Properties

Label 600.2.k.e.301.6
Level $600$
Weight $2$
Character 600.301
Analytic conductor $4.791$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [600,2,Mod(301,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("600.301");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.k (of order \(2\), degree \(1\), 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: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.214798336.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 301.6
Root \(-0.565036 - 1.29643i\) of defining polynomial
Character \(\chi\) \(=\) 600.301
Dual form 600.2.k.e.301.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.16863 + 0.796431i) q^{2} +1.00000i q^{3} +(0.731395 + 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} -4.72294 q^{7} +(-0.627801 + 2.75787i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.16863 + 0.796431i) q^{2} +1.00000i q^{3} +(0.731395 + 1.86147i) q^{4} +(-0.796431 + 1.16863i) q^{6} -4.72294 q^{7} +(-0.627801 + 2.75787i) q^{8} -1.00000 q^{9} +3.93012i q^{11} +(-1.86147 + 0.731395i) q^{12} -3.46733i q^{13} +(-5.51937 - 3.76149i) q^{14} +(-2.93012 + 2.72294i) q^{16} -3.51575 q^{17} +(-1.16863 - 0.796431i) q^{18} +5.44133i q^{19} -4.72294i q^{21} +(-3.13007 + 4.59286i) q^{22} +7.11585 q^{23} +(-2.75787 - 0.627801i) q^{24} +(2.76149 - 4.05203i) q^{26} -1.00000i q^{27} +(-3.45433 - 8.79159i) q^{28} +3.66998i q^{29} +5.23414 q^{31} +(-5.59286 + 0.848464i) q^{32} -3.93012 q^{33} +(-4.10861 - 2.80005i) q^{34} +(-0.731395 - 1.86147i) q^{36} -0.414376i q^{37} +(-4.33364 + 6.35890i) q^{38} +3.46733 q^{39} +3.00454 q^{41} +(3.76149 - 5.51937i) q^{42} +5.34450i q^{43} +(-7.31580 + 2.87447i) q^{44} +(8.31580 + 5.66728i) q^{46} +0.925579 q^{47} +(-2.72294 - 2.93012i) q^{48} +15.3061 q^{49} -3.51575i q^{51} +(6.45433 - 2.53599i) q^{52} -0.233196i q^{53} +(0.796431 - 1.16863i) q^{54} +(2.96506 - 13.0253i) q^{56} -5.44133 q^{57} +(-2.92288 + 4.28885i) q^{58} -14.3805i q^{59} +0.118290i q^{61} +(6.11677 + 4.16863i) q^{62} +4.72294 q^{63} +(-7.21173 - 3.46279i) q^{64} +(-4.59286 - 3.13007i) q^{66} +13.4504i q^{67} +(-2.57140 - 6.54445i) q^{68} +7.11585i q^{69} +2.19027 q^{71} +(0.627801 - 2.75787i) q^{72} +0.563219 q^{73} +(0.330022 - 0.484253i) q^{74} +(-10.1289 + 3.97976i) q^{76} -18.5617i q^{77} +(4.05203 + 2.76149i) q^{78} -10.2746 q^{79} +1.00000 q^{81} +(3.51120 + 2.39291i) q^{82} +11.3490i q^{83} +(8.79159 - 3.45433i) q^{84} +(-4.25653 + 6.24575i) q^{86} -3.66998 q^{87} +(-10.8388 - 2.46733i) q^{88} +8.88265 q^{89} +16.3760i q^{91} +(5.20449 + 13.2459i) q^{92} +5.23414i q^{93} +(1.08166 + 0.737160i) q^{94} +(-0.848464 - 5.59286i) q^{96} -7.27462 q^{97} +(17.8872 + 12.1903i) q^{98} -3.93012i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} + 4 q^{4} + 2 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 6 q^{14} + 8 q^{16} - 2 q^{18} - 12 q^{22} - 8 q^{23} - 8 q^{24} - 2 q^{26} + 4 q^{28} + 8 q^{31} - 28 q^{32} + 12 q^{34} - 4 q^{36} - 30 q^{38} + 6 q^{42} - 12 q^{44} + 20 q^{46} + 8 q^{48} + 20 q^{52} - 2 q^{54} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 30 q^{62} + 8 q^{63} - 32 q^{64} - 20 q^{66} + 28 q^{68} - 40 q^{71} + 4 q^{72} + 16 q^{73} + 8 q^{74} - 20 q^{76} + 22 q^{78} - 16 q^{79} + 8 q^{81} + 24 q^{82} + 24 q^{84} - 18 q^{86} - 24 q^{87} + 8 q^{88} + 36 q^{92} - 4 q^{94} + 12 q^{96} + 8 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16863 + 0.796431i 0.826347 + 0.563162i
\(3\) 1.00000i 0.577350i
\(4\) 0.731395 + 1.86147i 0.365697 + 0.930734i
\(5\) 0 0
\(6\) −0.796431 + 1.16863i −0.325142 + 0.477091i
\(7\) −4.72294 −1.78510 −0.892551 0.450947i \(-0.851086\pi\)
−0.892551 + 0.450947i \(0.851086\pi\)
\(8\) −0.627801 + 2.75787i −0.221961 + 0.975056i
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.93012i 1.18498i 0.805579 + 0.592488i \(0.201854\pi\)
−0.805579 + 0.592488i \(0.798146\pi\)
\(12\) −1.86147 + 0.731395i −0.537359 + 0.211135i
\(13\) 3.46733i 0.961665i −0.876812 0.480833i \(-0.840334\pi\)
0.876812 0.480833i \(-0.159666\pi\)
\(14\) −5.51937 3.76149i −1.47511 1.00530i
\(15\) 0 0
\(16\) −2.93012 + 2.72294i −0.732531 + 0.680734i
\(17\) −3.51575 −0.852694 −0.426347 0.904560i \(-0.640200\pi\)
−0.426347 + 0.904560i \(0.640200\pi\)
\(18\) −1.16863 0.796431i −0.275449 0.187721i
\(19\) 5.44133i 1.24833i 0.781294 + 0.624163i \(0.214560\pi\)
−0.781294 + 0.624163i \(0.785440\pi\)
\(20\) 0 0
\(21\) 4.72294i 1.03063i
\(22\) −3.13007 + 4.59286i −0.667334 + 0.979202i
\(23\) 7.11585 1.48376 0.741878 0.670534i \(-0.233935\pi\)
0.741878 + 0.670534i \(0.233935\pi\)
\(24\) −2.75787 0.627801i −0.562949 0.128149i
\(25\) 0 0
\(26\) 2.76149 4.05203i 0.541573 0.794669i
\(27\) 1.00000i 0.192450i
\(28\) −3.45433 8.79159i −0.652807 1.66145i
\(29\) 3.66998i 0.681498i 0.940154 + 0.340749i \(0.110681\pi\)
−0.940154 + 0.340749i \(0.889319\pi\)
\(30\) 0 0
\(31\) 5.23414 0.940079 0.470039 0.882645i \(-0.344240\pi\)
0.470039 + 0.882645i \(0.344240\pi\)
\(32\) −5.59286 + 0.848464i −0.988688 + 0.149989i
\(33\) −3.93012 −0.684147
\(34\) −4.10861 2.80005i −0.704621 0.480205i
\(35\) 0 0
\(36\) −0.731395 1.86147i −0.121899 0.310245i
\(37\) 0.414376i 0.0681231i −0.999420 0.0340615i \(-0.989156\pi\)
0.999420 0.0340615i \(-0.0108442\pi\)
\(38\) −4.33364 + 6.35890i −0.703010 + 1.03155i
\(39\) 3.46733 0.555218
\(40\) 0 0
\(41\) 3.00454 0.469231 0.234616 0.972088i \(-0.424617\pi\)
0.234616 + 0.972088i \(0.424617\pi\)
\(42\) 3.76149 5.51937i 0.580411 0.851657i
\(43\) 5.34450i 0.815029i 0.913199 + 0.407514i \(0.133604\pi\)
−0.913199 + 0.407514i \(0.866396\pi\)
\(44\) −7.31580 + 2.87447i −1.10290 + 0.433343i
\(45\) 0 0
\(46\) 8.31580 + 5.66728i 1.22610 + 0.835595i
\(47\) 0.925579 0.135010 0.0675048 0.997719i \(-0.478496\pi\)
0.0675048 + 0.997719i \(0.478496\pi\)
\(48\) −2.72294 2.93012i −0.393022 0.422927i
\(49\) 15.3061 2.18659
\(50\) 0 0
\(51\) 3.51575i 0.492303i
\(52\) 6.45433 2.53599i 0.895055 0.351679i
\(53\) 0.233196i 0.0320320i −0.999872 0.0160160i \(-0.994902\pi\)
0.999872 0.0160160i \(-0.00509826\pi\)
\(54\) 0.796431 1.16863i 0.108381 0.159030i
\(55\) 0 0
\(56\) 2.96506 13.0253i 0.396223 1.74057i
\(57\) −5.44133 −0.720721
\(58\) −2.92288 + 4.28885i −0.383794 + 0.563153i
\(59\) 14.3805i 1.87219i −0.351752 0.936093i \(-0.614414\pi\)
