i 0.0438560 0.333119i
\(78\) 0 0
\(79\) −4.83346 + 2.79060i −0.543806 + 0.313967i −0.746620 0.665251i \(-0.768325\pi\)
0.202814 + 0.979217i \(0.434991\pi\)
\(80\) 11.0405 4.45824i 1.23437 0.498447i
\(81\) 0 0
\(82\) 6.46864 9.63445i 0.714342 1.06395i
\(83\) 1.05266 + 0.807735i 0.115544 + 0.0886604i 0.664917 0.746917i \(-0.268467\pi\)
−0.549373 + 0.835577i \(0.685133\pi\)
\(84\) 0 0
\(85\) −3.45518 4.50288i −0.374767 0.488406i
\(86\) −8.04307 7.08536i −0.867306 0.764034i
\(87\) 0 0
\(88\) 4.82029 4.17060i 0.513845 0.444587i
\(89\) 2.84277 + 2.84277i 0.301333 + 0.301333i 0.841535 0.540202i \(-0.181652\pi\)
−0.540202 + 0.841535i \(0.681652\pi\)
\(90\) 0 0
\(91\) −4.75450 1.96938i −0.498407 0.206447i
\(92\) −9.93015 + 1.26232i −1.03529 + 0.131606i
\(93\) 0 0
\(94\) 5.45756 + 1.86617i 0.562904 + 0.192480i
\(95\) 5.84678 10.1269i 0.599867 1.03900i
\(96\) 0 0
\(97\) 4.30984 + 7.46486i 0.437598 + 0.757942i 0.997504 0.0706143i \(-0.0224960\pi\)
−0.559906 + 0.828556i \(0.689163\pi\)
\(98\) −1.44271 7.33843i −0.145736 0.741293i
\(99\) 0 0
\(100\) 7.12016 + 2.98652i 0.712016 + 0.298652i
\(101\) 1.03455 + 7.85821i 0.102942 + 0.781921i 0.962576 + 0.271011i \(0.0873580\pi\)
−0.859634 + 0.510910i \(0.829309\pi\)
\(102\) 0 0
\(103\) −9.77856 + 2.62016i −0.963510 + 0.258172i −0.706085 0.708127i \(-0.749541\pi\)
−0.257424 + 0.966298i \(0.582874\pi\)
\(104\) −4.85399 10.0111i −0.475973 0.981670i
\(105\) 0 0
\(106\) 15.3555 5.17435i 1.49146 0.502577i
\(107\) 0.810493 1.95670i 0.0783533 0.189162i −0.879849 0.475254i \(-0.842356\pi\)
0.958202 + 0.286092i \(0.0923563\pi\)
\(108\) 0 0
\(109\) 14.7640 6.11543i 1.41413 0.585752i 0.460752 0.887529i \(-0.347580\pi\)
0.953379 + 0.301776i \(0.0975796\pi\)
\(110\) 9.46507 + 0.641563i 0.902459 + 0.0611706i
\(111\) 0 0
\(112\) −2.65687 + 4.50854i −0.251051 + 0.426017i
\(113\) 3.74045 + 2.15955i 0.351872 + 0.203153i 0.665509 0.746389i \(-0.268214\pi\)
−0.313637 + 0.949543i \(0.601548\pi\)
\(114\) 0 0
\(115\) −11.8196 9.06953i −1.10219 0.845738i
\(116\) 7.25208 + 7.31702i 0.673338 + 0.679368i
\(117\) 0 0
\(118\) −2.42785 0.488558i −0.223502 0.0449754i
\(119\) 2.40957 + 0.645643i 0.220885 + 0.0591860i
\(120\) 0 0
\(121\) −5.71960 + 1.53256i −0.519964 + 0.139324i
\(122\) 3.84044 0.243121i 0.347697 0.0220111i
\(123\) 0 0
\(124\) −16.2967 12.6207i −1.46348 1.13337i
\(125\) −1.29795 3.13354i −0.116092 0.280272i
\(126\) 0 0
\(127\) 7.24850 0.643200 0.321600 0.946876i \(-0.395779\pi\)
0.321600 + 0.946876i \(0.395779\pi\)
\(128\) −10.7687 + 3.46910i −0.951830 + 0.306628i
\(129\) 0 0
\(130\) 5.35763 15.6682i 0.469895 1.37420i
\(131\) 16.5149 + 2.17423i 1.44292 + 0.189963i 0.810987 0.585064i \(-0.198931\pi\)
0.631928 + 0.775027i \(0.282264\pi\)
\(132\) 0 0
\(133\) 0.670837 + 5.09552i 0.0581690 + 0.441837i
\(134\) −7.80777 11.7417i −0.674489 1.01433i
\(135\) 0 0
\(136\) 2.96619 + 4.50413i 0.254349 + 0.386226i
\(137\) 13.3227 + 3.56981i 1.13824 + 0.304990i 0.778242 0.627964i \(-0.216112\pi\)
0.359995 + 0.932954i \(0.382778\pi\)
\(138\) 0 0
\(139\) 4.84849 + 6.31867i 0.411243 + 0.535943i 0.952348 0.305012i \(-0.0986606\pi\)
−0.541105 + 0.840955i \(0.681994\pi\)
\(140\) −7.53220 + 1.98230i −0.636587 + 0.167535i
\(141\) 0 0
\(142\) −1.47120 + 21.7049i −0.123460 + 1.82143i
\(143\) 8.86462i 0.741296i
\(144\) 0 0
\(145\) 15.3328i 1.27332i
\(146\) 16.0770 + 1.08973i 1.33054 + 0.0901868i
\(147\) 0 0
\(148\) −6.32540 + 10.8440i −0.519945 + 0.891371i
\(149\) −6.44398 8.39796i −0.527912 0.687988i 0.450941 0.892554i \(-0.351088\pi\)
−0.978853 + 0.204566i \(0.934422\pi\)
\(150\) 0 0
\(151\) −16.0157 4.29139i −1.30334 0.349228i −0.460626 0.887594i \(-0.652375\pi\)
−0.842711 + 0.538366i \(0.819042\pi\)
\(152\) −6.23469 + 9.19715i −0.505700 + 0.745987i
\(153\) 0 0
\(154\) −3.47203 + 2.30876i −0.279784 + 0.186045i
\(155\) −4.00427 30.4154i −0.321631 2.44303i
\(156\) 0 0
\(157\) 1.67848 + 0.220977i 0.133958 + 0.0176358i 0.197207 0.980362i \(-0.436813\pi\)
−0.0632492 + 0.997998i \(0.520146\pi\)
\(158\) 7.46845 + 2.55377i 0.594158 + 0.203167i
\(159\) 0 0
\(160\) −15.0181 7.61535i −1.18729 0.602046i
\(161\) 6.54802 0.516057
\(162\) 0 0
\(163\) −3.52458 8.50908i −0.276066 0.666483i 0.723653 0.690164i \(-0.242461\pi\)
−0.999720 + 0.0236810i \(0.992461\pi\)
\(164\) −16.2803 + 2.06956i −1.27128 + 0.161606i
\(165\) 0 0
\(166\) −0.118552 1.87270i −0.00920143 0.145350i
\(167\) 6.60936 1.77097i 0.511448 0.137042i 0.00613998 0.999981i \(-0.498046\pi\)
0.505308 + 0.862939i \(0.331379\pi\)
\(168\) 0 0
\(169\) −2.38868 0.640045i −0.183745 0.0492342i
\(170\) −1.58348 + 7.86899i −0.121447 + 0.603524i
\(171\) 0 0
\(172\) −0.0675698 + 15.1586i −0.00515215 + 1.15583i
\(173\) 0.233277 + 0.179000i 0.0177357 + 0.0136091i 0.617591 0.786499i \(-0.288109\pi\)
−0.599856 + 0.800108i \(0.704775\pi\)
\(174\) 0 0
\(175\) −4.37406 2.52537i −0.330648 0.190900i
\(176\) −8.92637 1.25623i −0.672850 0.0946922i
\(177\) 0 0
\(178\) 0.384496 5.67253i 0.0288192 0.425174i
\(179\) −12.0433 + 4.98852i −0.900162 + 0.372859i −0.784282 0.620404i \(-0.786969\pi\)
−0.115879 + 0.993263i \(0.536969\pi\)
\(180\) 0 0
\(181\) −2.44513 + 5.90306i −0.181745 + 0.438771i −0.988326 0.152352i \(-0.951315\pi\)
0.806581 + 0.591123i \(0.201315\pi\)
\(182\) 2.32403 + 6.89684i 0.172269 + 0.511228i
\(183\) 0 0
\(184\) 10.5807 + 9.40490i 0.780018 + 0.693338i
\(185\) −18.0479 + 4.83592i −1.32691 + 0.355544i
\(186\) 0 0
\(187\) 0.560873 + 4.26025i 0.0410151 + 0.311540i
\(188\) −3.08789 7.54983i −0.225207 0.550628i
\(189\) 0 0
