Properties

Label 507.2.e.g.484.1
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(22,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 484.1
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.g.22.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.780776 - 1.35234i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.219224 + 0.379706i) q^{4} +3.56155 q^{5} +(-0.780776 + 1.35234i) q^{6} +(0.280776 - 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.780776 - 1.35234i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.219224 + 0.379706i) q^{4} +3.56155 q^{5} +(-0.780776 + 1.35234i) q^{6} +(0.280776 - 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.78078 - 4.81645i) q^{10} +(-1.00000 - 1.73205i) q^{11} +0.438447 q^{12} -0.876894 q^{14} +(-1.78078 - 3.08440i) q^{15} +(2.34233 + 4.05703i) q^{16} +(0.780776 - 1.35234i) q^{17} +1.56155 q^{18} +(3.56155 - 6.16879i) q^{19} +(-0.780776 + 1.35234i) q^{20} -0.561553 q^{21} +(-1.56155 + 2.70469i) q^{22} +(-1.00000 - 1.73205i) q^{23} +(1.21922 + 2.11176i) q^{24} +7.68466 q^{25} +1.00000 q^{27} +(0.123106 + 0.213225i) q^{28} +(-3.34233 - 5.78908i) q^{29} +(-2.78078 + 4.81645i) q^{30} -2.56155 q^{31} +(1.21922 - 2.11176i) q^{32} +(-1.00000 + 1.73205i) q^{33} -2.43845 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.219224 - 0.379706i) q^{36} +(3.78078 + 6.54850i) q^{37} -11.1231 q^{38} -8.68466 q^{40} +(-0.780776 - 1.35234i) q^{41} +(0.438447 + 0.759413i) q^{42} +(-2.28078 + 3.95042i) q^{43} +0.876894 q^{44} +(-1.78078 + 3.08440i) q^{45} +(-1.56155 + 2.70469i) q^{46} -8.24621 q^{47} +(2.34233 - 4.05703i) q^{48} +(3.34233 + 5.78908i) q^{49} +(-6.00000 - 10.3923i) q^{50} -1.56155 q^{51} -0.684658 q^{53} +(-0.780776 - 1.35234i) q^{54} +(-3.56155 - 6.16879i) q^{55} +(-0.684658 + 1.18586i) q^{56} -7.12311 q^{57} +(-5.21922 + 9.03996i) q^{58} +(-1.43845 + 2.49146i) q^{59} +1.56155 q^{60} +(-1.93845 + 3.35749i) q^{61} +(2.00000 + 3.46410i) q^{62} +(0.280776 + 0.486319i) q^{63} +5.56155 q^{64} +3.12311 q^{66} +(2.28078 + 3.95042i) q^{67} +(0.342329 + 0.592932i) q^{68} +(-1.00000 + 1.73205i) q^{69} -3.12311 q^{70} +(7.00000 - 12.1244i) q^{71} +(1.21922 - 2.11176i) q^{72} +10.1231 q^{73} +(5.90388 - 10.2258i) q^{74} +(-3.84233 - 6.65511i) q^{75} +(1.56155 + 2.70469i) q^{76} -1.12311 q^{77} +5.43845 q^{79} +(8.34233 + 14.4493i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.21922 + 2.11176i) q^{82} +0.876894 q^{83} +(0.123106 - 0.213225i) q^{84} +(2.78078 - 4.81645i) q^{85} +7.12311 q^{86} +(-3.34233 + 5.78908i) q^{87} +(2.43845 + 4.22351i) q^{88} +(2.43845 + 4.22351i) q^{89} +5.56155 q^{90} +0.876894 q^{92} +(1.28078 + 2.21837i) q^{93} +(6.43845 + 11.1517i) q^{94} +(12.6847 - 21.9705i) q^{95} -2.43845 q^{96} +(-4.28078 + 7.41452i) q^{97} +(5.21922 - 9.03996i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9} - 7 q^{10} - 4 q^{11} + 10 q^{12} - 20 q^{14} - 3 q^{15} - 3 q^{16} - q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} + 2 q^{22} - 4 q^{23} + 9 q^{24} + 6 q^{25} + 4 q^{27} - 16 q^{28} - q^{29} - 7 q^{30} - 2 q^{31} + 9 q^{32} - 4 q^{33} - 18 q^{34} + 4 q^{35} - 5 q^{36} + 11 q^{37} - 28 q^{38} - 10 q^{40} + q^{41} + 10 q^{42} - 5 q^{43} + 20 q^{44} - 3 q^{45} + 2 q^{46} - 3 q^{48} + q^{49} - 24 q^{50} + 2 q^{51} + 22 q^{53} + q^{54} - 6 q^{55} + 22 q^{56} - 12 q^{57} - 25 q^{58} - 14 q^{59} - 2 q^{60} - 16 q^{61} + 8 q^{62} - 3 q^{63} + 14 q^{64} - 4 q^{66} + 5 q^{67} - 11 q^{68} - 4 q^{69} + 4 q^{70} + 28 q^{71} + 9 q^{72} + 24 q^{73} + 3 q^{74} - 3 q^{75} - 2 q^{76} + 12 q^{77} + 30 q^{79} + 21 q^{80} - 2 q^{81} - 9 q^{82} + 20 q^{83} - 16 q^{84} + 7 q^{85} + 12 q^{86} - q^{87} + 18 q^{88} + 18 q^{89} + 14 q^{90} + 20 q^{92} + q^{93} + 34 q^{94} + 26 q^{95} - 18 q^{96} - 13 q^{97} + 25 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.780776 1.35234i −0.552092 0.956252i −0.998123 0.0612344i \(-0.980496\pi\)