0.351752 0.936093i \(-0.385586\pi\)
\(60\) 0 0
\(61\) 0.118290i 0.0151454i 0.999971 + 0.00757271i \(0.00241049\pi\)
−0.999971 + 0.00757271i \(0.997590\pi\)
\(62\) 6.11677 + 4.16863i 0.776831 + 0.529417i
\(63\) 4.72294 0.595034
\(64\) −7.21173 3.46279i −0.901467 0.432849i
\(65\) 0 0
\(66\) −4.59286 3.13007i −0.565342 0.385285i
\(67\) 13.4504i 1.64323i 0.570043 + 0.821615i \(0.306927\pi\)
−0.570043 + 0.821615i \(0.693073\pi\)
\(68\) −2.57140 6.54445i −0.311828 0.793631i
\(69\) 7.11585i 0.856647i
\(70\) 0 0
\(71\) 2.19027 0.259937 0.129969 0.991518i \(-0.458512\pi\)
0.129969 + 0.991518i \(0.458512\pi\)
\(72\) 0.627801 2.75787i 0.0739870 0.325019i
\(73\) 0.563219 0.0659197 0.0329599 0.999457i \(-0.489507\pi\)
0.0329599 + 0.999457i \(0.489507\pi\)
\(74\) 0.330022 0.484253i 0.0383643 0.0562933i
\(75\) 0 0
\(76\) −10.1289 + 3.97976i −1.16186 + 0.456509i
\(77\) 18.5617i 2.11530i
\(78\) 4.05203 + 2.76149i 0.458802 + 0.312678i
\(79\) −10.2746 −1.15599 −0.577993 0.816042i \(-0.696164\pi\)
−0.577993 + 0.816042i \(0.696164\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 3.51120 + 2.39291i 0.387747 + 0.264253i
\(83\) 11.3490i 1.24572i 0.782334 + 0.622860i \(0.214029\pi\)
−0.782334 + 0.622860i \(0.785971\pi\)
\(84\) 8.79159 3.45433i 0.959241 0.376898i
\(85\) 0 0
\(86\) −4.25653 + 6.24575i −0.458993 + 0.673496i
\(87\) −3.66998 −0.393463
\(88\) −10.8388 2.46733i −1.15542 0.263019i
\(89\) 8.88265 0.941559 0.470780 0.882251i \(-0.343973\pi\)
0.470780 + 0.882251i \(0.343973\pi\)
\(90\) 0 0
\(91\) 16.3760i 1.71667i
\(92\) 5.20449 + 13.2459i 0.542606 + 1.38098i
\(93\) 5.23414i 0.542755i
\(94\) 1.08166 + 0.737160i 0.111565 + 0.0760322i
\(95\) 0 0
\(96\) −0.848464 5.59286i −0.0865960 0.570819i
\(97\) −7.27462 −0.738626 −0.369313 0.929305i \(-0.620407\pi\)
−0.369313 + 0.929305i \(0.620407\pi\)
\(98\) 17.8872 + 12.1903i 1.80688 + 1.23140i
\(99\) 3.93012i 0.394992i
\(100\) 0 0
\(101\) 4.23320i 0.421219i −0.977570 0.210609i \(-0.932455\pi\)
0.977570 0.210609i \(-0.0675448\pi\)
\(102\) 2.80005 4.10861i 0.277246 0.406813i
\(103\) −0.0429270 −0.00422972 −0.00211486 0.999998i \(-0.500673\pi\)
−0.00211486 + 0.999998i \(0.500673\pi\)
\(104\) 9.56247 + 2.17679i 0.937677 + 0.213452i
\(105\) 0 0
\(106\) 0.185725 0.272520i 0.0180392 0.0264695i
\(107\) 15.4728i 1.49581i −0.663804 0.747907i \(-0.731059\pi\)
0.663804 0.747907i \(-0.268941\pi\)
\(108\) 1.86147 0.731395i 0.179120 0.0703785i
\(109\) 12.9561i 1.24097i 0.784217 + 0.620486i \(0.213065\pi\)
−0.784217 + 0.620486i \(0.786935\pi\)
\(110\) 0 0
\(111\) 0.414376 0.0393309
\(112\) 13.8388 12.8602i 1.30764 1.21518i
\(113\) −3.86025 −0.363141 −0.181571 0.983378i \(-0.558118\pi\)
−0.181571 + 0.983378i \(0.558118\pi\)
\(114\) −6.35890 4.33364i −0.595566 0.405883i
\(115\) 0 0
\(116\) −6.83154 + 2.68420i −0.634293 + 0.249222i
\(117\) 3.46733i 0.320555i
\(118\) 11.4531 16.8055i 1.05434 1.54708i
\(119\) 16.6046 1.52215
\(120\) 0 0
\(121\) −4.44587 −0.404170
\(122\) −0.0942095 + 0.138237i −0.00852933 + 0.0125154i
\(123\) 3.00454i 0.270911i
\(124\) 3.82822 + 9.74318i 0.343784 + 0.874963i
\(125\) 0 0
\(126\) 5.51937 + 3.76149i 0.491704 + 0.335100i
\(127\) 18.3805 1.63101 0.815505 0.578751i \(-0.196460\pi\)
0.815505 + 0.578751i \(0.196460\pi\)
\(128\) −5.66998 9.79037i −0.501160 0.865355i
\(129\) −5.34450 −0.470557
\(130\) 0 0
\(131\) 3.41892i 0.298713i 0.988783 + 0.149356i \(0.0477201\pi\)
−0.988783 + 0.149356i \(0.952280\pi\)
\(132\) −2.87447 7.31580i −0.250191 0.636758i
\(133\) 25.6990i 2.22839i
\(134\) −10.7123 + 15.7186i −0.925404 + 1.35788i
\(135\) 0 0
\(136\) 2.20719 9.69599i 0.189265 0.831424i
\(137\) 16.3714 1.39871 0.699354 0.714776i \(-0.253471\pi\)
0.699354 + 0.714776i \(0.253471\pi\)
\(138\) −5.66728 + 8.31580i −0.482431 + 0.707888i
\(139\) 1.95707i 0.165997i 0.996550 + 0.0829984i \(0.0264496\pi\)
−0.996550 + 0.0829984i \(0.973550\pi\)
\(140\) 0 0
\(141\) 0.925579i 0.0779478i
\(142\) 2.55962 + 1.74440i 0.214798 + 0.146387i
\(143\) 13.6271 1.13955
\(144\) 2.93012 2.72294i 0.244177 0.226911i
\(145\) 0 0
\(146\) 0.658194 + 0.448565i 0.0544726 + 0.0371235i
\(147\) 15.3061i 1.26243i
\(148\) 0.771348 0.303073i 0.0634044 0.0249124i
\(149\) 12.0968i 0.991011i −0.868605 0.495505i \(-0.834983\pi\)
0.868605 0.495505i \(-0.165017\pi\)
\(150\) 0 0
\(151\) −4.87178 −0.396460 −0.198230 0.980156i \(-0.563519\pi\)
−0.198230 + 0.980156i \(0.563519\pi\)
\(152\) −15.0065 3.41607i −1.21719 0.277080i
\(153\) 3.51575 0.284231
\(154\) 14.7831 21.6918i 1.19126 1.74797i
\(155\) 0 0
\(156\) 2.53599 + 6.45433i 0.203042 + 0.516760i
\(157\) 21.6561i 1.72835i 0.503195 + 0.864173i \(0.332158\pi\)
−0.503195 + 0.864173i \(0.667842\pi\)
\(158\) −12.0072 8.18303i −0.955245 0.651007i
\(159\) 0.233196 0.0184937
\(160\) 0 0
\(161\) −33.6077 −2.64866
\(162\) 1.16863 + 0.796431i 0.0918163 + 0.0625735i
\(163\) 16.2362i 1.27172i 0.771804 + 0.635860i \(0.219355\pi\)
−0.771804 + 0.635860i \(0.780645\pi\)
\(164\) 2.19751 + 5.59286i 0.171597 + 0.436729i
\(165\) 0 0
\(166\) −9.03873 + 13.2628i −0.701542 + 1.02940i
\(167\) 6.69238 0.517872 0.258936 0.965894i \(-0.416628\pi\)
0.258936 + 0.965894i \(0.416628\pi\)
\(168\) 13.0253 + 2.96506i 1.00492 + 0.228759i
\(169\) 0.977595 0.0751996
\(170\) 0 0
\(171\) 5.44133i 0.416109i
\(172\) −9.94861 + 3.90894i −0.758575 + 0.298054i
\(173\) 22.4220i 1.70471i −0.522963 0.852355i \(-0.675173\pi\)
0.522963 0.852355i \(-0.324827\pi\)
\(174\) −4.28885 2.92288i −0.325137 0.221583i
\(175\) 0 0
\(176\) −10.7015 11.5157i −0.806654 0.868032i
\(177\) 14.3805 1.08091
\(178\) 10.3805 + 7.07442i 0.778054 + 0.530250i
\(179\) 0.148842i 0.0111250i 0.999985 + 0.00556249i \(0.00177060\pi\)
−0.999985 + 0.00556249i \(0.998229\pi\)
\(180\) 0 0
\(181\) 10.3929i 0.772499i −0.922394 0.386250i \(-0.873770\pi\)
0.922394 0.386250i \(-0.126230\pi\)
\(182\) −13.0424 + 19.1375i −0.966763 + 1.41856i
\(183\) −0.118290 −0.00874422
\(184\) −4.46733 + 19.6246i −0.329336 + 1.44675i
\(185\) 0 0
\(186\) −4.16863 + 6.11677i −0.305659 + 0.448504i
\(187\) 13.8173i 1.01042i
\(188\) 0.676964 + 1.72294i 0.0493726 + 0.125658i
\(189\) 4.72294i 0.343543i
\(190\) 0 0
\(191\) 6.23320 0.451018 0.225509 0.974241i \(-0.427595\pi\)
0.225509 + 0.974241i \(0.427595\pi\)
\(192\) 3.46279 7.21173i 0.249905 0.520462i