\(190\) −16.2266 + 3.19009i −1.17720 + 0.231434i
\(191\) 3.97607 + 6.88675i 0.287698 + 0.498308i 0.973260 0.229707i \(-0.0737767\pi\)
−0.685562 + 0.728014i \(0.740443\pi\)
\(192\) 0 0
\(193\) −12.9475 + 22.4257i −0.931979 + 1.61424i −0.152046 + 0.988373i \(0.548586\pi\)
−0.779934 + 0.625862i \(0.784747\pi\)
\(194\) 3.94409 11.5344i 0.283169 0.828121i
\(195\) 0 0
\(196\) −6.47607 + 8.36233i −0.462576 + 0.597309i
\(197\) −5.95844 2.46807i −0.424521 0.175843i 0.160186 0.987087i \(-0.448791\pi\)
−0.584707 + 0.811244i \(0.698791\pi\)
\(198\) 0 0
\(199\) −4.98853 4.98853i −0.353628 0.353628i 0.507830 0.861457i \(-0.330448\pi\)
−0.861457 + 0.507830i \(0.830448\pi\)
\(200\) −3.44069 10.3631i −0.243294 0.732781i
\(201\) 0 0
\(202\) 7.40942 8.41094i 0.521325 0.591792i
\(203\) −4.10244 5.34641i −0.287935 0.375244i
\(204\) 0 0
\(205\) −19.3781 14.8693i −1.35343 1.03852i
\(206\) 11.8862 + 7.98050i 0.828153 + 0.556028i
\(207\) 0 0
\(208\) −6.15059 + 14.4823i −0.426467 + 1.00417i
\(209\) −7.66691 + 4.42649i −0.530331 + 0.306187i
\(210\) 0 0
\(211\) 2.59652 19.7225i 0.178752 1.35776i −0.633180 0.774004i \(-0.718251\pi\)
0.811932 0.583752i \(-0.198416\pi\)
\(212\) −19.7943 11.5462i −1.35948 0.792997i
\(213\) 0 0
\(214\) −2.83837 + 0.956449i −0.194027 + 0.0653815i
\(215\) −15.9532 + 15.9532i −1.08800 + 1.08800i
\(216\) 0 0
\(217\) 9.53417 + 9.53417i 0.647222 + 0.647222i
\(218\) −20.2467 10.0407i −1.37128 0.680045i
\(219\) 0 0
\(220\) −8.11983 10.6802i −0.547439 0.720059i
\(221\) 7.43615 + 0.978987i 0.500209 + 0.0658538i
\(222\) 0 0
\(223\) −4.24938 7.36013i −0.284559 0.492871i 0.687943 0.725765i \(-0.258514\pi\)
−0.972502 + 0.232894i \(0.925181\pi\)
\(224\) 7.27423 1.36285i 0.486030 0.0910591i
\(225\) 0 0
\(226\) −1.17828 5.99340i −0.0783782 0.398675i
\(227\) −6.71686 + 8.75359i −0.445814 + 0.580996i −0.961162 0.275985i \(-0.910996\pi\)
0.515348 + 0.856981i \(0.327663\pi\)
\(228\) 0 0
\(229\) 4.97071 3.81416i 0.328474 0.252047i −0.431337 0.902191i \(-0.641958\pi\)
0.759811 + 0.650144i \(0.225291\pi\)
\(230\) 1.33115 + 21.0273i 0.0877731 + 1.38650i
\(231\) 0 0
\(232\) 1.05006 14.5313i 0.0689396 0.954030i
\(233\) 19.6950 19.6950i 1.29026 1.29026i 0.355635 0.934625i \(-0.384265\pi\)
0.934625 0.355635i \(-0.115735\pi\)
\(234\) 0 0
\(235\) 4.64585 11.2161i 0.303062 0.731657i
\(236\) 1.73763 + 3.04088i 0.113110 + 0.197945i
\(237\) 0 0
\(238\) −1.55328 3.16751i −0.100684 0.205319i
\(239\) −1.21666 0.702439i −0.0786992 0.0454370i 0.460134 0.887849i \(-0.347801\pi\)
−0.538833 + 0.842412i \(0.681135\pi\)
\(240\) 0 0
\(241\) 25.4367 14.6859i 1.63852 0.946001i 0.657178 0.753735i \(-0.271750\pi\)
0.981343 0.192266i \(-0.0615835\pi\)
\(242\) 6.95240 + 4.66789i 0.446917 + 0.300064i
\(243\) 0 0
\(244\) −3.83093 3.86524i −0.245250 0.247447i
\(245\) −15.6071 + 2.05471i −0.997101 + 0.131271i
\(246\) 0 0
\(247\) 3.99944 + 14.9261i 0.254478 + 0.949725i
\(248\) 1.71198 + 29.0998i 0.108711 + 1.84784i
\(249\) 0 0
\(250\) −2.13107 + 4.29721i −0.134781 + 0.271779i
\(251\) −17.0078 7.04486i −1.07352 0.444668i −0.225290 0.974292i \(-0.572333\pi\)
−0.848233 + 0.529624i \(0.822333\pi\)
\(252\) 0 0
\(253\) 4.31638 + 10.4207i 0.271369 + 0.655142i
\(254\) −6.74171 7.72210i −0.423012 0.484527i
\(255\) 0 0
\(256\) 13.7116 + 8.24578i 0.856973 + 0.515361i
\(257\) 15.0326 26.0373i 0.937709 1.62416i 0.167980 0.985790i \(-0.446276\pi\)
0.769730 0.638370i \(-0.220391\pi\)
\(258\) 0 0
\(259\) 4.99922 6.51511i 0.310637 0.404830i
\(260\) −21.6750 + 8.86510i −1.34423 + 0.549790i
\(261\) 0 0
\(262\) −13.0440 19.6162i −0.805859 1.21189i
\(263\) −4.63339 + 17.2920i −0.285707 + 1.06627i 0.662614 + 0.748961i \(0.269447\pi\)
−0.948321 + 0.317312i \(0.897220\pi\)
\(264\) 0 0
\(265\) −8.82735 32.9441i −0.542260 2.02374i
\(266\) 4.80451 5.45392i 0.294583 0.334402i
\(267\) 0 0
\(268\) −5.24702 + 19.2387i −0.320513 + 1.17519i
\(269\) −4.26202 + 1.76539i −0.259860 + 0.107638i −0.508810 0.860879i \(-0.669915\pi\)
0.248950 + 0.968516i \(0.419915\pi\)
\(270\) 0 0
\(271\) 24.9388i 1.51492i −0.652881 0.757461i \(-0.726440\pi\)
0.652881 0.757461i \(-0.273560\pi\)
\(272\) 2.03961 7.34921i 0.123669 0.445611i
\(273\) 0 0
\(274\) −8.58819 17.5134i −0.518832 1.05802i
\(275\) 1.13559 8.62568i 0.0684788 0.520148i
\(276\) 0 0
\(277\) 15.6557 2.06112i 0.940661 0.123840i 0.355426 0.934704i \(-0.384336\pi\)
0.585235 + 0.810864i \(0.301002\pi\)
\(278\) 2.22202 11.0422i 0.133268 0.662265i
\(279\) 0 0
\(280\) 9.11740 + 6.18063i 0.544869 + 0.369363i
\(281\) −2.39031 + 8.92077i −0.142594 + 0.532169i 0.857257 + 0.514890i \(0.172167\pi\)
−0.999851 + 0.0172792i \(0.994500\pi\)
\(282\) 0 0
\(283\) −19.8732 + 15.2493i −1.18134 + 0.906475i −0.997077 0.0764022i \(-0.975657\pi\)
−0.184264 + 0.982877i \(0.558990\pi\)
\(284\) 24.4913 18.6200i 1.45329 1.10489i
\(285\) 0 0
\(286\) −9.44381 + 8.24484i −0.558424 + 0.487527i
\(287\) 10.7354 0.633689
\(288\) 0 0
\(289\) 13.3643 0.786136
\(290\) 16.3347 14.2608i 0.959204 0.837425i
\(291\) 0 0
\(292\) −13.7920 18.1409i −0.807115 1.06162i
\(293\) −4.00589 + 3.07383i −0.234027 + 0.179575i −0.719117 0.694889i \(-0.755453\pi\)
0.485090 + 0.874464i \(0.338787\pi\)
\(294\) 0 0
\(295\) −1.34913 + 5.03503i −0.0785495 + 0.293151i
\(296\) 17.4357 3.34714i 1.01343 0.194548i
\(297\) 0 0
\(298\) −2.95322 + 14.6758i −0.171075 + 0.850148i
\(299\) 19.5192 2.56975i 1.12882 0.148613i
\(300\) 0 0
\(301\) 1.29429 9.83115i 0.0746019 0.566658i
\(302\) 10.3241 + 21.0534i 0.594088 + 1.21149i
\(303\) 0 0
\(304\) 15.5969 1.91207i 0.894541 0.109665i
\(305\) 8.09963i 0.463783i