0.446031 0.895017i \(-0.352837\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.219224 + 0.379706i −0.109612 + 0.189853i
\(5\) 3.56155 1.59277 0.796387 0.604787i \(-0.206742\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) −0.780776 + 1.35234i −0.318751 + 0.552092i
\(7\) 0.280776 0.486319i 0.106124 0.183811i −0.808073 0.589082i \(-0.799489\pi\)
0.914197 + 0.405271i \(0.132823\pi\)
\(8\) −2.43845 −0.862121
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −2.78078 4.81645i −0.879359 1.52309i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0.438447 0.126569
\(13\) 0 0
\(14\) −0.876894 −0.234360
\(15\) −1.78078 3.08440i −0.459794 0.796387i
\(16\) 2.34233 + 4.05703i 0.585582 + 1.01426i
\(17\) 0.780776 1.35234i 0.189366 0.327992i −0.755673 0.654949i \(-0.772690\pi\)
0.945039 + 0.326957i \(0.106023\pi\)
\(18\) 1.56155 0.368062
\(19\) 3.56155 6.16879i 0.817076 1.41522i −0.0907512 0.995874i \(-0.528927\pi\)
0.907827 0.419344i \(-0.137740\pi\)
\(20\) −0.780776 + 1.35234i −0.174587 + 0.302393i
\(21\) −0.561553 −0.122541
\(22\) −1.56155 + 2.70469i −0.332924 + 0.576642i
\(23\) −1.00000 1.73205i −0.208514 0.361158i 0.742732 0.669588i \(-0.233529\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(24\) 1.21922 + 2.11176i 0.248873 + 0.431061i
\(25\) 7.68466 1.53693
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.123106 + 0.213225i 0.0232648 + 0.0402958i
\(29\) −3.34233 5.78908i −0.620655 1.07501i −0.989364 0.145461i \(-0.953533\pi\)
0.368709 0.929545i \(-0.379800\pi\)
\(30\) −2.78078 + 4.81645i −0.507698 + 0.879359i
\(31\) −2.56155 −0.460068 −0.230034 0.973183i \(-0.573884\pi\)
−0.230034 + 0.973183i \(0.573884\pi\)
\(32\) 1.21922 2.11176i 0.215530 0.373309i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) −2.43845 −0.418190
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) −0.219224 0.379706i −0.0365373 0.0632844i
\(37\) 3.78078 + 6.54850i 0.621556 + 1.07657i 0.989196 + 0.146598i \(0.0468324\pi\)
−0.367640 + 0.929968i \(0.619834\pi\)
\(38\) −11.1231 −1.80441
\(39\) 0 0
\(40\) −8.68466 −1.37317
\(41\) −0.780776 1.35234i −0.121937 0.211201i 0.798595 0.601869i \(-0.205577\pi\)
−0.920531 + 0.390669i \(0.872244\pi\)
\(42\) 0.438447 + 0.759413i 0.0676539 + 0.117180i
\(43\) −2.28078 + 3.95042i −0.347815 + 0.602433i −0.985861 0.167565i \(-0.946410\pi\)
0.638046 + 0.769998i \(0.279743\pi\)
\(44\) 0.876894 0.132197
\(45\) −1.78078 + 3.08440i −0.265462 + 0.459794i
\(46\) −1.56155 + 2.70469i −0.230238 + 0.398785i
\(47\) −8.24621 −1.20283 −0.601417 0.798935i \(-0.705397\pi\)
−0.601417 + 0.798935i \(0.705397\pi\)
\(48\) 2.34233 4.05703i 0.338086 0.585582i
\(49\) 3.34233 + 5.78908i 0.477476 + 0.827012i
\(50\) −6.00000 10.3923i −0.848528 1.46969i
\(51\) −1.56155 −0.218661
\(52\) 0 0
\(53\) −0.684658 −0.0940451 −0.0470225 0.998894i \(-0.514973\pi\)
−0.0470225 + 0.998894i \(0.514973\pi\)
\(54\) −0.780776 1.35234i −0.106250 0.184031i
\(55\) −3.56155 6.16879i −0.480240 0.831800i
\(56\) −0.684658 + 1.18586i −0.0914913 + 0.158468i
\(57\) −7.12311 −0.943478
\(58\) −5.21922 + 9.03996i −0.685318 + 1.18700i
\(59\) −1.43845 + 2.49146i −0.187270 + 0.324361i −0.944339 0.328974i \(-0.893297\pi\)
0.757069 + 0.653335i \(0.226631\pi\)
\(60\) 1.56155 0.201596
\(61\) −1.93845 + 3.35749i −0.248193 + 0.429882i −0.963024 0.269414i \(-0.913170\pi\)