\(193\) 0.391971 0.0282147 0.0141074 0.999900i \(-0.495509\pi\)
0.0141074 + 0.999900i \(0.495509\pi\)
\(194\) −8.50135 5.79374i −0.610361 0.415966i
\(195\) 0 0
\(196\) 11.1948 + 28.4918i 0.799630 + 2.03513i
\(197\) 5.96616i 0.425071i −0.977153 0.212536i \(-0.931828\pi\)
0.977153 0.212536i \(-0.0681722\pi\)
\(198\) 3.13007 4.59286i 0.222445 0.326401i
\(199\) −17.9322 −1.27118 −0.635591 0.772026i \(-0.719243\pi\)
−0.635591 + 0.772026i \(0.719243\pi\)
\(200\) 0 0
\(201\) −13.4504 −0.948719
\(202\) 3.37145 4.94704i 0.237214 0.348073i
\(203\) 17.3331i 1.21654i
\(204\) 6.54445 2.57140i 0.458203 0.180034i
\(205\) 0 0
\(206\) −0.0501658 0.0341884i −0.00349521 0.00238202i
\(207\) −7.11585 −0.494586
\(208\) 9.44133 + 10.1597i 0.654638 + 0.704450i
\(209\) −21.3851 −1.47924
\(210\) 0 0
\(211\) 6.51575i 0.448563i −0.974524 0.224281i \(-0.927997\pi\)
0.974524 0.224281i \(-0.0720034\pi\)
\(212\) 0.434087 0.170558i 0.0298132 0.0117140i
\(213\) 2.19027i 0.150075i
\(214\) 12.3230 18.0820i 0.842385 1.23606i
\(215\) 0 0
\(216\) 2.75787 + 0.627801i 0.187650 + 0.0427164i
\(217\) −24.7205 −1.67814
\(218\) −10.3187 + 15.1409i −0.698868 + 1.02547i
\(219\) 0.563219i 0.0380588i
\(220\) 0 0
\(221\) 12.1903i 0.820006i
\(222\) 0.484253 + 0.330022i 0.0325009 + 0.0221496i
\(223\) −3.14640 −0.210699 −0.105349 0.994435i \(-0.533596\pi\)
−0.105349 + 0.994435i \(0.533596\pi\)
\(224\) 26.4147 4.00724i 1.76491 0.267745i
\(225\) 0 0
\(226\) −4.51120 3.07442i −0.300081 0.204507i
\(227\) 3.92103i 0.260248i 0.991498 + 0.130124i \(0.0415376\pi\)
−0.991498 + 0.130124i \(0.958462\pi\)
\(228\) −3.97976 10.1289i −0.263566 0.670800i
\(229\) 25.6899i 1.69764i −0.528683 0.848820i \(-0.677314\pi\)
0.528683 0.848820i \(-0.322686\pi\)
\(230\) 0 0
\(231\) 18.5617 1.22127
\(232\) −10.1213 2.30401i −0.664498 0.151266i
\(233\) −25.7565 −1.68737 −0.843683 0.536841i \(-0.819617\pi\)
−0.843683 + 0.536841i \(0.819617\pi\)
\(234\) −2.76149 + 4.05203i −0.180524 + 0.264890i
\(235\) 0 0
\(236\) 26.7689 10.5179i 1.74251 0.684654i
\(237\) 10.2746i 0.667409i
\(238\) 19.4047 + 13.2245i 1.25782 + 0.857214i
\(239\) −15.8727 −1.02672 −0.513360 0.858173i \(-0.671600\pi\)
−0.513360 + 0.858173i \(0.671600\pi\)
\(240\) 0 0
\(241\) 28.1664 1.81436 0.907178 0.420748i \(-0.138232\pi\)
0.907178 + 0.420748i \(0.138232\pi\)
\(242\) −5.19558 3.54083i −0.333985 0.227613i
\(243\) 1.00000i 0.0641500i
\(244\) −0.220192 + 0.0865164i −0.0140964 + 0.00553864i
\(245\) 0 0
\(246\) −2.39291 + 3.51120i −0.152567 + 0.223866i
\(247\) 18.8669 1.20047
\(248\) −3.28600 + 14.4351i −0.208661 + 0.916629i
\(249\) −11.3490 −0.719216
\(250\) 0 0
\(251\) 4.66004i 0.294139i 0.989126 + 0.147070i \(0.0469842\pi\)
−0.989126 + 0.147070i \(0.953016\pi\)
\(252\) 3.45433 + 8.79159i 0.217602 + 0.553818i
\(253\) 27.9662i 1.75822i
\(254\) 21.4801 + 14.6388i 1.34778 + 0.918522i
\(255\) 0 0
\(256\) 1.17125 15.9571i 0.0732029 0.997317i
\(257\) 3.33996 0.208341 0.104170 0.994559i \(-0.466781\pi\)
0.104170 + 0.994559i \(0.466781\pi\)
\(258\) −6.24575 4.25653i −0.388843 0.265000i
\(259\) 1.95707i 0.121607i
\(260\) 0 0
\(261\) 3.66998i 0.227166i
\(262\) −2.72294 + 3.99546i −0.168224 + 0.246840i
\(263\) −27.5932 −1.70147 −0.850735 0.525595i \(-0.823843\pi\)
−0.850735 + 0.525595i \(0.823843\pi\)
\(264\) 2.46733 10.8388i 0.151854 0.667081i
\(265\) 0 0
\(266\) 20.4675 30.0327i 1.25494 1.84142i
\(267\) 8.88265i 0.543609i
\(268\) −25.0375 + 9.83756i −1.52941 + 0.600925i
\(269\) 21.8727i 1.33360i 0.745235 + 0.666802i \(0.232337\pi\)
−0.745235 + 0.666802i \(0.767663\pi\)
\(270\) 0 0
\(271\) −8.78583 −0.533701 −0.266850 0.963738i \(-0.585983\pi\)
−0.266850 + 0.963738i \(0.585983\pi\)
\(272\) 10.3016 9.57315i 0.624625 0.580458i
\(273\) −16.3760 −0.991120
\(274\) 19.1322 + 13.0387i 1.15582 + 0.787699i
\(275\) 0 0
\(276\) −13.2459 + 5.20449i −0.797311 + 0.313274i
\(277\) 10.3838i 0.623904i 0.950098 + 0.311952i \(0.100983\pi\)
−0.950098 + 0.311952i \(0.899017\pi\)
\(278\) −1.55867 + 2.28710i −0.0934831 + 0.137171i
\(279\) −5.23414 −0.313360
\(280\) 0 0
\(281\) 17.0584 1.01762 0.508811 0.860878i \(-0.330085\pi\)
0.508811 + 0.860878i \(0.330085\pi\)
\(282\) −0.737160 + 1.08166i −0.0438972 + 0.0644119i
\(283\) 3.54724i 0.210862i 0.994427 + 0.105431i \(0.0336222\pi\)
−0.994427 + 0.105431i \(0.966378\pi\)
\(284\) 1.60195 + 4.07712i 0.0950583 + 0.241932i
\(285\) 0 0
\(286\) 15.9250 + 10.8530i 0.941664 + 0.641752i
\(287\) −14.1903 −0.837625
\(288\) 5.59286 0.848464i 0.329563 0.0499962i
\(289\) −4.63952 −0.272913
\(290\) 0 0
\(291\) 7.27462i 0.426446i
\(292\) 0.411935 + 1.04841i 0.0241067 + 0.0613537i
\(293\) 5.72538i 0.334480i −0.985916 0.167240i \(-0.946515\pi\)
0.985916 0.167240i \(-0.0534855\pi\)
\(294\) −12.1903 + 17.8872i −0.710951 + 1.04320i
\(295\) 0 0
\(296\) 1.14280 + 0.260146i 0.0664238 + 0.0151207i
\(297\) 3.93012 0.228049
\(298\) 9.63429 14.1367i 0.558099 0.818918i
\(299\) 24.6730i 1.42688i
\(300\) 0 0
\(301\) 25.2417i 1.45491i
\(302\) −5.69331 3.88004i −0.327613 0.223271i
\(303\) 4.23320 0.243191
\(304\) −14.8164 15.9438i −0.849778 0.914437i
\(305\) 0 0
\(306\) 4.10861 + 2.80005i 0.234874 + 0.160068i
\(307\) 12.3760i 0.706335i −0.935560 0.353168i \(-0.885105\pi\)
0.935560 0.353168i \(-0.114895\pi\)
\(308\) 34.5520 13.5759i 1.96879 0.773561i
\(309\) 0.0429270i 0.00244203i
\(310\) 0 0
\(311\) −18.2746 −1.03626 −0.518129 0.855302i \(-0.673371\pi\)
−0.518129 + 0.855302i \(0.673371\pi\)
\(312\) −2.17679 + 9.56247i −0.123237 + 0.541368i
\(313\) 12.7114 0.718491 0.359246 0.933243i \(-0.383034\pi\)
0.359246 + 0.933243i \(0.383034\pi\)
\(314\) −17.2476 + 25.3080i −0.973338 + 1.42821i
\(315\) 0 0
\(316\) −7.51481 19.1259i −0.422741 1.07591i
\(317\) 15.8602i 0.890800i −0.895332 0.445400i \(-0.853061\pi\)
0.895332 0.445400i \(-0.146939\pi\)
\(318\) 0.272520 + 0.185725i 0.0152822 + 0.0104149i
\(319\) −14.4235 −0.807559
\(320\) 0 0
\(321\) 15.4728 0.863609
\(322\) −39.2750 26.7662i −2.18871 1.49162i
\(323\) 19.1303i 1.06444i
\(324\) 0.731395 + 1.86147i 0.0406330 + 0.103415i
\(325\) 0 0
\(326\) −12.9310 + 18.9742i −0.716185 + 1.05088i
\(327\) −12.9561 −0.716476
\(328\) −1.88625 + 8.28615i −0.104151 + 0.457526i
\(329\) −4.37145 −0.241006
\(330\) 0 0
\(331\) 23.0315i 1.26593i −0.774182 0.632963i \(-0.781839\pi\)
0.774182 0.632963i \(-0.218161\pi\)