\(306\) 0 0
\(307\) −5.22156 + 2.16284i −0.298010 + 0.123440i −0.526679 0.850065i \(-0.676563\pi\)
0.228668 + 0.973504i \(0.426563\pi\)
\(308\) 5.68889 + 1.55154i 0.324154 + 0.0884074i
\(309\) 0 0
\(310\) −28.6784 + 32.5548i −1.62882 + 1.84899i
\(311\) −3.96542 14.7991i −0.224858 0.839182i −0.982461 0.186467i \(-0.940296\pi\)
0.757603 0.652716i \(-0.226370\pi\)
\(312\) 0 0
\(313\) 1.04694 3.90722i 0.0591763 0.220849i −0.930005 0.367547i \(-0.880198\pi\)
0.989181 + 0.146698i \(0.0468645\pi\)
\(314\) −1.32572 1.99368i −0.0748145 0.112510i
\(315\) 0 0
\(316\) −4.22565 10.3316i −0.237711 0.581200i
\(317\) −18.5493 + 24.1739i −1.04183 + 1.35774i −0.110377 + 0.993890i \(0.535206\pi\)
−0.931456 + 0.363854i \(0.881461\pi\)
\(318\) 0 0
\(319\) 5.80411 10.0530i 0.324968 0.562860i
\(320\) 5.85522 + 23.0823i 0.327317 + 1.29034i
\(321\) 0 0
\(322\) −6.09021 6.97586i −0.339394 0.388749i
\(323\) −2.86648 6.92030i −0.159495 0.385056i
\(324\) 0 0
\(325\) −14.0298 5.81135i −0.778236 0.322356i
\(326\) −5.78689 + 11.6690i −0.320506 + 0.646287i
\(327\) 0 0
\(328\) 17.3468 + 15.4192i 0.957819 + 0.851382i
\(329\) 1.38100 + 5.15397i 0.0761372 + 0.284148i
\(330\) 0 0
\(331\) −26.2231 + 3.45234i −1.44135 + 0.189758i −0.810315 0.585995i \(-0.800704\pi\)
−0.631037 + 0.775753i \(0.717370\pi\)
\(332\) −1.88479 + 1.86807i −0.103442 + 0.102523i
\(333\) 0 0
\(334\) −8.03395 5.39405i −0.439598 0.295149i
\(335\) −25.7032 + 14.8397i −1.40431 + 0.810781i
\(336\) 0 0
\(337\) 13.8814 + 8.01444i 0.756169 + 0.436574i 0.827918 0.560848i \(-0.189525\pi\)
−0.0717498 + 0.997423i \(0.522858\pi\)
\(338\) 1.53981 + 3.14004i 0.0837545 + 0.170796i
\(339\) 0 0
\(340\) 9.85590 5.63188i 0.534511 0.305432i
\(341\) −8.88808 + 21.4577i −0.481316 + 1.16200i
\(342\) 0 0
\(343\) 11.3680 11.3680i 0.613813 0.613813i
\(344\) 16.2118 14.0267i 0.874083 0.756271i
\(345\) 0 0
\(346\) −0.0262720 0.415004i −0.00141239 0.0223107i
\(347\) −12.3429 + 9.47101i −0.662599 + 0.508430i −0.884441 0.466652i \(-0.845460\pi\)
0.221842 + 0.975083i \(0.428793\pi\)
\(348\) 0 0
\(349\) 3.53080 4.60143i 0.188999 0.246309i −0.689237 0.724536i \(-0.742054\pi\)
0.878236 + 0.478228i \(0.158721\pi\)
\(350\) 1.37788 + 7.00866i 0.0736506 + 0.374629i
\(351\) 0 0
\(352\) 6.96396 + 10.6780i 0.371180 + 0.569139i
\(353\) 8.94237 + 15.4886i 0.475955 + 0.824377i 0.999621 0.0275462i \(-0.00876934\pi\)
−0.523666 + 0.851924i \(0.675436\pi\)
\(354\) 0 0
\(355\) 45.3980 + 5.97676i 2.40947 + 0.317213i
\(356\) −6.40077 + 4.86631i −0.339240 + 0.257914i
\(357\) 0 0
\(358\) 16.5158 + 8.19049i 0.872885 + 0.432881i
\(359\) 15.1625 + 15.1625i 0.800246 + 0.800246i 0.983134 0.182888i \(-0.0585445\pi\)
−0.182888 + 0.983134i \(0.558545\pi\)
\(360\) 0 0
\(361\) −2.52270 + 2.52270i −0.132774 + 0.132774i
\(362\) 8.56292 2.88545i 0.450057 0.151656i
\(363\) 0 0
\(364\) 5.18592 8.89052i 0.271816 0.465990i
\(365\) 4.42703 33.6267i 0.231722 1.76010i
\(366\) 0 0
\(367\) −2.59698 + 1.49937i −0.135561 + 0.0782663i −0.566247 0.824236i \(-0.691605\pi\)
0.430686 + 0.902502i \(0.358272\pi\)
\(368\) 0.178477 20.0193i 0.00930377 1.04358i
\(369\) 0 0
\(370\) 21.9379 + 14.7293i 1.14050 + 0.765740i
\(371\) 11.8925 + 9.12544i 0.617428 + 0.473769i
\(372\) 0 0
\(373\) 1.24427 + 1.62157i 0.0644261 + 0.0839617i 0.824455 0.565928i \(-0.191482\pi\)
−0.760029 + 0.649889i \(0.774815\pi\)
\(374\) 4.01695 4.55991i 0.207711 0.235787i
\(375\) 0 0
\(376\) −5.17113 + 10.3116i −0.266680 + 0.531781i
\(377\) −14.3273 14.3273i −0.737892 0.737892i
\(378\) 0 0
\(379\) 1.52367 + 0.631126i 0.0782658 + 0.0324188i 0.421473 0.906841i \(-0.361513\pi\)
−0.343207 + 0.939260i \(0.611513\pi\)
\(380\) 18.4906 + 14.3197i 0.948549 + 0.734588i
\(381\) 0 0
\(382\) 3.63864 10.6411i 0.186169 0.544446i
\(383\) −2.54407 + 4.40645i −0.129996 + 0.225159i −0.923675 0.383178i \(-0.874830\pi\)
0.793679 + 0.608337i \(0.208163\pi\)
\(384\) 0 0
\(385\) 4.38811 + 7.60043i 0.223639 + 0.387354i
\(386\) 35.9332 7.06433i 1.82895 0.359565i
\(387\) 0 0
\(388\) −15.9563 + 6.52616i −0.810061 + 0.331316i
\(389\) −4.86497 36.9531i −0.246664 1.87360i −0.447940 0.894064i \(-0.647842\pi\)
0.201276 0.979535i \(-0.435491\pi\)
\(390\) 0 0
\(391\) −9.21815 + 2.47000i −0.466182 + 0.124913i
\(392\) 14.9320 0.878469i 0.754179 0.0443694i
\(393\) 0 0
\(394\) 2.91253 + 8.64326i 0.146731 + 0.435441i
\(395\) 6.35766 15.3488i 0.319889 0.772280i
\(396\) 0 0
\(397\) 18.8052 7.78939i 0.943808 0.390938i 0.142908 0.989736i \(-0.454355\pi\)
0.800900 + 0.598798i \(0.204355\pi\)
\(398\) −0.674718 + 9.95423i −0.0338206 + 0.498960i
\(399\) 0 0
\(400\) −7.84005 + 13.3040i −0.392003 + 0.665202i
\(401\) 14.8951 + 8.59968i 0.743825 + 0.429447i 0.823458 0.567377i \(-0.192042\pi\)
−0.0796336 + 0.996824i \(0.525375\pi\)
\(402\) 0 0
\(403\) 32.1623 + 24.6790i 1.60212 + 1.22935i
\(404\) −15.8519 0.0706602i −0.788660 0.00351548i
\(405\) 0 0
\(406\) −1.88011 + 9.34309i −0.0933084 + 0.463690i
\(407\) 13.6637 + 3.66119i 0.677286 + 0.181478i
\(408\) 0 0
\(409\) −28.0188 + 7.50762i −1.38544 + 0.371228i −0.873095 0.487551i \(-0.837890\pi\)
−0.512347 + 0.858779i \(0.671224\pi\)
\(410\) 2.18239 + 34.4740i 0.107781 + 1.70255i
\(411\) 0 0
\(412\) −2.55326 20.0854i −0.125790 0.989535i
\(413\) −0.876739 2.11664i −0.0431415 0.104153i
\(414\) 0 0
\(415\) −3.94959 −0.193878
\(416\) 21.1491 6.91730i 1.03692 0.339149i
\(417\) 0 0
\(418\) 11.8466 + 4.05084i 0.579435 + 0.198133i
\(419\) −11.7155 1.54237i −0.572339 0.0753498i −0.161199 0.986922i \(-0.551536\pi\)
−0.411140 + 0.911572i \(0.634869\pi\)
\(420\) 0 0