0.714832 + 0.699297i \(0.246503\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) 0.280776 + 0.486319i 0.0353745 + 0.0612704i
\(64\) 5.56155 0.695194
\(65\) 0 0
\(66\) 3.12311 0.384428
\(67\) 2.28078 + 3.95042i 0.278641 + 0.482621i 0.971047 0.238887i \(-0.0767826\pi\)
−0.692406 + 0.721508i \(0.743449\pi\)
\(68\) 0.342329 + 0.592932i 0.0415135 + 0.0719035i
\(69\) −1.00000 + 1.73205i −0.120386 + 0.208514i
\(70\) −3.12311 −0.373283
\(71\) 7.00000 12.1244i 0.830747 1.43890i −0.0666994 0.997773i \(-0.521247\pi\)
0.897447 0.441123i \(-0.145420\pi\)
\(72\) 1.21922 2.11176i 0.143687 0.248873i
\(73\) 10.1231 1.18482 0.592410 0.805637i \(-0.298177\pi\)
0.592410 + 0.805637i \(0.298177\pi\)
\(74\) 5.90388 10.2258i 0.686312 1.18873i
\(75\) −3.84233 6.65511i −0.443674 0.768466i
\(76\) 1.56155 + 2.70469i 0.179122 + 0.310249i
\(77\) −1.12311 −0.127990
\(78\) 0 0
\(79\) 5.43845 0.611873 0.305937 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(80\) 8.34233 + 14.4493i 0.932701 + 1.61549i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.21922 + 2.11176i −0.134641 + 0.233205i
\(83\) 0.876894 0.0962517 0.0481258 0.998841i \(-0.484675\pi\)
0.0481258 + 0.998841i \(0.484675\pi\)
\(84\) 0.123106 0.213225i 0.0134319 0.0232648i
\(85\) 2.78078 4.81645i 0.301618 0.522417i
\(86\) 7.12311 0.768104
\(87\) −3.34233 + 5.78908i −0.358335 + 0.620655i
\(88\) 2.43845 + 4.22351i 0.259939 + 0.450228i
\(89\) 2.43845 + 4.22351i 0.258475 + 0.447692i 0.965834 0.259163i \(-0.0834467\pi\)
−0.707359 + 0.706855i \(0.750113\pi\)
\(90\) 5.56155 0.586239
\(91\) 0 0
\(92\) 0.876894 0.0914226
\(93\) 1.28078 + 2.21837i 0.132810 + 0.230034i
\(94\) 6.43845 + 11.1517i 0.664075 + 1.15021i
\(95\) 12.6847 21.9705i 1.30142 2.25412i
\(96\) −2.43845 −0.248873
\(97\) −4.28078 + 7.41452i −0.434647 + 0.752831i −0.997267 0.0738851i \(-0.976460\pi\)
0.562620 + 0.826716i \(0.309794\pi\)
\(98\) 5.21922 9.03996i 0.527221 0.913174i
\(99\) 2.00000 0.201008
\(100\) −1.68466 + 2.91791i −0.168466 + 0.291791i
\(101\) 3.78078 + 6.54850i 0.376201 + 0.651600i 0.990506 0.137469i \(-0.0438968\pi\)
−0.614305 + 0.789069i \(0.710563\pi\)
\(102\) 1.21922 + 2.11176i 0.120721 + 0.209095i
\(103\) −3.43845 −0.338800 −0.169400 0.985547i \(-0.554183\pi\)
−0.169400 + 0.985547i \(0.554183\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 0.534565 + 0.925894i 0.0519216 + 0.0899308i
\(107\) 4.12311 + 7.14143i 0.398596 + 0.690388i 0.993553 0.113369i \(-0.0361644\pi\)
−0.594957 + 0.803757i \(0.702831\pi\)
\(108\) −0.219224 + 0.379706i −0.0210948 + 0.0365373i
\(109\) 2.80776 0.268935 0.134468 0.990918i \(-0.457068\pi\)
0.134468 + 0.990918i \(0.457068\pi\)
\(110\) −5.56155 + 9.63289i −0.530273 + 0.918460i
\(111\) 3.78078 6.54850i 0.358855 0.621556i
\(112\) 2.63068 0.248576
\(113\) −2.90388 + 5.02967i −0.273174 + 0.473152i −0.969673 0.244406i \(-0.921407\pi\)
0.696499 + 0.717558i \(0.254740\pi\)
\(114\) 5.56155 + 9.63289i 0.520887 + 0.902203i
\(115\) −3.56155 6.16879i −0.332117 0.575243i
\(116\) 2.93087 0.272124
\(117\) 0 0
\(118\) 4.49242 0.413561
\(119\) −0.438447 0.759413i −0.0401924 0.0696153i
\(120\) 4.34233 + 7.52113i 0.396399 + 0.686583i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 6.05398 0.548101
\(123\) −0.780776 + 1.35234i −0.0704002 + 0.121937i
\(124\) 0.561553 0.972638i 0.0504289 0.0873455i
\(125\) 9.56155 0.855211
\(126\) 0.438447 0.759413i 0.0390600 0.0676539i
\(127\) −2.71922 4.70983i −0.241292 0.417930i 0.719791 0.694191i \(-0.244238\pi\)
−0.961083 + 0.276261i \(0.910905\pi\)
\(128\) −6.78078 11.7446i −0.599342 1.03809i
\(129\) 4.56155 0.401622
\(130\) 0 0
\(131\) 7.36932 0.643860 0.321930 0.946763i \(-0.395668\pi\)