\(332\) −21.1259 + 8.30063i −1.15943 + 0.455556i
\(333\) 0.414376i 0.0227077i
\(334\) 7.82092 + 5.33002i 0.427942 + 0.291646i
\(335\) 0 0
\(336\) 12.8602 + 13.8388i 0.701584 + 0.754968i
\(337\) 0.860247 0.0468606 0.0234303 0.999725i \(-0.492541\pi\)
0.0234303 + 0.999725i \(0.492541\pi\)
\(338\) 1.14245 + 0.778587i 0.0621409 + 0.0423496i
\(339\) 3.86025i 0.209660i
\(340\) 0 0
\(341\) 20.5708i 1.11397i
\(342\) 4.33364 6.35890i 0.234337 0.343850i
\(343\) −39.2293 −2.11818
\(344\) −14.7395 3.35528i −0.794698 0.180905i
\(345\) 0 0
\(346\) 17.8576 26.2030i 0.960028 1.40868i
\(347\) 32.2856i 1.73318i 0.499019 + 0.866591i \(0.333694\pi\)
−0.499019 + 0.866591i \(0.666306\pi\)
\(348\) −2.68420 6.83154i −0.143888 0.366209i
\(349\) 0.742899i 0.0397665i −0.999802 0.0198832i \(-0.993671\pi\)
0.999802 0.0198832i \(-0.00632945\pi\)
\(350\) 0 0
\(351\) −3.46733 −0.185073
\(352\) −3.33457 21.9806i −0.177733 1.17157i
\(353\) 32.6392 1.73721 0.868604 0.495506i \(-0.165018\pi\)
0.868604 + 0.495506i \(0.165018\pi\)
\(354\) 16.8055 + 11.4531i 0.893204 + 0.608726i
\(355\) 0 0
\(356\) 6.49672 + 16.5348i 0.344326 + 0.876341i
\(357\) 16.6046i 0.878811i
\(358\) −0.118542 + 0.173941i −0.00626517 + 0.00919309i
\(359\) −2.71056 −0.143058 −0.0715290 0.997439i \(-0.522788\pi\)
−0.0715290 + 0.997439i \(0.522788\pi\)
\(360\) 0 0
\(361\) −10.6080 −0.558317
\(362\) 8.27724 12.1455i 0.435042 0.638352i
\(363\) 4.44587i 0.233348i
\(364\) −30.4834 + 11.9773i −1.59776 + 0.627782i
\(365\) 0 0
\(366\) −0.138237 0.0942095i −0.00722575 0.00492441i
\(367\) −0.680008 −0.0354961 −0.0177481 0.999842i \(-0.505650\pi\)
−0.0177481 + 0.999842i \(0.505650\pi\)
\(368\) −20.8503 + 19.3760i −1.08690 + 1.01004i
\(369\) −3.00454 −0.156410
\(370\) 0 0
\(371\) 1.10137i 0.0571803i
\(372\) −9.74318 + 3.82822i −0.505160 + 0.198484i
\(373\) 3.47642i 0.180002i 0.995942 + 0.0900012i \(0.0286871\pi\)
−0.995942 + 0.0900012i \(0.971313\pi\)
\(374\) 11.0045 16.1473i 0.569031 0.834959i
\(375\) 0 0
\(376\) −0.581079 + 2.55263i −0.0299669 + 0.131642i
\(377\) 12.7250 0.655373
\(378\) −3.76149 + 5.51937i −0.193470 + 0.283886i
\(379\) 23.0650i 1.18477i 0.805655 + 0.592385i \(0.201813\pi\)
−0.805655 + 0.592385i \(0.798187\pi\)
\(380\) 0 0
\(381\) 18.3805i 0.941664i
\(382\) 7.28430 + 4.96431i 0.372697 + 0.253996i
\(383\) 9.81544 0.501545 0.250773 0.968046i \(-0.419315\pi\)
0.250773 + 0.968046i \(0.419315\pi\)
\(384\) 9.79037 5.66998i 0.499613 0.289345i
\(385\) 0 0
\(386\) 0.458070 + 0.312178i 0.0233151 + 0.0158895i
\(387\) 5.34450i 0.271676i
\(388\) −5.32062 13.5415i −0.270114 0.687464i
\(389\) 9.86175i 0.500010i −0.968244 0.250005i \(-0.919568\pi\)
0.968244 0.250005i \(-0.0804323\pi\)
\(390\) 0 0
\(391\) −25.0175 −1.26519
\(392\) −9.60919 + 42.2123i −0.485337 + 2.13204i
\(393\) −3.41892 −0.172462
\(394\) 4.75164 6.97224i 0.239384 0.351256i
\(395\) 0 0
\(396\) 7.31580 2.87447i 0.367633 0.144448i
\(397\) 12.7783i 0.641326i −0.947193 0.320663i \(-0.896094\pi\)
0.947193 0.320663i \(-0.103906\pi\)
\(398\) −20.9561 14.2818i −1.05044 0.715881i
\(399\) 25.6990 1.28656
\(400\) 0 0
\(401\) 3.17325 0.158465 0.0792323 0.996856i \(-0.474753\pi\)
0.0792323 + 0.996856i \(0.474753\pi\)
\(402\) −15.7186 10.7123i −0.783971 0.534282i
\(403\) 18.1485i 0.904041i
\(404\) 7.87996 3.09614i 0.392043 0.154039i
\(405\) 0 0
\(406\) 13.8046 20.2560i 0.685111 1.00529i
\(407\) 1.62855 0.0807243
\(408\) 9.69599 + 2.20719i 0.480023 + 0.109272i
\(409\) 12.1125 0.598923 0.299461 0.954108i \(-0.403193\pi\)
0.299461 + 0.954108i \(0.403193\pi\)
\(410\) 0 0
\(411\) 16.3714i 0.807544i
\(412\) −0.0313965 0.0799071i −0.00154680 0.00393674i
\(413\) 67.9184i 3.34204i
\(414\) −8.31580 5.66728i −0.408699 0.278532i
\(415\) 0 0
\(416\) 2.94191 + 19.3923i 0.144239 + 0.950787i
\(417\) −1.95707 −0.0958383
\(418\) −24.9913 17.0317i −1.22236 0.833050i
\(419\) 4.24767i 0.207512i 0.994603 + 0.103756i \(0.0330862\pi\)
−0.994603 + 0.103756i \(0.966914\pi\)
\(420\) 0 0
\(421\) 3.77928i 0.184191i −0.995750 0.0920953i \(-0.970644\pi\)
0.995750 0.0920953i \(-0.0293564\pi\)
\(422\) 5.18934 7.61450i 0.252613 0.370668i
\(423\) −0.925579 −0.0450032
\(424\) 0.643126 + 0.146401i 0.0312329 + 0.00710985i
\(425\) 0 0
\(426\) −1.74440 + 2.55962i −0.0845164 + 0.124014i
\(427\) 0.558674i 0.0270361i
\(428\) 28.8022 11.3167i 1.39220 0.547015i
\(429\) 13.6271i 0.657920i
\(430\) 0 0
\(431\) 25.6271 1.23441 0.617206 0.786802i \(-0.288265\pi\)
0.617206 + 0.786802i \(0.288265\pi\)
\(432\) 2.72294 + 2.93012i 0.131007 + 0.140976i
\(433\) 2.03149 0.0976274 0.0488137 0.998808i \(-0.484456\pi\)
0.0488137 + 0.998808i \(0.484456\pi\)
\(434\) −28.8891 19.6882i −1.38672 0.945063i
\(435\) 0 0
\(436\) −24.1174 + 9.47605i −1.15501 + 0.453820i
\(437\) 38.7196i 1.85221i
\(438\) −0.448565 + 0.658194i −0.0214333 + 0.0314497i
\(439\) −22.4864 −1.07322 −0.536608 0.843832i \(-0.680294\pi\)
−0.536608 + 0.843832i \(0.680294\pi\)
\(440\) 0 0
\(441\) −15.3061 −0.728863
\(442\) −9.70871 + 14.2459i −0.461796 + 0.677609i
\(443\) 3.39385i 0.161247i 0.996745 + 0.0806234i \(0.0256911\pi\)
−0.996745 + 0.0806234i \(0.974309\pi\)
\(444\) 0.303073 + 0.771348i 0.0143832 + 0.0366066i
\(445\) 0 0
\(446\) −3.67698 2.50589i −0.174110 0.118657i
\(447\) 12.0968 0.572160
\(448\) 34.0605 + 16.3545i 1.60921 + 0.772679i
\(449\) −2.17780 −0.102777 −0.0513883 0.998679i \(-0.516365\pi\)
−0.0513883 + 0.998679i \(0.516365\pi\)
\(450\) 0 0
\(451\) 11.8082i 0.556028i
\(452\) −2.82336 7.18572i −0.132800 0.337988i
\(453\) 4.87178i 0.228896i
\(454\) −3.12283 + 4.58224i −0.146562 + 0.215055i
\(455\) 0 0
\(456\) 3.41607 15.0065i 0.159972 0.702743i
\(457\) 3.57653 0.167303 0.0836516 0.996495i \(-0.473342\pi\)
0.0836516 + 0.996495i \(0.473342\pi\)
\(458\) 20.4603 30.0221i 0.956046 1.40284i
\(459\) 3.51575i 0.164101i
\(460\) 0 0
\(461\) 13.1158i 0.610866i 0.952214 + 0.305433i \(0.0988012\pi\)
−0.952214 + 0.305433i \(0.901199\pi\)
\(462\) 21.6918 + 14.7831i 1.00919 + 0.687774i
\(463\) 3.21417 0.149375 0.0746877 0.997207i \(-0.476204\pi\)
0.0746877 + 0.997207i \(0.476204\pi\)
\(464\) −9.99311 10.7535i −0.463919 0.499218i
\(465\) 0 0
\(466\) −30.0999 20.5133i −1.39435 0.950261i
\(467\) 30.3016i 1.40219i −0.713068 0.701095i \(-0.752695\pi\)
0.713068 0.701095i \(-0.247305\pi\)
\(468\) −6.45433 + 2.53599i −0.298352 + 0.117226i