\(421\) 0.902867 + 6.85795i 0.0440030 + 0.334236i 0.999260 + 0.0384596i \(0.0122451\pi\)
−0.955257 + 0.295777i \(0.904422\pi\)
\(422\) −23.4262 + 15.5774i −1.14037 + 0.758298i
\(423\) 0 0
\(424\) 6.10977 + 31.8266i 0.296717 + 1.54564i
\(425\) 7.11030 + 1.90520i 0.344900 + 0.0924157i
\(426\) 0 0
\(427\) 2.16713 + 2.82426i 0.104875 + 0.136675i
\(428\) 3.65887 + 2.13425i 0.176858 + 0.103163i
\(429\) 0 0
\(430\) 31.8334 + 2.15773i 1.53514 + 0.104055i
\(431\) 7.84780i 0.378015i −0.981976 0.189008i \(-0.939473\pi\)
0.981976 0.189008i \(-0.0605271\pi\)
\(432\) 0 0
\(433\) 3.65459i 0.175628i −0.996137 0.0878141i \(-0.972012\pi\)
0.996137 0.0878141i \(-0.0279882\pi\)
\(434\) 1.28953 19.0247i 0.0618996 0.913214i
\(435\) 0 0
\(436\) 8.13437 + 30.9083i 0.389566 + 1.48024i
\(437\) −11.9693 15.5988i −0.572571 0.746190i
\(438\) 0 0
\(439\) 28.1839 + 7.55186i 1.34515 + 0.360431i 0.858341 0.513080i \(-0.171496\pi\)
0.486805 + 0.873511i \(0.338162\pi\)
\(440\) −3.82590 + 18.5838i −0.182393 + 0.885950i
\(441\) 0 0
\(442\) −5.87329 8.83255i −0.279364 0.420122i
\(443\) −4.14921 31.5164i −0.197135 1.49739i −0.748505 0.663129i \(-0.769228\pi\)
0.551370 0.834261i \(-0.314105\pi\)
\(444\) 0 0
\(445\) −11.8647 1.56202i −0.562440 0.0740466i
\(446\) −3.88875 + 11.3726i −0.184138 + 0.538506i
\(447\) 0 0
\(448\) −8.21753 6.48195i −0.388242 0.306243i
\(449\) −35.0894 −1.65597 −0.827986 0.560749i \(-0.810513\pi\)
−0.827986 + 0.560749i \(0.810513\pi\)
\(450\) 0 0
\(451\) 7.07664 + 17.0845i 0.333226 + 0.804479i
\(452\) −5.28910 + 6.82964i −0.248778 + 0.321239i
\(453\) 0 0
\(454\) 15.5728 0.985842i 0.730866 0.0462678i
\(455\) 14.7967 3.96476i 0.693679 0.185871i
\(456\) 0 0
\(457\) 24.1884 + 6.48127i 1.13149 + 0.303181i 0.775523 0.631319i \(-0.217486\pi\)
0.355964 + 0.934500i \(0.384153\pi\)
\(458\) −8.68655 1.74800i −0.405896 0.0816786i
\(459\) 0 0
\(460\) 21.1631 20.9753i 0.986736 0.977978i
\(461\) 12.9871 + 9.96538i 0.604871 + 0.464134i 0.865228 0.501378i \(-0.167174\pi\)
−0.260357 + 0.965512i \(0.583840\pi\)
\(462\) 0 0
\(463\) −11.0701 6.39130i −0.514469 0.297029i 0.220200 0.975455i \(-0.429329\pi\)
−0.734669 + 0.678426i \(0.762662\pi\)
\(464\) −16.4574 + 12.3967i −0.764017 + 0.575503i
\(465\) 0 0
\(466\) −39.2998 2.66382i −1.82053 0.123399i
\(467\) 23.4018 9.69335i 1.08291 0.448555i 0.231379 0.972864i \(-0.425676\pi\)
0.851528 + 0.524309i \(0.175676\pi\)
\(468\) 0 0
\(469\) 4.99193 12.0516i 0.230506 0.556490i
\(470\) −16.2699 + 5.48249i −0.750477 + 0.252889i
\(471\) 0 0
\(472\) 1.62343 4.67944i 0.0747244 0.215389i
\(473\) 16.4987 4.42081i 0.758611 0.203269i
\(474\) 0 0
\(475\) 1.97954 + 15.0361i 0.0908277 + 0.689905i
\(476\) −1.92979 + 4.60082i −0.0884518 + 0.210878i
\(477\) 0 0
\(478\) 0.383261 + 1.94948i 0.0175299 + 0.0891672i
\(479\) 7.24608 + 12.5506i 0.331082 + 0.573450i 0.982724 0.185076i \(-0.0592531\pi\)
−0.651643 + 0.758526i \(0.725920\pi\)
\(480\) 0 0
\(481\) 12.3455 21.3830i 0.562906 0.974982i
\(482\) −39.3037 13.4396i −1.79023 0.612155i
\(483\) 0 0
\(484\) −1.49343 11.7482i −0.0678834 0.534009i
\(485\) −23.7049 9.81887i −1.07638 0.445852i
\(486\) 0 0
\(487\) −10.1166 10.1166i −0.458428 0.458428i 0.439711 0.898139i \(-0.355081\pi\)
−0.898139 + 0.439711i \(0.855081\pi\)
\(488\) −0.554696 + 7.67624i −0.0251099 + 0.347487i
\(489\) 0 0
\(490\) 16.7049 + 14.7158i 0.754649 + 0.664791i
\(491\) 2.50040 + 3.25859i 0.112842 + 0.147058i 0.846359 0.532612i \(-0.178790\pi\)
−0.733518 + 0.679670i \(0.762123\pi\)
\(492\) 0 0
\(493\) 7.79205 + 5.97905i 0.350936 + 0.269283i
\(494\) 12.1815 18.1433i 0.548073 0.816305i
\(495\) 0 0
\(496\) 29.4088 28.8890i 1.32049 1.29716i
\(497\) −17.4289 + 10.0626i −0.781795 + 0.451370i
\(498\) 0 0
\(499\) 1.99836 15.1790i 0.0894588 0.679507i −0.886684 0.462376i \(-0.846997\pi\)
0.976143 0.217131i \(-0.0696697\pi\)
\(500\) 6.56005 1.72646i 0.293374 0.0772095i
\(501\) 0 0
\(502\) 8.31352 + 24.6714i 0.371051 + 1.10114i
\(503\) −26.7836 + 26.7836i −1.19422 + 1.19422i −0.218354 + 0.975870i \(0.570069\pi\)
−0.975870 + 0.218354i \(0.929931\pi\)
\(504\) 0 0
\(505\) −16.6829 16.6829i −0.742378 0.742378i
\(506\) 7.08694 14.2905i 0.315053 0.635290i
\(507\) 0 0
\(508\) −1.95629 + 14.3644i −0.0867961 + 0.637317i
\(509\) 21.5968 + 2.84327i 0.957262 + 0.126026i 0.592939 0.805247i \(-0.297967\pi\)
0.364322 + 0.931273i \(0.381301\pi\)
\(510\) 0 0
\(511\) 7.45346 + 12.9098i 0.329722 + 0.571095i
\(512\) −3.96838 22.2767i −0.175379 0.984501i
\(513\) 0 0
\(514\) −41.7201 + 8.20202i −1.84019 + 0.361776i
\(515\) 18.3446 23.9072i 0.808361 1.05348i
\(516\) 0 0
\(517\) −7.29181 + 5.59520i −0.320693 + 0.246077i
\(518\) −11.5905 + 0.733741i −0.509257 + 0.0322387i
\(519\) 0 0
\(520\) 29.6039 + 14.8459i 1.29822 + 0.651037i
\(521\) 21.4239 21.4239i 0.938598 0.938598i −0.0596231 0.998221i \(-0.518990\pi\)
0.998221 + 0.0596231i \(0.0189899\pi\)
\(522\) 0 0
\(523\) 4.94049 11.9274i 0.216032 0.521549i −0.778296 0.627897i \(-0.783916\pi\)
0.994329 + 0.106348i \(0.0339159\pi\)
\(524\) −8.76587 + 32.1409i −0.382939 + 1.40408i
\(525\) 0 0
\(526\) 22.7313 11.1469i 0.991132 0.486029i
\(527\) −17.0184 9.82557i −0.741332 0.428008i
\(528\) 0 0
\(529\) −1.77566 + 1.02518i −0.0772027 + 0.0445730i
\(530\) −26.8864 + 40.0449i −1.16787 + 1.73944i
\(531\) 0 0
\(532\) −10.2789 0.0458184i −0.445645 0.00198648i
\(533\) 32.0014 4.21306i 1.38613 0.182488i
\(534\) 0 0
\(535\) 1.63169 + 6.08953i 0.0705439 + 0.263273i
\(536\) 25.3759 12.3038i 1.09607 0.531441i
\(537\) 0 0
\(538\) 5.84477 + 2.89854i 0.251986 + 0.124965i