0.321930 + 0.946763i \(0.395668\pi\)
\(132\) −0.438447 0.759413i −0.0381619 0.0660984i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 3.56155 6.16879i 0.307671 0.532902i
\(135\) 3.56155 0.306530
\(136\) −1.90388 + 3.29762i −0.163257 + 0.282769i
\(137\) −2.78078 + 4.81645i −0.237578 + 0.411497i −0.960019 0.279936i \(-0.909687\pi\)
0.722441 + 0.691433i \(0.243020\pi\)
\(138\) 3.12311 0.265856
\(139\) 8.96543 15.5286i 0.760438 1.31712i −0.182187 0.983264i \(-0.558318\pi\)
0.942625 0.333854i \(-0.108349\pi\)
\(140\) 0.438447 + 0.759413i 0.0370556 + 0.0641821i
\(141\) 4.12311 + 7.14143i 0.347228 + 0.601417i
\(142\) −21.8617 −1.83460
\(143\) 0 0
\(144\) −4.68466 −0.390388
\(145\) −11.9039 20.6181i −0.988564 1.71224i
\(146\) −7.90388 13.6899i −0.654130 1.13299i
\(147\) 3.34233 5.78908i 0.275671 0.477476i
\(148\) −3.31534 −0.272519
\(149\) −1.21922 + 2.11176i −0.0998827 + 0.173002i −0.911636 0.410999i \(-0.865180\pi\)
0.811753 + 0.584001i \(0.198513\pi\)
\(150\) −6.00000 + 10.3923i −0.489898 + 0.848528i
\(151\) 9.36932 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(152\) −8.68466 + 15.0423i −0.704419 + 1.22009i
\(153\) 0.780776 + 1.35234i 0.0631220 + 0.109331i
\(154\) 0.876894 + 1.51883i 0.0706622 + 0.122390i
\(155\) −9.12311 −0.732785
\(156\) 0 0
\(157\) 20.3693 1.62565 0.812824 0.582509i \(-0.197929\pi\)
0.812824 + 0.582509i \(0.197929\pi\)
\(158\) −4.24621 7.35465i −0.337810 0.585105i
\(159\) 0.342329 + 0.592932i 0.0271485 + 0.0470225i
\(160\) 4.34233 7.52113i 0.343291 0.594598i
\(161\) −1.12311 −0.0885131
\(162\) −0.780776 + 1.35234i −0.0613436 + 0.106250i
\(163\) −2.40388 + 4.16365i −0.188287 + 0.326122i −0.944679 0.327996i \(-0.893627\pi\)
0.756393 + 0.654118i \(0.226960\pi\)
\(164\) 0.684658 0.0534628
\(165\) −3.56155 + 6.16879i −0.277267 + 0.480240i
\(166\) −0.684658 1.18586i −0.0531398 0.0920408i
\(167\) 5.12311 + 8.87348i 0.396438 + 0.686650i 0.993284 0.115706i \(-0.0369129\pi\)
−0.596846 + 0.802356i \(0.703580\pi\)
\(168\) 1.36932 0.105645
\(169\) 0 0
\(170\) −8.68466 −0.666083
\(171\) 3.56155 + 6.16879i 0.272359 + 0.471739i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) −10.1231 + 17.5337i −0.769645 + 1.33307i 0.168110 + 0.985768i \(0.446234\pi\)
−0.937755 + 0.347297i \(0.887100\pi\)
\(174\) 10.4384 0.791337
\(175\) 2.15767 3.73720i 0.163105 0.282505i
\(176\) 4.68466 8.11407i 0.353119 0.611621i
\(177\) 2.87689 0.216241
\(178\) 3.80776 6.59524i 0.285404 0.494334i
\(179\) 2.43845 + 4.22351i 0.182258 + 0.315680i 0.942649 0.333785i \(-0.108326\pi\)
−0.760391 + 0.649466i \(0.774993\pi\)
\(180\) −0.780776 1.35234i −0.0581956 0.100798i
\(181\) −2.68466 −0.199549 −0.0997745 0.995010i \(-0.531812\pi\)
−0.0997745 + 0.995010i \(0.531812\pi\)
\(182\) 0 0
\(183\) 3.87689 0.286588
\(184\) 2.43845 + 4.22351i 0.179765 + 0.311362i
\(185\) 13.4654 + 23.3228i 0.989998 + 1.71473i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) −3.12311 −0.228384
\(188\) 1.80776 3.13114i 0.131845 0.228362i
\(189\) 0.280776 0.486319i 0.0204235 0.0353745i
\(190\) −39.6155 −2.87401
\(191\) 4.56155 7.90084i 0.330062 0.571685i −0.652461 0.757822i \(-0.726264\pi\)
0.982524 + 0.186137i \(0.0595969\pi\)
\(192\) −2.78078 4.81645i −0.200685 0.347597i
\(193\) −6.74621 11.6848i −0.485603 0.841089i 0.514260 0.857634i \(-0.328067\pi\)
−0.999863 + 0.0165453i \(0.994733\pi\)
\(194\) 13.3693 0.959861
\(195\) 0 0
\(196\) −2.93087 −0.209348
\(197\) 6.68466 + 11.5782i 0.476262 + 0.824910i 0.999630 0.0271965i \(-0.00865798\pi\)
−0.523368 + 0.852107i \(0.675325\pi\)
\(198\) −1.56155 2.70469i −0.110975 0.192214i
\(199\) −11.0885 + 19.2059i −0.786046 + 1.36147i 0.142327 + 0.989820i \(0.454542\pi\)