\(469\) 63.5254i 2.93333i
\(470\) 0 0
\(471\) −21.6561 −0.997861
\(472\) 39.6597 + 9.02811i 1.82549 + 0.415552i
\(473\) −21.0045 −0.965790
\(474\) 8.18303 12.0072i 0.375859 0.551511i
\(475\) 0 0
\(476\) 12.1446 + 30.9090i 0.556645 + 1.41671i
\(477\) 0.233196i 0.0106773i
\(478\) −18.5493 12.6415i −0.848427 0.578210i
\(479\) 35.0896 1.60328 0.801642 0.597804i \(-0.203960\pi\)
0.801642 + 0.597804i \(0.203960\pi\)
\(480\) 0 0
\(481\) −1.43678 −0.0655116
\(482\) 32.9161 + 22.4326i 1.49929 + 1.02178i
\(483\) 33.6077i 1.52920i
\(484\) −3.25169 8.27584i −0.147804 0.376175i
\(485\) 0 0
\(486\) −0.796431 + 1.16863i −0.0361269 + 0.0530102i
\(487\) −36.9117 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(488\) −0.326228 0.0742623i −0.0147676 0.00336169i
\(489\) −16.2362 −0.734228
\(490\) 0 0
\(491\) 20.9867i 0.947116i −0.880763 0.473558i \(-0.842969\pi\)
0.880763 0.473558i \(-0.157031\pi\)
\(492\) −5.59286 + 2.19751i −0.252146 + 0.0990713i
\(493\) 12.9027i 0.581109i
\(494\) 22.0484 + 15.0262i 0.992006 + 0.676060i
\(495\) 0 0
\(496\) −15.3367 + 14.2522i −0.688637 + 0.639943i
\(497\) −10.3445 −0.464014
\(498\) −13.2628 9.03873i −0.594322 0.405035i
\(499\) 15.9906i 0.715836i 0.933753 + 0.357918i \(0.116513\pi\)
−0.933753 + 0.357918i \(0.883487\pi\)
\(500\) 0 0
\(501\) 6.69238i 0.298994i
\(502\) −3.71140 + 5.44587i −0.165648 + 0.243061i
\(503\) 37.6023 1.67660 0.838302 0.545206i \(-0.183549\pi\)
0.838302 + 0.545206i \(0.183549\pi\)
\(504\) −2.96506 + 13.0253i −0.132074 + 0.580191i
\(505\) 0 0
\(506\) −22.2731 + 32.6821i −0.990161 + 1.45290i
\(507\) 0.977595i 0.0434165i
\(508\) 13.4434 + 34.2148i 0.596456 + 1.51804i
\(509\) 12.8579i 0.569917i −0.958540 0.284958i \(-0.908020\pi\)
0.958540 0.284958i \(-0.0919797\pi\)
\(510\) 0 0
\(511\) −2.66004 −0.117673
\(512\) 14.0775 17.7151i 0.622142 0.782904i
\(513\) 5.44133 0.240240
\(514\) 3.90317 + 2.66004i 0.172162 + 0.117330i
\(515\) 0 0
\(516\) −3.90894 9.94861i −0.172081 0.437963i
\(517\) 3.63764i 0.159983i
\(518\) −1.55867 + 2.28710i −0.0684842 + 0.100489i
\(519\) 22.4220 0.984215
\(520\) 0 0
\(521\) 37.0015 1.62107 0.810534 0.585692i \(-0.199177\pi\)
0.810534 + 0.585692i \(0.199177\pi\)
\(522\) 2.92288 4.28885i 0.127931 0.187718i
\(523\) 17.4952i 0.765013i 0.923953 + 0.382506i \(0.124939\pi\)
−0.923953 + 0.382506i \(0.875061\pi\)
\(524\) −6.36421 + 2.50058i −0.278022 + 0.109238i
\(525\) 0 0
\(526\) −32.2463 21.9761i −1.40600 0.958203i
\(527\) −18.4019 −0.801600
\(528\) 11.5157 10.7015i 0.501159 0.465722i
\(529\) 27.6353 1.20153
\(530\) 0 0
\(531\) 14.3805i 0.624062i
\(532\) 47.8379 18.7961i 2.07404 0.814916i
\(533\) 10.4178i 0.451243i
\(534\) −7.07442 + 10.3805i −0.306140 + 0.449210i
\(535\) 0 0
\(536\) −37.0945 8.44418i −1.60224 0.364733i
\(537\) −0.148842 −0.00642301
\(538\) −17.4201 + 25.5611i −0.751035 + 1.10202i
\(539\) 60.1549i 2.59106i
\(540\) 0 0
\(541\) 38.1225i 1.63901i 0.573069 + 0.819507i \(0.305753\pi\)
−0.573069 + 0.819507i \(0.694247\pi\)
\(542\) −10.2674 6.99731i −0.441022 0.300560i
\(543\) 10.3929 0.446003
\(544\) 19.6631 2.98298i 0.843048 0.127894i
\(545\) 0 0
\(546\) −19.1375 13.0424i −0.819009 0.558161i
\(547\) 35.7406i 1.52816i −0.645124 0.764078i \(-0.723194\pi\)
0.645124 0.764078i \(-0.276806\pi\)
\(548\) 11.9740 + 30.4749i 0.511504 + 1.30182i
\(549\) 0.118290i 0.00504848i
\(550\) 0 0
\(551\) −19.9695 −0.850731
\(552\) −19.6246 4.46733i −0.835279 0.190142i
\(553\) 48.5264 2.06355
\(554\) −8.27000 + 12.1349i −0.351359 + 0.515561i
\(555\) 0 0
\(556\) −3.64303 + 1.43139i −0.154499 + 0.0607046i
\(557\) 2.65516i 0.112503i 0.998417 + 0.0562514i \(0.0179148\pi\)
−0.998417 + 0.0562514i \(0.982085\pi\)
\(558\) −6.11677 4.16863i −0.258944 0.176472i
\(559\) 18.5312 0.783785
\(560\) 0 0
\(561\) 13.8173 0.583368
\(562\) 19.9350 + 13.5859i 0.840908 + 0.573086i
\(563\) 20.3107i 0.855992i −0.903781 0.427996i \(-0.859220\pi\)
0.903781 0.427996i \(-0.140780\pi\)
\(564\) −1.72294 + 0.676964i −0.0725487 + 0.0285053i
\(565\) 0 0
\(566\) −2.82513 + 4.14541i −0.118749 + 0.174245i
\(567\) −4.72294 −0.198345
\(568\) −1.37505 + 6.04049i −0.0576959 + 0.253453i
\(569\) −28.4274 −1.19174 −0.595868 0.803082i \(-0.703192\pi\)
−0.595868 + 0.803082i \(0.703192\pi\)
\(570\) 0 0
\(571\) 16.1485i 0.675794i −0.941183 0.337897i \(-0.890284\pi\)
0.941183 0.337897i \(-0.109716\pi\)
\(572\) 9.96675 + 25.3663i 0.416731 + 1.06062i
\(573\) 6.23320i 0.260396i
\(574\) −16.5832 11.3016i −0.692169 0.471719i
\(575\) 0 0
\(576\) 7.21173 + 3.46279i 0.300489 + 0.144283i
\(577\) 30.3600 1.26390 0.631952 0.775008i \(-0.282254\pi\)
0.631952 + 0.775008i \(0.282254\pi\)
\(578\) −5.42189 3.69506i −0.225521 0.153694i
\(579\) 0.391971i 0.0162898i
\(580\) 0 0
\(581\) 53.6008i 2.22374i
\(582\) 5.79374 8.50135i 0.240158 0.352392i
\(583\) 0.916490 0.0379571
\(584\) −0.353589 + 1.55329i −0.0146316 + 0.0642754i
\(585\) 0 0
\(586\) 4.55987 6.69085i 0.188366 0.276396i
\(587\) 2.74070i 0.113121i −0.998399 0.0565604i \(-0.981987\pi\)
0.998399 0.0565604i \(-0.0180133\pi\)
\(588\) −28.4918 + 11.1948i −1.17498 + 0.461666i
\(589\) 28.4807i 1.17352i
\(590\) 0 0
\(591\) 5.96616 0.245415
\(592\) 1.12832 + 1.21417i 0.0463737 + 0.0499022i
\(593\) 22.2586 0.914053 0.457027 0.889453i \(-0.348914\pi\)
0.457027 + 0.889453i \(0.348914\pi\)
\(594\) 4.59286 + 3.13007i 0.188447 + 0.128428i
\(595\) 0 0
\(596\) 22.5179 8.84755i 0.922367 0.362410i
\(597\) 17.9322i 0.733917i
\(598\) 19.6504 28.8336i 0.803563 1.17910i
\(599\) 48.4526 1.97972 0.989860 0.142046i \(-0.0453680\pi\)
0.989860 + 0.142046i \(0.0453680\pi\)
\(600\) 0 0
\(601\) 5.26553 0.214786 0.107393 0.994217i \(-0.465750\pi\)
0.107393 + 0.994217i \(0.465750\pi\)
\(602\) 20.1033 29.4983i 0.819349 1.20226i
\(603\) 13.4504i 0.547743i
\(604\) −3.56319 9.06866i −0.144984 0.368998i
\(605\) 0 0
\(606\) 4.94704 + 3.37145i 0.200960 + 0.136956i
\(607\) 7.38288 0.299662 0.149831 0.988712i \(-0.452127\pi\)
0.149831 + 0.988712i \(0.452127\pi\)
\(608\) −4.61677 30.4326i −0.187235 1.23420i
\(609\) 17.3331 0.702371
\(610\) 0 0
\(611\) 3.20929i 0.129834i
\(612\) 2.57140 + 6.54445i 0.103943 + 0.264544i
\(613\) 2.64607i 0.106874i 0.998571 + 0.0534369i \(0.0170176\pi\)
−0.998571 + 0.0534369i \(0.982982\pi\)
\(614\) 9.85663 14.4630i 0.397781 0.583678i
\(615\) 0 0