\(539\) 11.0106 + 4.56075i 0.474261 + 0.196445i
\(540\) 0 0
\(541\) 3.73279 + 9.01175i 0.160485 + 0.387445i 0.983584 0.180453i \(-0.0577565\pi\)
−0.823098 + 0.567899i \(0.807756\pi\)
\(542\) −26.5682 + 23.1951i −1.14120 + 0.996316i
\(543\) 0 0
\(544\) −9.72640 + 4.66251i −0.417016 + 0.199904i
\(545\) −23.7842 + 41.1954i −1.01880 + 1.76462i
\(546\) 0 0
\(547\) 11.9594 15.5858i 0.511346 0.666400i −0.464318 0.885668i \(-0.653701\pi\)
0.975664 + 0.219269i \(0.0703672\pi\)
\(548\) −10.6700 + 25.4383i −0.455799 + 1.08667i
\(549\) 0 0
\(550\) −10.2455 + 6.81281i −0.436868 + 0.290499i
\(551\) −5.23726 + 19.5457i −0.223115 + 0.832676i
\(552\) 0 0
\(553\) 1.88985 + 7.05300i 0.0803645 + 0.299924i
\(554\) −16.7569 14.7616i −0.711933 0.627161i
\(555\) 0 0
\(556\) −13.8303 + 7.90294i −0.586535 + 0.335159i
\(557\) 21.6370 8.96234i 0.916789 0.379747i 0.126138 0.992013i \(-0.459742\pi\)
0.790652 + 0.612266i \(0.209742\pi\)
\(558\) 0 0
\(559\) 29.8139i 1.26099i
\(560\) −1.89549 15.4616i −0.0800991 0.653372i
\(561\) 0 0
\(562\) 11.7268 5.75057i 0.494666 0.242573i
\(563\) 0.818810 6.21948i 0.0345087 0.262120i −0.965490 0.260441i \(-0.916132\pi\)
0.999999 0.00167918i \(-0.000534499\pi\)
\(564\) 0 0
\(565\) −12.7465 + 1.67811i −0.536251 + 0.0705988i
\(566\) 34.7294 + 6.98860i 1.45978 + 0.293753i
\(567\) 0 0
\(568\) −42.6156 8.77338i −1.78811 0.368123i
\(569\) 6.47069 24.1489i 0.271266 1.01238i −0.687037 0.726622i \(-0.741089\pi\)
0.958303 0.285755i \(-0.0922442\pi\)
\(570\) 0 0
\(571\) 14.7674 11.3314i 0.617997 0.474206i −0.251691 0.967808i \(-0.580987\pi\)
0.869688 + 0.493602i \(0.164320\pi\)
\(572\) 17.5671 + 2.39246i 0.734516 + 0.100034i
\(573\) 0 0
\(574\) −9.98480 11.4368i −0.416758 0.477363i
\(575\) 19.3223 0.805794
\(576\) 0 0
\(577\) −27.1476 −1.13017 −0.565084 0.825033i \(-0.691156\pi\)
−0.565084 + 0.825033i \(0.691156\pi\)
\(578\) −12.4299 14.2375i −0.517017 0.592202i
\(579\) 0 0
\(580\) −30.3852 4.13816i −1.26168 0.171828i
\(581\) 1.37718 1.05675i 0.0571352 0.0438414i
\(582\) 0 0
\(583\) −6.68303 + 24.9414i −0.276783 + 1.03297i
\(584\) −6.49851 + 31.5657i −0.268910 + 1.30620i
\(585\) 0 0
\(586\) 7.00048 + 1.40871i 0.289187 + 0.0581933i
\(587\) −0.628096 + 0.0826904i −0.0259243 + 0.00341300i −0.143477 0.989654i \(-0.545828\pi\)
0.117553 + 0.993067i \(0.462495\pi\)
\(588\) 0 0
\(589\) 5.28456 40.1402i 0.217746 1.65395i
\(590\) 6.61881 3.24572i 0.272492 0.133624i
\(591\) 0 0
\(592\) −19.7825 15.4618i −0.813054 0.635474i
\(593\) 33.5624i 1.37824i 0.724645 + 0.689122i \(0.242004\pi\)
−0.724645 + 0.689122i \(0.757996\pi\)
\(594\) 0 0
\(595\) −6.86029 + 2.84163i −0.281244 + 0.116495i
\(596\) 18.3814 10.5036i 0.752933 0.430243i
\(597\) 0 0
\(598\) −20.8921 18.4045i −0.854343 0.752614i
\(599\) 0.784321 + 2.92713i 0.0320465 + 0.119599i 0.980096 0.198523i \(-0.0636144\pi\)
−0.948050 + 0.318122i \(0.896948\pi\)
\(600\) 0 0
\(601\) −6.55487 + 24.4631i −0.267379 + 0.997871i 0.693400 + 0.720553i \(0.256112\pi\)
−0.960778 + 0.277317i \(0.910555\pi\)
\(602\) −11.6773 + 7.76493i −0.475931 + 0.316475i
\(603\) 0 0
\(604\) 12.8267 30.5802i 0.521912 1.24429i
\(605\) 10.7300 13.9836i 0.436237 0.568515i
\(606\) 0 0
\(607\) 14.9250 25.8508i 0.605786 1.04925i −0.386141 0.922440i \(-0.626192\pi\)
0.991927 0.126812i \(-0.0404746\pi\)
\(608\) −16.5434 14.8375i −0.670923 0.601741i
\(609\) 0 0
\(610\) −8.62884 + 7.53333i −0.349371 + 0.305016i
\(611\) 6.13933 + 14.8217i 0.248371 + 0.599620i
\(612\) 0 0
\(613\) −34.2219 14.1752i −1.38221 0.572530i −0.437139 0.899394i \(-0.644008\pi\)
−0.945071 + 0.326864i \(0.894008\pi\)
\(614\) 7.16064 + 3.55110i 0.288980 + 0.143311i
\(615\) 0 0
\(616\) −3.63822 7.50365i −0.146588 0.302331i
\(617\) 3.40150 + 12.6946i 0.136939 + 0.511064i 0.999982 + 0.00593386i \(0.00188882\pi\)
−0.863043 + 0.505130i \(0.831445\pi\)
\(618\) 0 0
\(619\) −40.4459 + 5.32480i −1.62566 + 0.214022i −0.887567 0.460679i \(-0.847606\pi\)
−0.738091 + 0.674701i \(0.764273\pi\)
\(620\) 61.3552 + 0.273493i 2.46408 + 0.0109837i
\(621\) 0 0
\(622\) −12.0779 + 17.9890i −0.484280 + 0.721291i
\(623\) 4.55503 2.62985i 0.182493 0.105363i
\(624\) 0 0
\(625\) 25.4602 + 14.6994i 1.01841 + 0.587977i
\(626\) −5.13625 + 2.51870i −0.205286 + 0.100667i
\(627\) 0 0
\(628\) −0.890914 + 3.26662i −0.0355513 + 0.130352i
\(629\) −4.58020 + 11.0576i −0.182625 + 0.440895i
\(630\) 0 0
\(631\) −14.7473 + 14.7473i −0.587079 + 0.587079i −0.936839 0.349760i \(-0.886263\pi\)
0.349760 + 0.936839i \(0.386263\pi\)
\(632\) −7.07648 + 14.1110i −0.281487 + 0.561307i
\(633\) 0 0
\(634\) 43.0058 2.72250i 1.70798 0.108124i
\(635\) −17.1177 + 13.1349i −0.679295 + 0.521241i
\(636\) 0 0
\(637\) 12.6636 16.5035i 0.501749 0.653892i
\(638\) −16.1082 + 3.16681i −0.637728 + 0.125375i
\(639\) 0 0
\(640\) 19.1446 27.7063i 0.756757 1.09519i
\(641\) −24.2693 42.0357i −0.958580 1.66031i −0.725953 0.687744i \(-0.758601\pi\)
−0.232627 0.972566i \(-0.574732\pi\)
\(642\) 0 0
\(643\) 17.0898 + 2.24991i 0.673954 + 0.0887278i 0.459733 0.888057i \(-0.347945\pi\)
0.214222 + 0.976785i \(0.431279\pi\)
\(644\) −1.76724 + 12.9763i −0.0696389 + 0.511336i
\(645\) 0 0
\(646\) −4.70638 + 9.49022i −0.185170 + 0.373388i
\(647\) −0.859997 0.859997i −0.0338100 0.0338100i 0.690000 0.723810i \(-0.257611\pi\)
−0.723810 + 0.690000i \(0.757611\pi\)
\(648\) 0 0
\(649\) 2.79052 2.79052i 0.109538 0.109538i
\(650\) 6.85788 + 20.3516i 0.268988 + 0.798254i
\(651\) 0 0
\(652\) 17.8137 4.68817i 0.697640 0.183603i
\(653\) −0.680657 + 5.17011i −0.0266362 + 0.202322i −0.999589 0.0286840i \(-0.990868\pi\)