−0.928372 + 0.371651i \(0.878792\pi\)
\(200\) −18.7386 −1.32502
\(201\) 2.28078 3.95042i 0.160874 0.278641i
\(202\) 5.90388 10.2258i 0.415396 0.719486i
\(203\) −3.75379 −0.263464
\(204\) 0.342329 0.592932i 0.0239678 0.0415135i
\(205\) −2.78078 4.81645i −0.194218 0.336395i
\(206\) 2.68466 + 4.64996i 0.187049 + 0.323978i
\(207\) 2.00000 0.139010
\(208\) 0 0
\(209\) −14.2462 −0.985431
\(210\) 1.56155 + 2.70469i 0.107757 + 0.186641i
\(211\) −9.84233 17.0474i −0.677574 1.17359i −0.975709 0.219069i \(-0.929698\pi\)
0.298136 0.954524i \(-0.403635\pi\)
\(212\) 0.150093 0.259969i 0.0103084 0.0178548i
\(213\) −14.0000 −0.959264
\(214\) 6.43845 11.1517i 0.440123 0.762316i
\(215\) −8.12311 + 14.0696i −0.553991 + 0.959541i
\(216\) −2.43845 −0.165915
\(217\) −0.719224 + 1.24573i −0.0488241 + 0.0845658i
\(218\) −2.19224 3.79706i −0.148477 0.257170i
\(219\) −5.06155 8.76687i −0.342028 0.592410i
\(220\) 3.12311 0.210560
\(221\) 0 0
\(222\) −11.8078 −0.792485
\(223\) 4.00000 + 6.92820i 0.267860 + 0.463947i 0.968309 0.249756i \(-0.0803503\pi\)
−0.700449 + 0.713702i \(0.747017\pi\)
\(224\) −0.684658 1.18586i −0.0457457 0.0792338i
\(225\) −3.84233 + 6.65511i −0.256155 + 0.443674i
\(226\) 9.06913 0.603270
\(227\) 3.56155 6.16879i 0.236389 0.409437i −0.723287 0.690548i \(-0.757370\pi\)
0.959675 + 0.281111i \(0.0907028\pi\)
\(228\) 1.56155 2.70469i 0.103416 0.179122i
\(229\) 16.2462 1.07358 0.536790 0.843716i \(-0.319637\pi\)
0.536790 + 0.843716i \(0.319637\pi\)
\(230\) −5.56155 + 9.63289i −0.366718 + 0.635174i
\(231\) 0.561553 + 0.972638i 0.0369475 + 0.0639949i
\(232\) 8.15009 + 14.1164i 0.535080 + 0.926785i
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 0 0
\(235\) −29.3693 −1.91584
\(236\) −0.630683 1.09238i −0.0410540 0.0711076i
\(237\) −2.71922 4.70983i −0.176633 0.305937i
\(238\) −0.684658 + 1.18586i −0.0443798 + 0.0768681i
\(239\) 25.3693 1.64100 0.820502 0.571643i \(-0.193694\pi\)
0.820502 + 0.571643i \(0.193694\pi\)
\(240\) 8.34233 14.4493i 0.538495 0.932701i
\(241\) −8.90388 + 15.4220i −0.573549 + 0.993417i 0.422648 + 0.906294i \(0.361101\pi\)
−0.996198 + 0.0871229i \(0.972233\pi\)
\(242\) −10.9309 −0.702663
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −0.849907 1.47208i −0.0544097 0.0942404i
\(245\) 11.9039 + 20.6181i 0.760511 + 1.31724i
\(246\) 2.43845 0.155470
\(247\) 0 0
\(248\) 6.24621 0.396635
\(249\) −0.438447 0.759413i −0.0277855 0.0481258i
\(250\) −7.46543 12.9305i −0.472156 0.817797i
\(251\) −9.36932 + 16.2281i −0.591386 + 1.02431i 0.402660 + 0.915350i \(0.368086\pi\)
−0.994046 + 0.108961i \(0.965248\pi\)
\(252\) −0.246211 −0.0155099
\(253\) −2.00000 + 3.46410i −0.125739 + 0.217786i
\(254\) −4.24621 + 7.35465i −0.266431 + 0.461472i
\(255\) −5.56155 −0.348278
\(256\) −5.02699 + 8.70700i −0.314187 + 0.544187i
\(257\) −14.5885 25.2681i −0.910008 1.57618i −0.814050 0.580795i \(-0.802742\pi\)
−0.0959583 0.995385i \(-0.530592\pi\)
\(258\) −3.56155 6.16879i −0.221733 0.384052i
\(259\) 4.24621 0.263847
\(260\) 0 0
\(261\) 6.68466 0.413770
\(262\) −5.75379 9.96585i −0.355470 0.615693i
\(263\) −4.68466 8.11407i −0.288868 0.500335i 0.684672 0.728852i \(-0.259946\pi\)
−0.973540 + 0.228517i \(0.926612\pi\)
\(264\) 2.43845 4.22351i 0.150076 0.259939i
\(265\) −2.43845 −0.149793
\(266\) −3.12311 + 5.40938i −0.191490 + 0.331670i
\(267\) 2.43845 4.22351i 0.149231 0.258475i
\(268\) −2.00000 −0.122169
\(269\) 10.6847 18.5064i 0.651455 1.12835i −0.331315 0.943520i \(-0.607492\pi\)
0.982770 0.184833i \(-0.0591745\pi\)
\(270\) −2.78078 4.81645i −0.169233 0.293120i
\(271\) −14.9654 25.9209i −0.909085 1.57458i −0.815337 0.578986i \(-0.803449\pi\)