\(616\) 51.1909 + 11.6531i 2.06254 + 0.469515i
\(617\) 21.0136 0.845977 0.422989 0.906135i \(-0.360981\pi\)
0.422989 + 0.906135i \(0.360981\pi\)
\(618\) 0.0341884 0.0501658i 0.00137526 0.00201796i
\(619\) 24.0874i 0.968154i 0.875025 + 0.484077i \(0.160845\pi\)
−0.875025 + 0.484077i \(0.839155\pi\)
\(620\) 0 0
\(621\) 7.11585i 0.285549i
\(622\) −21.3563 14.5545i −0.856309 0.583581i
\(623\) −41.9522 −1.68078
\(624\) −10.1597 + 9.44133i −0.406714 + 0.377956i
\(625\) 0 0
\(626\) 14.8549 + 10.1238i 0.593723 + 0.404627i
\(627\) 21.3851i 0.854038i
\(628\) −40.3121 + 15.8392i −1.60863 + 0.632051i
\(629\) 1.45684i 0.0580881i
\(630\) 0 0
\(631\) 25.2094 1.00357 0.501785 0.864992i \(-0.332677\pi\)
0.501785 + 0.864992i \(0.332677\pi\)
\(632\) 6.45042 28.3361i 0.256584 1.12715i
\(633\) 6.51575 0.258978
\(634\) 12.6316 18.5348i 0.501665 0.736110i
\(635\) 0 0
\(636\) 0.170558 + 0.434087i 0.00676308 + 0.0172127i
\(637\) 53.0714i 2.10277i
\(638\) −16.8557 11.4873i −0.667324 0.454786i
\(639\) −2.19027 −0.0866457
\(640\) 0 0
\(641\) −18.4755 −0.729738 −0.364869 0.931059i \(-0.618886\pi\)
−0.364869 + 0.931059i \(0.618886\pi\)
\(642\) 18.0820 + 12.3230i 0.713640 + 0.486351i
\(643\) 0.636984i 0.0251202i 0.999921 + 0.0125601i \(0.00399811\pi\)
−0.999921 + 0.0125601i \(0.996002\pi\)
\(644\) −24.5805 62.5596i −0.968607 2.46519i
\(645\) 0 0
\(646\) 15.2360 22.3563i 0.599452 0.879596i
\(647\) 32.0182 1.25876 0.629382 0.777096i \(-0.283308\pi\)
0.629382 + 0.777096i \(0.283308\pi\)
\(648\) −0.627801 + 2.75787i −0.0246623 + 0.108340i
\(649\) 56.5173 2.21850
\(650\) 0 0
\(651\) 24.7205i 0.968873i
\(652\) −30.2232 + 11.8751i −1.18363 + 0.465065i
\(653\) 25.9769i 1.01656i 0.861193 + 0.508278i \(0.169718\pi\)
−0.861193 + 0.508278i \(0.830282\pi\)
\(654\) −15.1409 10.3187i −0.592057 0.403492i
\(655\) 0 0
\(656\) −8.80369 + 8.18118i −0.343726 + 0.319421i
\(657\) −0.563219 −0.0219732
\(658\) −5.10861 3.48156i −0.199154 0.135725i
\(659\) 21.3422i 0.831372i −0.909508 0.415686i \(-0.863541\pi\)
0.909508 0.415686i \(-0.136459\pi\)
\(660\) 0 0
\(661\) 14.8397i 0.577198i 0.957450 + 0.288599i \(0.0931895\pi\)
−0.957450 + 0.288599i \(0.906810\pi\)
\(662\) 18.3430 26.9153i 0.712921 1.04609i
\(663\) −12.1903 −0.473431
\(664\) −31.2992 7.12494i −1.21465 0.276501i
\(665\) 0 0
\(666\) −0.330022 + 0.484253i −0.0127881 + 0.0187644i
\(667\) 26.1150i 1.01118i
\(668\) 4.89477 + 12.4577i 0.189384 + 0.482001i
\(669\) 3.14640i 0.121647i
\(670\) 0 0
\(671\) −0.464893 −0.0179470
\(672\) 4.00724 + 26.4147i 0.154583 + 1.01897i
\(673\) 18.1167 0.698347 0.349174 0.937058i \(-0.386462\pi\)
0.349174 + 0.937058i \(0.386462\pi\)
\(674\) 1.00531 + 0.685127i 0.0387231 + 0.0263901i
\(675\) 0 0
\(676\) 0.715008 + 1.81976i 0.0275003 + 0.0699908i
\(677\) 30.5617i 1.17458i 0.809376 + 0.587291i \(0.199806\pi\)
−0.809376 + 0.587291i \(0.800194\pi\)
\(678\) 3.07442 4.51120i 0.118072 0.173252i
\(679\) 34.3576 1.31852
\(680\) 0 0
\(681\) −3.92103 −0.150254
\(682\) −16.3832 + 24.0397i −0.627346 + 0.920527i
\(683\) 22.2027i 0.849564i 0.905296 + 0.424782i \(0.139649\pi\)
−0.905296 + 0.424782i \(0.860351\pi\)
\(684\) 10.1289 3.97976i 0.387286 0.152170i
\(685\) 0 0
\(686\) −45.8445 31.2434i −1.75035 1.19288i
\(687\) 25.6899 0.980132
\(688\) −14.5527 15.6600i −0.554818 0.597034i
\(689\) −0.808569 −0.0308040
\(690\) 0 0
\(691\) 12.6890i 0.482712i −0.970437 0.241356i \(-0.922408\pi\)
0.970437 0.241356i \(-0.0775922\pi\)
\(692\) 41.7378 16.3993i 1.58663 0.623408i
\(693\) 18.5617i 0.705101i
\(694\) −25.7133 + 37.7299i −0.976062 + 1.43221i
\(695\) 0 0
\(696\) 2.30401 10.1213i 0.0873334 0.383648i
\(697\) −10.5632 −0.400110
\(698\) 0.591668 0.868174i 0.0223950 0.0328609i
\(699\) 25.7565i 0.974202i
\(700\) 0 0
\(701\) 34.9241i 1.31906i 0.751676 + 0.659532i \(0.229246\pi\)
−0.751676 + 0.659532i \(0.770754\pi\)
\(702\) −4.05203 2.76149i −0.152934 0.104226i
\(703\) 2.25476 0.0850398
\(704\) 13.6092 28.3430i 0.512916 1.06822i
\(705\) 0 0
\(706\) 38.1431 + 25.9949i 1.43554 + 0.978330i
\(707\) 19.9931i 0.751918i
\(708\) 10.5179 + 26.7689i 0.395285 + 1.00604i
\(709\) 5.65610i 0.212419i 0.994344 + 0.106210i \(0.0338715\pi\)
−0.994344 + 0.106210i \(0.966129\pi\)
\(710\) 0 0
\(711\) 10.2746 0.385328
\(712\) −5.57653 + 24.4972i −0.208989 + 0.918073i
\(713\) 37.2453 1.39485
\(714\) −13.2245 + 19.4047i −0.494913 + 0.726203i
\(715\) 0 0
\(716\) −0.277065 + 0.108862i −0.0103544 + 0.00406838i
\(717\) 15.8727i 0.592778i
\(718\) −3.16764 2.15878i −0.118215 0.0805648i
\(719\) −20.0844 −0.749020 −0.374510 0.927223i \(-0.622189\pi\)
−0.374510 + 0.927223i \(0.622189\pi\)
\(720\) 0 0
\(721\) 0.202741 0.00755048
\(722\) −12.3969 8.44856i −0.461364 0.314423i
\(723\) 28.1664i 1.04752i
\(724\) 19.3461 7.60132i 0.718991 0.282501i
\(725\) 0 0
\(726\) 3.54083 5.19558i 0.131413 0.192826i
\(727\) 13.0424 0.483715 0.241857 0.970312i \(-0.422243\pi\)
0.241857 + 0.970312i \(0.422243\pi\)
\(728\) −45.1629 10.2809i −1.67385 0.381034i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 18.7899i 0.694970i
\(732\) −0.0865164 0.220192i −0.00319774 0.00813854i
\(733\) 34.8917i 1.28876i 0.764707 + 0.644378i \(0.222884\pi\)
−0.764707 + 0.644378i \(0.777116\pi\)
\(734\) −0.794678 0.541580i −0.0293321 0.0199901i
\(735\) 0 0
\(736\) −39.7980 + 6.03754i −1.46697 + 0.222547i
\(737\) −52.8618 −1.94719
\(738\) −3.51120 2.39291i −0.129249 0.0880843i
\(739\) 41.5040i 1.52675i −0.645957 0.763374i \(-0.723541\pi\)
0.645957 0.763374i \(-0.276459\pi\)
\(740\) 0 0
\(741\) 18.8669i 0.693093i
\(742\) −0.877166 + 1.28710i −0.0322018 + 0.0472508i
\(743\) 7.63764 0.280198 0.140099 0.990138i \(-0.455258\pi\)
0.140099 + 0.990138i \(0.455258\pi\)
\(744\) −14.4351 3.28600i −0.529216 0.120470i
\(745\) 0 0
\(746\) −2.76873 + 4.06265i −0.101370 + 0.148744i
\(747\) 11.3490i 0.415240i
\(748\) 25.7205 10.1059i 0.940434 0.369509i
\(749\) 73.0771i 2.67018i
\(750\) 0 0
\(751\) −19.4029 −0.708023 −0.354012 0.935241i \(-0.615183\pi\)
−0.354012 + 0.935241i \(0.615183\pi\)
\(752\) −2.71206 + 2.52029i −0.0988987 + 0.0919056i
\(753\) −4.66004 −0.169821
\(754\) 14.8709 + 10.1346i 0.541565 + 0.369081i
\(755\) 0 0
\(756\) −8.79159 + 3.45433i −0.319747 + 0.125633i
\(757\) 43.7959i 1.59179i 0.605436 + 0.795894i \(0.292999\pi\)
−0.605436 + 0.795894i \(0.707001\pi\)