0.972952 + 0.231006i \(0.0742017\pi\)
\(654\) 0 0
\(655\) −42.9407 + 24.7918i −1.67783 + 0.968697i
\(656\) 0.292610 32.8214i 0.0114245 1.28146i
\(657\) 0 0
\(658\) 4.20627 6.26486i 0.163978 0.244230i
\(659\) −19.0018 14.5806i −0.740207 0.567981i 0.168357 0.985726i \(-0.446154\pi\)
−0.908564 + 0.417745i \(0.862820\pi\)
\(660\) 0 0
\(661\) −13.1012 17.0738i −0.509577 0.664094i 0.465735 0.884924i \(-0.345790\pi\)
−0.975312 + 0.220830i \(0.929123\pi\)
\(662\) 28.0676 + 24.7255i 1.09088 + 0.960983i
\(663\) 0 0
\(664\) 3.74314 + 0.270485i 0.145262 + 0.0104968i
\(665\) −10.8177 10.8177i −0.419493 0.419493i
\(666\) 0 0
\(667\) 23.8185 + 9.86594i 0.922256 + 0.382011i
\(668\) 1.72576 + 13.5758i 0.0667716 + 0.525263i
\(669\) 0 0
\(670\) 39.7154 + 13.5804i 1.53434 + 0.524655i
\(671\) −3.06604 + 5.31054i −0.118363 + 0.205011i
\(672\) 0 0
\(673\) −8.46765 14.6664i −0.326404 0.565348i 0.655392 0.755289i \(-0.272504\pi\)
−0.981795 + 0.189941i \(0.939170\pi\)
\(674\) −4.37279 22.2425i −0.168434 0.856749i
\(675\) 0 0
\(676\) 1.91306 4.56092i 0.0735791 0.175420i
\(677\) 4.59712 + 34.9186i 0.176682 + 1.34203i 0.818205 + 0.574927i \(0.194969\pi\)
−0.641523 + 0.767103i \(0.721697\pi\)
\(678\) 0 0
\(679\) 10.8928 2.91871i 0.418026 0.112010i
\(680\) −15.1667 5.26174i −0.581615 0.201779i
\(681\) 0 0
\(682\) 31.1264 10.4887i 1.19189 0.401632i
\(683\) −11.7098 + 28.2700i −0.448064 + 1.08172i 0.524982 + 0.851113i \(0.324072\pi\)
−0.973046 + 0.230610i \(0.925928\pi\)
\(684\) 0 0
\(685\) −37.9311 + 15.7116i −1.44927 + 0.600308i
\(686\) −22.6839 1.53756i −0.866075 0.0587044i
\(687\) 0 0
\(688\) −30.0216 4.22502i −1.14456 0.161078i
\(689\) 39.0320 + 22.5351i 1.48700 + 0.858520i
\(690\) 0 0
\(691\) −13.8511 10.6283i −0.526919 0.404319i 0.310755 0.950490i \(-0.399418\pi\)
−0.837674 + 0.546171i \(0.816085\pi\)
\(692\) −0.417684 + 0.413977i −0.0158780 + 0.0157370i
\(693\) 0 0
\(694\) 21.5697 + 4.34048i 0.818775 + 0.164762i
\(695\) −22.8999 6.13601i −0.868643 0.232752i
\(696\) 0 0
\(697\) −15.1130 + 4.04952i −0.572446 + 0.153386i
\(698\) −8.18602 + 0.518220i −0.309845 + 0.0196149i
\(699\) 0 0
\(700\) 6.18505 7.98654i 0.233773 0.301863i
\(701\) 12.2330 + 29.5331i 0.462035 + 1.11545i 0.967561 + 0.252639i \(0.0812984\pi\)
−0.505526 + 0.862811i \(0.668702\pi\)
\(702\) 0 0
\(703\) −24.6586 −0.930016
\(704\) 4.89861 17.3504i 0.184623 0.653918i
\(705\) 0 0
\(706\) 8.18348 23.9324i 0.307989 0.900707i
\(707\) 10.2808 + 1.35349i 0.386649 + 0.0509033i
\(708\) 0 0
\(709\) −1.13476 8.61936i −0.0426168 0.323707i −0.999453 0.0330782i \(-0.989469\pi\)
0.956836 0.290629i \(-0.0938644\pi\)
\(710\) −35.8567 53.9231i −1.34568 2.02370i
\(711\) 0 0
\(712\) 11.1375 + 2.29291i 0.417396 + 0.0859303i
\(713\) −49.8248 13.3505i −1.86595 0.499981i
\(714\) 0 0
\(715\) 16.0634 + 20.9342i 0.600738 + 0.782897i
\(716\) −6.63541 25.2127i −0.247977 0.942243i
\(717\) 0 0
\(718\) 2.05079 30.2556i 0.0765347 1.12913i
\(719\) 25.2984i 0.943471i −0.881740 0.471736i \(-0.843628\pi\)
0.881740 0.471736i \(-0.156372\pi\)
\(720\) 0 0
\(721\) 13.2445i 0.493249i
\(722\) 5.03385 + 0.341205i 0.187340 + 0.0126983i
\(723\) 0 0
\(724\) −11.0382 6.43869i −0.410232 0.239292i
\(725\) −12.1057 15.7765i −0.449595 0.585923i
\(726\) 0 0
\(727\) 17.2575 + 4.62413i 0.640044 + 0.171499i 0.564223 0.825622i \(-0.309176\pi\)
0.0758207 + 0.997121i \(0.475842\pi\)
\(728\) −14.2947 + 2.74417i −0.529798 + 0.101706i
\(729\) 0 0
\(730\) −39.9413 + 26.5593i −1.47829 + 0.983005i
\(731\) 1.88635 + 14.3283i 0.0697693 + 0.529950i
\(732\) 0 0
\(733\) −41.6879 5.48832i −1.53978 0.202716i −0.687648 0.726044i \(-0.741357\pi\)
−0.852131 + 0.523328i \(0.824690\pi\)
\(734\) 4.01274 + 1.37212i 0.148113 + 0.0506460i
\(735\) 0 0
\(736\) −21.4934 + 18.4295i −0.792255 + 0.679321i
\(737\) 22.4698 0.827685
\(738\) 0 0
\(739\) 5.90691 + 14.2605i 0.217289 + 0.524582i 0.994510 0.104646i \(-0.0333710\pi\)
−0.777220 + 0.629229i \(0.783371\pi\)
\(740\) −4.71245 37.0708i −0.173233 1.36275i
\(741\) 0 0
\(742\) −1.33935 21.1570i −0.0491691 0.776696i
\(743\) −25.6711 + 6.87855i −0.941781 + 0.252349i −0.696871 0.717197i \(-0.745425\pi\)
−0.244910 + 0.969546i \(0.578758\pi\)
\(744\) 0 0
\(745\) 30.4356 + 8.15519i 1.11507 + 0.298783i
\(746\) 0.570240 2.83377i 0.0208780 0.103752i
\(747\) 0 0
\(748\) −8.59394 0.0383078i −0.314225 0.00140067i
\(749\) −2.19826 1.68679i −0.0803227 0.0616338i
\(750\) 0 0
\(751\) 25.5144 + 14.7308i 0.931034 + 0.537533i 0.887138 0.461503i \(-0.152690\pi\)
0.0438957 + 0.999036i \(0.486023\pi\)
\(752\) 15.7949 4.08167i 0.575982 0.148843i
\(753\) 0 0
\(754\) −1.93782 + 28.5889i −0.0705712 + 1.04115i
\(755\) 45.5982 18.8874i 1.65949 0.687382i
\(756\) 0 0
\(757\) −14.9103 + 35.9968i −0.541926 + 1.30832i 0.381437 + 0.924395i \(0.375429\pi\)
−0.923362 + 0.383929i \(0.874571\pi\)
\(758\) −0.744781 2.21023i −0.0270517 0.0802790i
\(759\) 0 0
\(760\) −1.94245 33.0173i −0.0704602 1.19766i
\(761\) −22.9268 + 6.14321i −0.831095 + 0.222691i −0.649191 0.760625i \(-0.724893\pi\)
−0.181904 + 0.983316i \(0.558226\pi\)
\(762\) 0 0
\(763\) −2.72891 20.7281i −0.0987930 0.750408i
\(764\) −14.7206 + 6.02074i −0.532573 + 0.217823i
\(765\) 0 0
\(766\) 7.06055 1.38808i 0.255108 0.0501534i
\(767\) −3.44416 5.96547i −0.124362 0.215401i
\(768\) 0 0
\(769\) −6.92890 + 12.0012i −0.249862 + 0.432774i −0.963487 0.267754i \(-0.913719\pi\)
0.713625 + 0.700528i \(0.247052\pi\)
\(770\) 4.01571 11.7439i 0.144716 0.423219i
\(771\) 0 0
\(772\) −40.9467 31.7105i −1.47371 1.14129i