−0.0937481 0.995596i \(-0.529885\pi\)
\(272\) 7.31534 0.443558
\(273\) 0 0
\(274\) 8.68466 0.524659
\(275\) −7.68466 13.3102i −0.463402 0.802636i
\(276\) −0.438447 0.759413i −0.0263914 0.0457113i
\(277\) −2.65767 + 4.60322i −0.159684 + 0.276581i −0.934755 0.355294i \(-0.884381\pi\)
0.775071 + 0.631874i \(0.217714\pi\)
\(278\) −28.0000 −1.67933
\(279\) 1.28078 2.21837i 0.0766781 0.132810i
\(280\) −2.43845 + 4.22351i −0.145725 + 0.252403i
\(281\) −17.8078 −1.06232 −0.531161 0.847271i \(-0.678244\pi\)
−0.531161 + 0.847271i \(0.678244\pi\)
\(282\) 6.43845 11.1517i 0.383404 0.664075i
\(283\) 6.84233 + 11.8513i 0.406734 + 0.704484i 0.994522 0.104531i \(-0.0333342\pi\)
−0.587787 + 0.809015i \(0.700001\pi\)
\(284\) 3.06913 + 5.31589i 0.182119 + 0.315440i
\(285\) −25.3693 −1.50275
\(286\) 0 0
\(287\) −0.876894 −0.0517614
\(288\) 1.21922 + 2.11176i 0.0718434 + 0.124436i
\(289\) 7.28078 + 12.6107i 0.428281 + 0.741804i
\(290\) −18.5885 + 32.1963i −1.09156 + 1.89063i
\(291\) 8.56155 0.501887
\(292\) −2.21922 + 3.84381i −0.129870 + 0.224942i
\(293\) 10.2192 17.7002i 0.597013 1.03406i −0.396246 0.918144i \(-0.629687\pi\)
0.993259 0.115913i \(-0.0369794\pi\)
\(294\) −10.4384 −0.608783
\(295\) −5.12311 + 8.87348i −0.298279 + 0.516634i
\(296\) −9.21922 15.9682i −0.535856 0.928131i
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) 3.80776 0.220578
\(299\) 0 0
\(300\) 3.36932 0.194528
\(301\) 1.28078 + 2.21837i 0.0738227 + 0.127865i
\(302\) −7.31534 12.6705i −0.420951 0.729108i
\(303\) 3.78078 6.54850i 0.217200 0.376201i
\(304\) 33.3693 1.91386
\(305\) −6.90388 + 11.9579i −0.395315 + 0.684706i
\(306\) 1.21922 2.11176i 0.0696984 0.120721i
\(307\) −30.8078 −1.75829 −0.879146 0.476553i \(-0.841886\pi\)
−0.879146 + 0.476553i \(0.841886\pi\)
\(308\) 0.246211 0.426450i 0.0140292 0.0242993i
\(309\) 1.71922 + 2.97778i 0.0978032 + 0.169400i
\(310\) 7.12311 + 12.3376i 0.404565 + 0.700728i
\(311\) −19.1231 −1.08437 −0.542186 0.840259i \(-0.682403\pi\)
−0.542186 + 0.840259i \(0.682403\pi\)
\(312\) 0 0
\(313\) −13.6847 −0.773503 −0.386751 0.922184i \(-0.626403\pi\)
−0.386751 + 0.922184i \(0.626403\pi\)
\(314\) −15.9039 27.5463i −0.897508 1.55453i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) −1.19224 + 2.06501i −0.0670685 + 0.116166i
\(317\) −14.0540 −0.789350 −0.394675 0.918821i \(-0.629143\pi\)
−0.394675 + 0.918821i \(0.629143\pi\)
\(318\) 0.534565 0.925894i 0.0299769 0.0519216i
\(319\) −6.68466 + 11.5782i −0.374269 + 0.648253i
\(320\) 19.8078 1.10729
\(321\) 4.12311 7.14143i 0.230129 0.398596i
\(322\) 0.876894 + 1.51883i 0.0488674 + 0.0846408i
\(323\) −5.56155 9.63289i −0.309453 0.535988i
\(324\) 0.438447 0.0243582
\(325\) 0 0
\(326\) 7.50758 0.415806
\(327\) −1.40388 2.43160i −0.0776349 0.134468i
\(328\) 1.90388 + 3.29762i 0.105124 + 0.182081i
\(329\) −2.31534 + 4.01029i −0.127649 + 0.221094i
\(330\) 11.1231 0.612307
\(331\) −1.59612 + 2.76456i −0.0877306 + 0.151954i −0.906552 0.422095i \(-0.861295\pi\)
0.818821 + 0.574049i \(0.194628\pi\)
\(332\) −0.192236 + 0.332962i −0.0105503 + 0.0182737i
\(333\) −7.56155 −0.414371
\(334\) 8.00000 13.8564i 0.437741 0.758189i
\(335\) 8.12311 + 14.0696i 0.443813 + 0.768706i
\(336\) −1.31534 2.27824i −0.0717578 0.124288i
\(337\) −6.12311 −0.333547 −0.166773 0.985995i \(-0.553335\pi\)
−0.166773 + 0.985995i \(0.553335\pi\)
\(338\) 0 0
\(339\) 5.80776 0.315434
\(340\) 1.21922 + 2.11176i 0.0661217 + 0.114526i
\(341\) 2.56155 + 4.43674i 0.138716 + 0.240263i
\(342\) 5.56155 9.63289i 0.300734 0.520887i
\(343\) 7.68466 0.414933
\(344\) 5.56155 9.63289i 0.299859 0.519371i