\(758\) −18.3697 + 26.9545i −0.667217 + 0.979030i
\(759\) −27.9662 −1.01511
\(760\) 0 0
\(761\) 9.95519 0.360875 0.180438 0.983586i \(-0.442249\pi\)
0.180438 + 0.983586i \(0.442249\pi\)
\(762\) −14.6388 + 21.4801i −0.530309 + 0.778140i
\(763\) 61.1910i 2.21526i
\(764\) 4.55893 + 11.6029i 0.164936 + 0.419778i
\(765\) 0 0
\(766\) 11.4706 + 7.81732i 0.414450 + 0.282451i
\(767\) −49.8621 −1.80042
\(768\) 15.9571 + 1.17125i 0.575801 + 0.0422637i
\(769\) −17.9008 −0.645520 −0.322760 0.946481i \(-0.604611\pi\)
−0.322760 + 0.946481i \(0.604611\pi\)
\(770\) 0 0
\(771\) 3.33996i 0.120286i
\(772\) 0.286686 + 0.729642i 0.0103180 + 0.0262604i
\(773\) 20.8182i 0.748777i −0.927272 0.374389i \(-0.877853\pi\)
0.927272 0.374389i \(-0.122147\pi\)
\(774\) 4.25653 6.24575i 0.152998 0.224499i
\(775\) 0 0
\(776\) 4.56701 20.0625i 0.163946 0.720201i
\(777\) −1.95707 −0.0702096
\(778\) 7.85420 11.5247i 0.281587 0.413182i
\(779\) 16.3487i 0.585753i
\(780\) 0 0
\(781\) 8.60803i 0.308019i
\(782\) −29.2362 19.9247i −1.04549 0.712507i
\(783\) 3.66998 0.131154
\(784\) −44.8488 + 41.6776i −1.60174 + 1.48848i
\(785\) 0 0
\(786\) −3.99546 2.72294i −0.142513 0.0971239i
\(787\) 27.2047i 0.969744i −0.874585 0.484872i \(-0.838866\pi\)
0.874585 0.484872i \(-0.161134\pi\)
\(788\) 11.1058 4.36362i 0.395628 0.155448i
\(789\) 27.5932i 0.982344i
\(790\) 0 0
\(791\) 18.2317 0.648244
\(792\) 10.8388 + 2.46733i 0.385139 + 0.0876729i
\(793\) 0.410149 0.0145648
\(794\) 10.1771 14.9332i 0.361170 0.529958i
\(795\) 0 0
\(796\) −13.1155 33.3803i −0.464868 1.18313i
\(797\) 16.4344i 0.582138i 0.956702 + 0.291069i \(0.0940109\pi\)
−0.956702 + 0.291069i \(0.905989\pi\)
\(798\) 30.0327 + 20.4675i 1.06315 + 0.724542i
\(799\) −3.25410 −0.115122
\(800\) 0 0
\(801\) −8.88265 −0.313853
\(802\) 3.70836 + 2.52728i 0.130947 + 0.0892413i
\(803\) 2.21352i 0.0781134i
\(804\) −9.83756 25.0375i −0.346944 0.883005i
\(805\) 0 0
\(806\) 14.4540 21.2089i 0.509122 0.747052i
\(807\) −21.8727 −0.769956
\(808\) 11.6746 + 2.65760i 0.410712 + 0.0934942i
\(809\) 28.7698 1.01149 0.505747 0.862682i \(-0.331217\pi\)
0.505747 + 0.862682i \(0.331217\pi\)
\(810\) 0 0
\(811\) 14.3512i 0.503940i 0.967735 + 0.251970i \(0.0810785\pi\)
−0.967735 + 0.251970i \(0.918922\pi\)
\(812\) 32.2649 12.6773i 1.13228 0.444887i
\(813\) 8.78583i 0.308132i
\(814\) 1.90317 + 1.29703i 0.0667062 + 0.0454608i
\(815\) 0 0
\(816\) 9.57315 + 10.3016i 0.335127 + 0.360627i
\(817\) −29.0812 −1.01742
\(818\) 14.1550 + 9.64675i 0.494918 + 0.337291i
\(819\) 16.3760i 0.572224i
\(820\) 0 0
\(821\) 4.97271i 0.173549i 0.996228 + 0.0867744i \(0.0276559\pi\)
−0.996228 + 0.0867744i \(0.972344\pi\)
\(822\) −13.0387 + 19.1322i −0.454778 + 0.667311i
\(823\) −20.3625 −0.709791 −0.354895 0.934906i \(-0.615483\pi\)
−0.354895 + 0.934906i \(0.615483\pi\)
\(824\) 0.0269496 0.118387i 0.000938833 0.00412421i
\(825\) 0 0
\(826\) −54.0923 + 79.3715i −1.88211 + 2.76169i
\(827\) 36.0039i 1.25198i 0.779832 + 0.625989i \(0.215304\pi\)
−0.779832 + 0.625989i \(0.784696\pi\)
\(828\) −5.20449 13.2459i −0.180869 0.460328i
\(829\) 7.68666i 0.266969i −0.991051 0.133484i \(-0.957383\pi\)
0.991051 0.133484i \(-0.0426166\pi\)
\(830\) 0 0
\(831\) −10.3838 −0.360211
\(832\) −12.0066 + 25.0055i −0.416256 + 0.866909i
\(833\) −53.8124 −1.86449
\(834\) −2.28710 1.55867i −0.0791956 0.0539725i
\(835\) 0 0
\(836\) −15.6409 39.8076i −0.540953 1.37678i
\(837\) 5.23414i 0.180918i
\(838\) −3.38298 + 4.96396i −0.116863 + 0.171477i
\(839\) −25.3725 −0.875956 −0.437978 0.898986i \(-0.644305\pi\)
−0.437978 + 0.898986i \(0.644305\pi\)
\(840\) 0 0
\(841\) 15.5313 0.535561
\(842\) 3.00993 4.41658i 0.103729 0.152205i
\(843\) 17.0584i 0.587524i
\(844\) 12.1289 4.76558i 0.417492 0.164038i
\(845\) 0 0
\(846\) −1.08166 0.737160i −0.0371882 0.0253441i
\(847\) 20.9976 0.721485
\(848\) 0.634978 + 0.683294i 0.0218052 + 0.0234644i
\(849\) −3.54724 −0.121741
\(850\) 0 0
\(851\) 2.94864i 0.101078i
\(852\) −4.07712 + 1.60195i −0.139680 + 0.0548820i
\(853\) 20.1365i 0.689460i −0.938702 0.344730i \(-0.887971\pi\)
0.938702 0.344730i \(-0.112029\pi\)
\(854\) 0.444945 0.652884i 0.0152257 0.0223412i
\(855\) 0 0
\(856\) 42.6721 + 9.71385i 1.45850 + 0.332012i
\(857\) −42.0380 −1.43599 −0.717996 0.696047i \(-0.754940\pi\)
−0.717996 + 0.696047i \(0.754940\pi\)
\(858\) −10.8530 + 15.9250i −0.370516 + 0.543670i
\(859\) 12.4095i 0.423406i −0.977334 0.211703i \(-0.932099\pi\)
0.977334 0.211703i \(-0.0679010\pi\)
\(860\) 0 0
\(861\) 14.1903i 0.483603i
\(862\) 29.9486 + 20.4102i 1.02005 + 0.695174i
\(863\) −21.8154 −0.742606 −0.371303 0.928512i \(-0.621089\pi\)
−0.371303 + 0.928512i \(0.621089\pi\)
\(864\) 0.848464 + 5.59286i 0.0288653 + 0.190273i
\(865\) 0 0
\(866\) 2.37407 + 1.61795i 0.0806740 + 0.0549800i
\(867\) 4.63952i 0.157566i
\(868\) −18.0804 46.0164i −0.613690 1.56190i
\(869\) 40.3805i 1.36982i
\(870\) 0 0
\(871\) 46.6371 1.58024
\(872\) −35.7314 8.13387i −1.21002 0.275448i
\(873\) 7.27462 0.246209
\(874\) −30.8375 + 45.2490i −1.04310 + 1.53057i
\(875\) 0 0
\(876\) −1.04841 + 0.411935i −0.0354226 + 0.0139180i
\(877\) 5.83690i 0.197098i −0.995132 0.0985491i \(-0.968580\pi\)
0.995132 0.0985491i \(-0.0314201\pi\)
\(878\) −26.2782 17.9088i −0.886848 0.604394i
\(879\) 5.72538 0.193112
\(880\) 0 0
\(881\) −11.9613 −0.402986 −0.201493 0.979490i \(-0.564579\pi\)
−0.201493 + 0.979490i \(0.564579\pi\)
\(882\) −17.8872 12.1903i −0.602293 0.410468i
\(883\) 3.74810i 0.126134i 0.998009 + 0.0630668i \(0.0200881\pi\)
−0.998009 + 0.0630668i \(0.979912\pi\)
\(884\) −22.6918 + 8.91590i −0.763208 + 0.299874i
\(885\) 0 0
\(886\) −2.70297 + 3.96616i −0.0908081 + 0.133246i
\(887\) −42.8101 −1.43742 −0.718711 0.695309i \(-0.755268\pi\)
−0.718711 + 0.695309i \(0.755268\pi\)
\(888\) −0.260146 + 1.14280i −0.00872992 + 0.0383498i
\(889\) −86.8101 −2.91152
\(890\) 0 0
\(891\) 3.93012i 0.131664i
\(892\) −2.30126 5.85692i −0.0770519 0.196104i
\(893\) 5.03638i 0.168536i
\(894\) 14.1367 + 9.63429i 0.472803 + 0.322219i
\(895\) 0 0
\(896\) 26.7789 + 46.2393i 0.894622 + 1.54475i
\(897\) 24.6730 0.823808
\(898\) −2.54504 1.73447i −0.0849291 0.0578799i
\(899\) 19.2092i 0.640662i
\(900\) 0 0
\(901\) 0.819859i 0.0273135i
\(902\) −9.40444 + 13.7995i −0.313134 + 0.459472i
\(903\) 25.2417 0.839992
\(904\) 2.42347 10.6461i 0.0806033 0.354083i