\(773\) −20.9246 8.66725i −0.752605 0.311739i −0.0268012 0.999641i \(-0.508532\pi\)
−0.725804 + 0.687901i \(0.758532\pi\)
\(774\) 0 0
\(775\) 28.1340 + 28.1340i 1.01060 + 1.01060i
\(776\) 21.7933 + 10.9290i 0.782334 + 0.392329i
\(777\) 0 0
\(778\) −34.8427 + 39.5523i −1.24917 + 1.41802i
\(779\) −19.6235 25.5739i −0.703086 0.916280i
\(780\) 0 0
\(781\) −27.5028 21.1037i −0.984129 0.755148i
\(782\) 11.2050 + 7.52314i 0.400691 + 0.269027i
\(783\) 0 0
\(784\) −14.8239 15.0906i −0.529424 0.538948i
\(785\) −4.36425 + 2.51970i −0.155767 + 0.0899320i
\(786\) 0 0
\(787\) −1.83936 + 13.9713i −0.0655662 + 0.498024i 0.926881 + 0.375354i \(0.122479\pi\)
−0.992448 + 0.122670i \(0.960854\pi\)
\(788\) 6.49910 11.1418i 0.231521 0.396909i
\(789\) 0 0
\(790\) −22.2648 + 7.50257i −0.792145 + 0.266929i
\(791\) 3.99560 3.99560i 0.142067 0.142067i
\(792\) 0 0
\(793\) 7.56843 + 7.56843i 0.268763 + 0.268763i
\(794\) −25.7888 12.7892i −0.915210 0.453870i
\(795\) 0 0
\(796\) 11.2322 8.53946i 0.398113 0.302673i
\(797\) −16.4630 2.16739i −0.583149 0.0767730i −0.166820 0.985987i \(-0.553350\pi\)
−0.416328 + 0.909214i \(0.636683\pi\)
\(798\) 0 0
\(799\) −3.88829 6.73471i −0.137558 0.238257i
\(800\) 21.4652 4.02156i 0.758909 0.142184i
\(801\) 0 0
\(802\) −4.69211 23.8667i −0.165684 0.842763i
\(803\) −15.6317 + 20.3716i −0.551629 + 0.718897i
\(804\) 0 0
\(805\) −15.4635 + 11.8656i −0.545017 + 0.418206i
\(806\) −3.62217 57.2173i −0.127585 2.01539i
\(807\) 0 0
\(808\) 14.6683 + 16.9533i 0.516029 + 0.596416i
\(809\) 9.57260 9.57260i 0.336555 0.336555i −0.518514 0.855069i \(-0.673515\pi\)
0.855069 + 0.518514i \(0.173515\pi\)
\(810\) 0 0
\(811\) 2.74499 6.62700i 0.0963897 0.232705i −0.868329 0.495989i \(-0.834806\pi\)
0.964718 + 0.263284i \(0.0848056\pi\)
\(812\) 11.7022 6.68690i 0.410667 0.234664i
\(813\) 0 0
\(814\) −8.80802 17.9617i −0.308721 0.629557i
\(815\) 23.7426 + 13.7078i 0.831668 + 0.480164i
\(816\) 0 0
\(817\) −25.7857 + 14.8874i −0.902128 + 0.520844i
\(818\) 34.0580 + 22.8668i 1.19081 + 0.799518i
\(819\) 0 0
\(820\) 34.6966 34.3887i 1.21166 1.20090i
\(821\) 22.5064 2.96302i 0.785478 0.103410i 0.272890 0.962045i \(-0.412020\pi\)
0.512587 + 0.858635i \(0.328687\pi\)
\(822\) 0 0
\(823\) 7.39009 + 27.5802i 0.257602 + 0.961386i 0.966624 + 0.256199i \(0.0824702\pi\)
−0.709022 + 0.705187i \(0.750863\pi\)
\(824\) −19.0230 + 21.4012i −0.662696 + 0.745545i
\(825\) 0 0
\(826\) −1.43949 + 2.90267i −0.0500863 + 0.100997i
\(827\) 6.15565 + 2.54975i 0.214053 + 0.0886636i 0.487133 0.873328i \(-0.338043\pi\)
−0.273081 + 0.961991i \(0.588043\pi\)
\(828\) 0 0
\(829\) 8.24368 + 19.9020i 0.286315 + 0.691225i 0.999957 0.00928553i \(-0.00295572\pi\)
−0.713642 + 0.700510i \(0.752956\pi\)
\(830\) 3.67345 + 4.20765i 0.127507 + 0.146050i
\(831\) 0 0
\(832\) −27.0397 16.0973i −0.937433 0.558073i
\(833\) −5.04180 + 8.73266i −0.174688 + 0.302569i
\(834\) 0 0
\(835\) −12.3992 + 16.1590i −0.429092 + 0.559204i
\(836\) −6.70280 16.3882i −0.231821 0.566799i
\(837\) 0 0
\(838\) 9.25323 + 13.9155i 0.319648 + 0.480702i
\(839\) −2.11838 + 7.90589i −0.0731345 + 0.272942i −0.992804 0.119752i \(-0.961790\pi\)
0.919669 + 0.392694i \(0.128457\pi\)
\(840\) 0 0
\(841\) 0.638548 + 2.38309i 0.0220189 + 0.0821757i
\(842\) 6.46629 7.34033i 0.222843 0.252964i
\(843\) 0 0
\(844\) 38.3835 + 10.4684i 1.32122 + 0.360338i
\(845\) 6.80080 2.81698i 0.233955 0.0969072i
\(846\) 0 0
\(847\) 7.74685i 0.266185i
\(848\) 28.2234 36.1103i 0.969197 1.24003i
\(849\) 0 0
\(850\) −4.58349 9.34687i −0.157213 0.320595i
\(851\) −4.10069 + 31.1478i −0.140570 + 1.06773i
\(852\) 0 0
\(853\) 25.4147 3.34591i 0.870184 0.114562i 0.317806 0.948156i \(-0.397054\pi\)
0.552378 + 0.833594i \(0.313721\pi\)
\(854\) 0.993176 4.93552i 0.0339858 0.168890i
\(855\) 0 0
\(856\) −1.12936 5.88296i −0.0386006 0.201075i
\(857\) 7.02833 26.2301i 0.240083 0.896002i −0.735708 0.677298i \(-0.763151\pi\)
0.975791 0.218704i \(-0.0701828\pi\)
\(858\) 0 0
\(859\) −9.26688 + 7.11073i −0.316182 + 0.242615i −0.754644 0.656135i \(-0.772190\pi\)
0.438462 + 0.898750i \(0.355524\pi\)
\(860\) −27.3090 35.9202i −0.931229 1.22487i
\(861\) 0 0
\(862\) −8.36055 + 7.29911i −0.284762 + 0.248609i
\(863\) −19.5080 −0.664060 −0.332030 0.943269i \(-0.607734\pi\)
−0.332030 + 0.943269i \(0.607734\pi\)
\(864\) 0 0
\(865\) −0.875259 −0.0297597
\(866\) −3.89337 + 3.39907i −0.132302 + 0.115505i
\(867\) 0 0
\(868\) −21.4671 + 16.3208i −0.728641 + 0.553963i
\(869\) −9.97854 + 7.65681i −0.338499 + 0.259739i
\(870\) 0 0
\(871\) 10.1510 37.8840i 0.343953 1.28365i
\(872\) 25.3622 37.4132i 0.858871 1.26697i
\(873\) 0 0
\(874\) −5.48545 + 27.2595i −0.185548 + 0.922068i
\(875\) −4.39938 + 0.579189i −0.148726 + 0.0195802i
\(876\) 0 0
\(877\) 1.73803 13.2016i 0.0586891 0.445788i −0.936720 0.350079i \(-0.886155\pi\)
0.995409 0.0957091i \(-0.0305118\pi\)
\(878\) −18.1681 37.0493i −0.613145 1.25035i
\(879\) 0 0
\(880\) 23.3565 13.2087i 0.787347 0.445264i
\(881\) 5.68957i 0.191687i 0.995396 + 0.0958433i \(0.0305548\pi\)
−0.995396 + 0.0958433i \(0.969445\pi\)
\(882\) 0 0
\(883\) 43.3255 17.9460i 1.45802 0.603931i 0.493927 0.869503i \(-0.335561\pi\)
0.964091 + 0.265573i \(0.0855610\pi\)
\(884\) −3.94700 + 14.4720i −0.132752 + 0.486748i
\(885\) 0 0
\(886\) −29.7165 + 33.7332i −0.998345 + 1.13329i
\(887\) 3.30130 + 12.3206i 0.110847 + 0.413686i 0.998943 0.0459720i \(-0.0146385\pi\)
−0.888096 + 0.459658i \(0.847972\pi\)
\(888\) 0 0
\(889\) 2.45441 9.15999i 0.0823183 0.307216i
\(890\) 9.37108 + 14.0927i 0.314119 + 0.472388i
\(891\) 0 0
\(892\) 15.7325 6.43460i 0.526763 0.215446i