\(345\) −3.56155 + 6.16879i −0.191748 + 0.332117i
\(346\) 31.6155 1.69966
\(347\) −13.8078 + 23.9157i −0.741240 + 1.28386i 0.210692 + 0.977553i \(0.432428\pi\)
−0.951931 + 0.306312i \(0.900905\pi\)
\(348\) −1.46543 2.53821i −0.0785556 0.136062i
\(349\) 3.40388 + 5.89570i 0.182206 + 0.315589i 0.942631 0.333836i \(-0.108343\pi\)
−0.760426 + 0.649425i \(0.775010\pi\)
\(350\) −6.73863 −0.360195
\(351\) 0 0
\(352\) −4.87689 −0.259939
\(353\) 2.65767 + 4.60322i 0.141454 + 0.245005i 0.928044 0.372470i \(-0.121489\pi\)
−0.786591 + 0.617475i \(0.788156\pi\)
\(354\) −2.24621 3.89055i −0.119385 0.206781i
\(355\) 24.9309 43.1815i 1.32319 2.29184i
\(356\) −2.13826 −0.113328
\(357\) −0.438447 + 0.759413i −0.0232051 + 0.0401924i
\(358\) 3.80776 6.59524i 0.201247 0.348569i
\(359\) 9.36932 0.494494 0.247247 0.968953i \(-0.420474\pi\)
0.247247 + 0.968953i \(0.420474\pi\)
\(360\) 4.34233 7.52113i 0.228861 0.396399i
\(361\) −15.8693 27.4865i −0.835227 1.44666i
\(362\) 2.09612 + 3.63058i 0.110170 + 0.190819i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 36.0540 1.88715
\(366\) −3.02699 5.24290i −0.158223 0.274051i
\(367\) 8.52699 + 14.7692i 0.445105 + 0.770945i 0.998060 0.0622668i \(-0.0198330\pi\)
−0.552954 + 0.833212i \(0.686500\pi\)
\(368\) 4.68466 8.11407i 0.244205 0.422975i
\(369\) 1.56155 0.0812912
\(370\) 21.0270 36.4198i 1.09314 1.89338i
\(371\) −0.192236 + 0.332962i −0.00998039 + 0.0172865i
\(372\) −1.12311 −0.0582303
\(373\) −14.1847 + 24.5685i −0.734454 + 1.27211i 0.220509 + 0.975385i \(0.429228\pi\)
−0.954963 + 0.296726i \(0.904105\pi\)
\(374\) 2.43845 + 4.22351i 0.126089 + 0.218393i
\(375\) −4.78078 8.28055i −0.246878 0.427606i
\(376\) 20.1080 1.03699
\(377\) 0 0
\(378\) −0.876894 −0.0451026
\(379\) 11.8423 + 20.5115i 0.608300 + 1.05361i 0.991521 + 0.129949i \(0.0414814\pi\)
−0.383221 + 0.923657i \(0.625185\pi\)
\(380\) 5.56155 + 9.63289i 0.285302 + 0.494157i
\(381\) −2.71922 + 4.70983i −0.139310 + 0.241292i
\(382\) −14.2462 −0.728900
\(383\) −11.3693 + 19.6922i −0.580945 + 1.00623i 0.414423 + 0.910085i \(0.363984\pi\)
−0.995368 + 0.0961417i \(0.969350\pi\)
\(384\) −6.78078 + 11.7446i −0.346030 + 0.599342i
\(385\) −4.00000 −0.203859
\(386\) −10.5346 + 18.2464i −0.536195 + 0.928717i
\(387\) −2.28078 3.95042i −0.115938 0.200811i
\(388\) −1.87689 3.25088i −0.0952849 0.165038i
\(389\) 34.0540 1.72661 0.863303 0.504687i \(-0.168392\pi\)
0.863303 + 0.504687i \(0.168392\pi\)
\(390\) 0 0
\(391\) −3.12311 −0.157942
\(392\) −8.15009 14.1164i −0.411642 0.712985i
\(393\) −3.68466 6.38202i −0.185866 0.321930i
\(394\) 10.4384 18.0799i 0.525881 0.910853i
\(395\) 19.3693 0.974576
\(396\) −0.438447 + 0.759413i −0.0220328 + 0.0381619i
\(397\) 12.5270 21.6974i 0.628711 1.08896i −0.359099 0.933299i \(-0.616916\pi\)
0.987811 0.155661i \(-0.0497507\pi\)
\(398\) 34.6307 1.73588
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) 18.0000 + 31.1769i 0.900000 + 1.55885i
\(401\) 7.21922 + 12.5041i 0.360511 + 0.624423i 0.988045 0.154166i \(-0.0492691\pi\)
−0.627534 + 0.778589i \(0.715936\pi\)
\(402\) −7.12311 −0.355268
\(403\) 0 0
\(404\) −3.31534 −0.164944
\(405\) −1.78078 3.08440i −0.0884875 0.153265i
\(406\) 2.93087 + 5.07642i 0.145457 + 0.251938i
\(407\) 7.56155 13.0970i 0.374812 0.649194i
\(408\) 3.80776 0.188512
\(409\) 3.18466 5.51599i 0.157471 0.272748i −0.776485 0.630136i \(-0.782999\pi\)
0.933956 + 0.357388i \(0.116333\pi\)
\(410\) −4.34233 + 7.52113i −0.214452 + 0.371442i
\(411\) 5.56155 0.274331
\(412\) 0.753789 1.30560i 0.0371365 0.0643223i
\(413\) 0.807764 + 1.39909i 0.0397475 + 0.0688446i
\(414\) −1.56155 2.70469i −0.0767461 0.132928i
\(415\) 3.12311 0.153307