\(905\) 0 0
\(906\) 3.88004 5.69331i 0.128906 0.189147i
\(907\) 6.97759i 0.231687i −0.993267 0.115844i \(-0.963043\pi\)
0.993267 0.115844i \(-0.0369571\pi\)
\(908\) −7.29888 + 2.86782i −0.242222 + 0.0951721i
\(909\) 4.23320i 0.140406i
\(910\) 0 0
\(911\) 24.2837 0.804555 0.402278 0.915518i \(-0.368219\pi\)
0.402278 + 0.915518i \(0.368219\pi\)
\(912\) 15.9438 14.8164i 0.527951 0.490619i
\(913\) −44.6031 −1.47615
\(914\) 4.17965 + 2.84846i 0.138250 + 0.0942188i
\(915\) 0 0
\(916\) 47.8210 18.7895i 1.58005 0.620822i
\(917\) 16.1473i 0.533232i
\(918\) −2.80005 + 4.10861i −0.0924154 + 0.135604i
\(919\) −1.25720 −0.0414712 −0.0207356 0.999785i \(-0.506601\pi\)
−0.0207356 + 0.999785i \(0.506601\pi\)
\(920\) 0 0
\(921\) 12.3760 0.407803
\(922\) −10.4459 + 15.3276i −0.344016 + 0.504787i
\(923\) 7.59440i 0.249973i
\(924\) 13.5759 + 34.5520i 0.446616 + 1.13668i
\(925\) 0 0
\(926\) 3.75618 + 2.55987i 0.123436 + 0.0841225i
\(927\) 0.0429270 0.00140991
\(928\) −3.11384 20.5257i −0.102217 0.673788i
\(929\) 10.4933 0.344275 0.172138 0.985073i \(-0.444933\pi\)
0.172138 + 0.985073i \(0.444933\pi\)
\(930\) 0 0
\(931\) 83.2856i 2.72957i
\(932\) −18.8382 47.9450i −0.617066 1.57049i
\(933\) 18.2746i 0.598284i
\(934\) 24.1331 35.4113i 0.789660 1.15869i
\(935\) 0 0
\(936\) −9.56247 2.17679i −0.312559 0.0711508i
\(937\) −12.9680 −0.423648 −0.211824 0.977308i \(-0.567940\pi\)
−0.211824 + 0.977308i \(0.567940\pi\)
\(938\) 50.5936 74.2378i 1.65194 2.42395i
\(939\) 12.7114i 0.414821i
\(940\) 0 0
\(941\) 44.9947i 1.46678i −0.679806 0.733392i \(-0.737936\pi\)
0.679806 0.733392i \(-0.262064\pi\)
\(942\) −25.3080 17.2476i −0.824579 0.561957i
\(943\) 21.3799 0.696225
\(944\) 39.1573 + 42.1368i 1.27446 + 1.37143i
\(945\) 0 0
\(946\) −24.5466 16.7287i −0.798077 0.543896i
\(947\) 30.6282i 0.995283i 0.867383 + 0.497642i \(0.165801\pi\)
−0.867383 + 0.497642i \(0.834199\pi\)
\(948\) 19.1259 7.51481i 0.621180 0.244070i
\(949\) 1.95287i 0.0633927i
\(950\) 0 0
\(951\) 15.8602 0.514304
\(952\) −10.4244 + 45.7935i −0.337857 + 1.48418i
\(953\) −17.5717 −0.569202 −0.284601 0.958646i \(-0.591861\pi\)
−0.284601 + 0.958646i \(0.591861\pi\)
\(954\) −0.185725 + 0.272520i −0.00601306 + 0.00882317i
\(955\) 0 0
\(956\) −11.6092 29.5466i −0.375469 0.955604i
\(957\) 14.4235i 0.466244i
\(958\) 41.0068 + 27.9465i 1.32487 + 0.902909i
\(959\) −77.3213 −2.49683
\(960\) 0 0
\(961\) −3.60380 −0.116252
\(962\) −1.67907 1.14430i −0.0541353 0.0368936i
\(963\) 15.4728i 0.498605i
\(964\) 20.6007 + 52.4308i 0.663505 + 1.68868i
\(965\) 0 0
\(966\) 26.7662 39.2750i 0.861189 1.26365i
\(967\) −4.50932 −0.145010 −0.0725050 0.997368i \(-0.523099\pi\)
−0.0725050 + 0.997368i \(0.523099\pi\)
\(968\) 2.79112 12.2611i 0.0897100 0.394088i
\(969\) 19.1303 0.614555
\(970\) 0 0
\(971\) 35.8512i 1.15052i −0.817971 0.575259i \(-0.804901\pi\)
0.817971 0.575259i \(-0.195099\pi\)
\(972\) −1.86147 + 0.731395i −0.0597066 + 0.0234595i
\(973\) 9.24313i 0.296321i
\(974\) −43.1361 29.3976i −1.38217 0.941961i
\(975\) 0 0
\(976\) −0.322095 0.346603i −0.0103100 0.0110945i
\(977\) 43.9704 1.40674 0.703368 0.710826i \(-0.251678\pi\)
0.703368 + 0.710826i \(0.251678\pi\)
\(978\) −18.9742 12.9310i −0.606727 0.413489i
\(979\) 34.9099i 1.11573i
\(980\) 0 0
\(981\) 12.9561i 0.413657i
\(982\) 16.7144 24.5257i 0.533380 0.782646i
\(983\) 4.64187 0.148053 0.0740263 0.997256i \(-0.476415\pi\)
0.0740263 + 0.997256i \(0.476415\pi\)
\(984\) −8.28615 1.88625i −0.264153 0.0601316i
\(985\) 0 0
\(986\) 10.2761 15.0785i 0.327258 0.480197i
\(987\) 4.37145i 0.139145i
\(988\) 13.7991 + 35.1201i 0.439009 + 1.11732i
\(989\) 38.0307i 1.20930i
\(990\) 0 0
\(991\) −52.9117 −1.68080 −0.840398 0.541970i \(-0.817679\pi\)
−0.840398 + 0.541970i \(0.817679\pi\)
\(992\) −29.2738 + 4.44098i −0.929444 + 0.141001i
\(993\) 23.0315 0.730882
\(994\) −12.0889 8.23868i −0.383437 0.261315i
\(995\) 0 0
\(996\) −8.30063 21.1259i −0.263016 0.669399i
\(997\) 39.4228i 1.24853i 0.781211 + 0.624266i \(0.214602\pi\)
−0.781211 + 0.624266i \(0.785398\pi\)
\(998\) −12.7354 + 18.6871i −0.403132 + 0.591529i
\(999\) −0.414376 −0.0131103
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 600.2.k.e.301.6 yes 8
3.2 odd 2 1800.2.k.q.901.3 8
4.3 odd 2 2400.2.k.e.1201.4 8
5.2 odd 4 600.2.d.h.349.2 8
5.3 odd 4 600.2.d.g.349.7 8
5.4 even 2 600.2.k.d.301.3 8
8.3 odd 2 2400.2.k.e.1201.8 8
8.5 even 2 inner 600.2.k.e.301.5 yes 8
12.11 even 2 7200.2.k.s.3601.8 8
15.2 even 4 1800.2.d.s.1549.7 8
15.8 even 4 1800.2.d.t.1549.2 8
15.14 odd 2 1800.2.k.t.901.6 8
20.3 even 4 2400.2.d.h.49.1 8
20.7 even 4 2400.2.d.g.49.8 8
20.19 odd 2 2400.2.k.d.1201.5 8
24.5 odd 2 1800.2.k.q.901.4 8
24.11 even 2 7200.2.k.s.3601.7 8
40.3 even 4 2400.2.d.g.49.1 8
40.13 odd 4 600.2.d.h.349.1 8
40.19 odd 2 2400.2.k.d.1201.1 8
40.27 even 4 2400.2.d.h.49.8 8
40.29 even 2 600.2.k.d.301.4 yes 8
40.37 odd 4 600.2.d.g.349.8 8
60.23 odd 4 7200.2.d.t.2449.1 8
60.47 odd 4 7200.2.d.s.2449.8 8
60.59 even 2 7200.2.k.r.3601.2 8
120.29 odd 2 1800.2.k.t.901.5 8
120.53 even 4 1800.2.d.s.1549.8 8
120.59 even 2 7200.2.k.r.3601.1 8
120.77 even 4 1800.2.d.t.1549.1 8
120.83 odd 4 7200.2.d.s.2449.1 8
120.107 odd 4 7200.2.d.t.2449.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.2.d.g.349.7 8 5.3 odd 4
600.2.d.g.349.8 8 40.37 odd 4
600.2.d.h.349.1 8 40.13 odd 4
600.2.d.h.349.2 8 5.2 odd 4
600.2.k.d.301.3 8 5.4 even 2
600.2.k.d.301.4 yes 8 40.29 even 2
600.2.k.e.301.5 yes 8 8.5 even 2 inner
600.2.k.e.301.6 yes 8 1.1 even 1 trivial
1800.2.d.s.1549.7 8 15.2 even 4
1800.2.d.s.1549.8 8 120.53 even 4
1800.2.d.t.1549.1 8 120.77 even 4
1800.2.d.t.1549.2 8 15.8 even 4
1800.2.k.q.901.3 8 3.2 odd 2
1800.2.k.q.901.4 8 24.5 odd 2
1800.2.k.t.901.5 8 120.29 odd 2
1800.2.k.t.901.6 8 15.14 odd 2
2400.2.d.g.49.1 8 40.3 even 4
2400.2.d.g.49.8 8 20.7 even 4
2400.2.d.h.49.1 8 20.3 even 4
2400.2.d.h.49.8 8 40.27 even 4
2400.2.k.d.1201.1 8 40.19 odd 2
2400.2.k.d.1201.5 8 20.19 odd 2
2400.2.k.e.1201.4 8 4.3 odd 2
2400.2.k.e.1201.8 8 8.3 odd 2
7200.2.d.s.2449.1 8 120.83 odd 4
7200.2.d.s.2449.8 8 60.47 odd 4
7200.2.d.t.2449.1 8 60.23 odd 4
7200.2.d.t.2449.8 8 120.107 odd 4
7200.2.k.r.3601.1 8 120.59 even 2
7200.2.k.r.3601.2 8 60.59 even 2
7200.2.k.s.3601.7 8 24.11 even 2
7200.2.k.s.3601.8 8 12.11 even 2