\(893\) 9.75345 12.7109i 0.326387 0.425356i
\(894\) 0 0
\(895\) 19.4014 33.6042i 0.648516 1.12326i
\(896\) 0.737533 + 14.7832i 0.0246392 + 0.493872i
\(897\) 0 0
\(898\) 32.6361 + 37.3821i 1.08908 + 1.24746i
\(899\) 20.3154 + 49.0458i 0.677558 + 1.63577i
\(900\) 0 0
\(901\) −20.1842 8.36057i −0.672434 0.278531i
\(902\) 11.6189 23.4290i 0.386868 0.780102i
\(903\) 0 0
\(904\) 12.1952 0.717458i 0.405605 0.0238623i
\(905\) −4.92253 18.3711i −0.163630 0.610677i
\(906\) 0 0
\(907\) 7.59347 0.999700i 0.252137 0.0331945i −0.00339808 0.999994i \(-0.501082\pi\)
0.255535 + 0.966800i \(0.417748\pi\)
\(908\) −15.5342 15.6733i −0.515522 0.520138i
\(909\) 0 0
\(910\) −17.9860 12.0759i −0.596229 0.400312i
\(911\) 19.5408 11.2819i 0.647415 0.373785i −0.140050 0.990144i \(-0.544726\pi\)
0.787465 + 0.616359i \(0.211393\pi\)
\(912\) 0 0
\(913\) 2.58956 + 1.49508i 0.0857019 + 0.0494800i
\(914\) −15.5925 31.7970i −0.515755 1.05175i
\(915\) 0 0
\(916\) 6.21701 + 10.8799i 0.205416 + 0.359482i
\(917\) 8.33971 20.1338i 0.275401 0.664878i
\(918\) 0 0
\(919\) −15.9941 + 15.9941i −0.527598 + 0.527598i −0.919856 0.392257i \(-0.871694\pi\)
0.392257 + 0.919856i \(0.371694\pi\)
\(920\) −42.0293 3.03710i −1.38566 0.100130i
\(921\) 0 0
\(922\) −1.46263 23.1043i −0.0481692 0.760900i
\(923\) −48.0054 + 36.8359i −1.58012 + 1.21247i
\(924\) 0 0
\(925\) 14.7520 19.2252i 0.485042 0.632119i
\(926\) 3.48719 + 17.7378i 0.114596 + 0.582900i
\(927\) 0 0
\(928\) 28.5135 + 6.00275i 0.936000 + 0.197050i
\(929\) 4.55956 + 7.89740i 0.149594 + 0.259105i 0.931078 0.364821i \(-0.118870\pi\)
−0.781483 + 0.623926i \(0.785537\pi\)
\(930\) 0 0
\(931\) −20.5972 2.71167i −0.675045 0.0888714i
\(932\) 33.7142 + 44.3451i 1.10435 + 1.45257i
\(933\) 0 0
\(934\) −32.0923 15.9152i −1.05009 0.520761i
\(935\) −9.04445 9.04445i −0.295785 0.295785i
\(936\) 0 0
\(937\) −18.2296 + 18.2296i −0.595534 + 0.595534i −0.939121 0.343587i \(-0.888358\pi\)
0.343587 + 0.939121i \(0.388358\pi\)
\(938\) −17.4819 + 5.89089i −0.570805 + 0.192344i
\(939\) 0 0
\(940\) 20.9731 + 12.2338i 0.684068 + 0.399023i
\(941\) 2.31515 17.5853i 0.0754719 0.573266i −0.911371 0.411585i \(-0.864975\pi\)
0.986843 0.161681i \(-0.0516914\pi\)
\(942\) 0 0
\(943\) −35.5674 + 20.5348i −1.15823 + 0.668706i
\(944\) −6.49511 + 2.62277i −0.211398 + 0.0853639i
\(945\) 0 0
\(946\) −20.0548 13.4650i −0.652039 0.437783i
\(947\) 14.4728 + 11.1054i 0.470302 + 0.360876i 0.816557 0.577265i \(-0.195880\pi\)
−0.346255 + 0.938141i \(0.612547\pi\)
\(948\) 0 0
\(949\) 27.2846 + 35.5580i 0.885696 + 1.15426i
\(950\) 14.1774 16.0937i 0.459976 0.522150i
\(951\) 0 0
\(952\) 6.69629 2.22326i 0.217028 0.0720564i
\(953\) 7.34701 + 7.34701i 0.237993 + 0.237993i 0.816019 0.578026i \(-0.196177\pi\)
−0.578026 + 0.816019i \(0.696177\pi\)
\(954\) 0 0
\(955\) −21.8690 9.05845i −0.707665 0.293125i
\(956\) 1.72039 2.22148i 0.0556414 0.0718479i
\(957\) 0 0
\(958\) 6.63114 19.3926i 0.214242 0.626546i
\(959\) 9.02241 15.6273i 0.291349 0.504631i
\(960\) 0 0
\(961\) −37.6079 65.1388i −1.21316 2.10125i
\(962\) −34.2625 + 6.73588i −1.10467 + 0.217174i
\(963\) 0 0
\(964\) 22.2380 + 54.3716i 0.716239 + 1.75119i
\(965\) −10.0611 76.4213i −0.323877 2.46009i
\(966\) 0 0
\(967\) −29.8276 + 7.99229i −0.959192 + 0.257015i −0.704258 0.709944i \(-0.748720\pi\)
−0.254934 + 0.966959i \(0.582054\pi\)
\(968\) −11.1268 + 12.5178i −0.357628 + 0.402338i
\(969\) 0 0
\(970\) 11.5871 + 34.3861i 0.372039 + 1.10407i
\(971\) −1.22392 + 2.95481i −0.0392776 + 0.0948245i −0.942301 0.334767i \(-0.891342\pi\)
0.903023 + 0.429591i \(0.141342\pi\)
\(972\) 0 0
\(973\) 9.62671 3.98751i 0.308618 0.127834i
\(974\) −1.36831 + 20.1869i −0.0438436 + 0.646831i
\(975\) 0 0
\(976\) 8.69370 6.54860i 0.278278 0.209616i
\(977\) −5.02272 2.89987i −0.160691 0.0927749i 0.417498 0.908678i \(-0.362907\pi\)
−0.578189 + 0.815903i \(0.696240\pi\)
\(978\) 0 0
\(979\) 7.18782 + 5.51541i 0.229724 + 0.176273i
\(980\) 0.140338 31.4832i 0.00448292 1.00569i
\(981\) 0 0
\(982\) 1.14591 5.69453i 0.0365675 0.181720i
\(983\) 23.2872 + 6.23978i 0.742745 + 0.199018i 0.610298 0.792172i \(-0.291050\pi\)
0.132447 + 0.991190i \(0.457716\pi\)
\(984\) 0 0
\(985\) 18.5435 4.96872i 0.590845 0.158317i
\(986\) −0.877551 13.8622i −0.0279469 0.441462i
\(987\) 0 0
\(988\) −30.6586 + 3.89733i −0.975379 + 0.123990i
\(989\) 14.5171 + 35.0473i 0.461616 + 1.11444i
\(990\) 0 0
\(991\) 23.4723 0.745623 0.372812 0.927907i \(-0.378394\pi\)
0.372812 + 0.927907i \(0.378394\pi\)
\(992\) −58.1292 4.46105i −1.84560 0.141639i
\(993\) 0 0
\(994\) 26.9305 + 9.20865i 0.854182 + 0.292081i
\(995\) 20.8203 + 2.74105i 0.660048 + 0.0868970i
\(996\) 0 0
\(997\) 4.25966 + 32.3554i 0.134905 + 1.02470i 0.916251 + 0.400606i \(0.131200\pi\)
−0.781346 + 0.624099i \(0.785466\pi\)
\(998\) −18.0294 + 11.9888i −0.570712 + 0.379500i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 864.2.bk.a.37.11 368
3.2 odd 2 288.2.bc.a.229.36 yes 368
9.2 odd 6 288.2.bc.a.133.28 yes 368
9.7 even 3 inner 864.2.bk.a.613.19 368
32.13 even 8 inner 864.2.bk.a.685.19 368
96.77 odd 8 288.2.bc.a.13.28 368
288.173 odd 24 288.2.bc.a.205.36 yes 368
288.205 even 24 inner 864.2.bk.a.397.11 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bc.a.13.28 368 96.77 odd 8
288.2.bc.a.133.28 yes 368 9.2 odd 6
288.2.bc.a.205.36 yes 368 288.173 odd 24
288.2.bc.a.229.36 yes 368 3.2 odd 2
864.2.bk.a.37.11 368 1.1 even 1 trivial
864.2.bk.a.397.11 368 288.205 even 24 inner
864.2.bk.a.613.19 368 9.7 even 3 inner
864.2.bk.a.685.19 368 32.13 even 8 inner