\(416\) 0 0
\(417\) −17.9309 −0.878078
\(418\) 11.1231 + 19.2658i 0.544049 + 0.942320i
\(419\) 17.1231 + 29.6581i 0.836518 + 1.44889i 0.892788 + 0.450477i \(0.148746\pi\)
−0.0562697 + 0.998416i \(0.517921\pi\)
\(420\) 0.438447 0.759413i 0.0213940 0.0370556i
\(421\) −31.2462 −1.52285 −0.761424 0.648255i \(-0.775499\pi\)
−0.761424 + 0.648255i \(0.775499\pi\)
\(422\) −15.3693 + 26.6204i −0.748167 + 1.29586i
\(423\) 4.12311 7.14143i 0.200472 0.347228i
\(424\) 1.66950 0.0810783
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 10.9309 + 18.9328i 0.529602 + 0.917298i
\(427\) 1.08854 + 1.88541i 0.0526782 + 0.0912413i
\(428\) −3.61553 −0.174763
\(429\) 0 0
\(430\) 25.3693 1.22342
\(431\) −5.56155 9.63289i −0.267891 0.464000i 0.700426 0.713725i \(-0.252993\pi\)
−0.968317 + 0.249725i \(0.919660\pi\)
\(432\) 2.34233 + 4.05703i 0.112695 + 0.195194i
\(433\) −4.37689 + 7.58100i −0.210340 + 0.364320i −0.951821 0.306654i \(-0.900790\pi\)
0.741481 + 0.670974i \(0.234124\pi\)
\(434\) 2.24621 0.107822
\(435\) −11.9039 + 20.6181i −0.570747 + 0.988564i
\(436\) −0.615528 + 1.06613i −0.0294785 + 0.0510582i
\(437\) −14.2462 −0.681489
\(438\) −7.90388 + 13.6899i −0.377662 + 0.654130i
\(439\) 6.84233 + 11.8513i 0.326567 + 0.565630i 0.981828 0.189772i \(-0.0607749\pi\)
−0.655262 + 0.755402i \(0.727442\pi\)
\(440\) 8.68466 + 15.0423i 0.414025 + 0.717112i
\(441\) −6.68466 −0.318317
\(442\) 0 0
\(443\) −34.7386 −1.65048 −0.825241 0.564781i \(-0.808961\pi\)
−0.825241 + 0.564781i \(0.808961\pi\)
\(444\) 1.65767 + 2.87117i 0.0786696 + 0.136260i
\(445\) 8.68466 + 15.0423i 0.411692 + 0.713072i
\(446\) 6.24621 10.8188i 0.295767 0.512283i
\(447\) 2.43845 0.115335
\(448\) 1.56155 2.70469i 0.0737764 0.127785i
\(449\) −4.12311 + 7.14143i −0.194581 + 0.337025i −0.946763 0.321931i \(-0.895668\pi\)
0.752182 + 0.658956i \(0.229002\pi\)
\(450\) 12.0000 0.565685
\(451\) −1.56155 + 2.70469i −0.0735307 + 0.127359i
\(452\) −1.27320 2.20525i −0.0598862 0.103726i
\(453\) −4.68466 8.11407i −0.220104 0.381232i
\(454\) −11.1231 −0.522033
\(455\) 0 0
\(456\) 17.3693 0.813393
\(457\) 6.30776 + 10.9254i 0.295065 + 0.511067i 0.975000 0.222205i \(-0.0713254\pi\)
−0.679935 + 0.733272i \(0.737992\pi\)
\(458\) −12.6847 21.9705i −0.592715 1.02661i
\(459\) 0.780776 1.35234i 0.0364435 0.0631220i
\(460\) 3.12311 0.145616
\(461\) −8.09612 + 14.0229i −0.377074 + 0.653111i −0.990635 0.136536i \(-0.956403\pi\)
0.613561 + 0.789647i \(0.289736\pi\)
\(462\) 0.876894 1.51883i 0.0407968 0.0706622i
\(463\) 14.3153 0.665290 0.332645 0.943052i \(-0.392059\pi\)
0.332645 + 0.943052i \(0.392059\pi\)
\(464\) 15.6577 27.1199i 0.726889 1.25901i
\(465\) 4.56155 + 7.90084i 0.211537 + 0.366393i
\(466\) −20.3002 35.1610i −0.940388 1.62880i
\(467\) −26.0000 −1.20314 −0.601568 0.798821i \(-0.705457\pi\)
−0.601568 + 0.798821i \(0.705457\pi\)
\(468\) 0 0
\(469\) 2.56155 0.118282
\(470\) 22.9309 + 39.7174i 1.05772 + 1.83203i
\(471\) −10.1847 17.6403i −0.469284 0.812824i
\(472\) 3.50758 6.07530i 0.161449 0.279638i
\(473\) 9.12311 0.419481
\(474\) −4.24621 + 7.35465i −0.195035 + 0.337810i
\(475\) 27.3693 47.4050i 1.25579 2.17509i
\(476\) 0.384472 0.0176222
\(477\) 0.342329 0.592932i 0.0156742 0.0271485i
\(478\) −19.8078 34.3081i −0.905986 1.56921i
\(479\) 5.12311 + 8.87348i 0.234081 + 0.405440i 0.959005 0.283389i \(-0.0914587\pi\)
−0.724924 + 0.688828i \(0.758125\pi\)
\(480\) −8.68466 −0.396399
\(481\) 0 0
\(482\) 27.8078 1.26661
\(483\) 0.561553 + 0.972638i 0.0255515 + 0.0442566i
\(484\) 1.53457 + 2.65794i 0.0697530 + 0.120816i
\(485\) −15.2462 + 26.4072i −0.692295 + 1.19909i
\(486\) 1.56155 0.0708335
\(487\) 3.56155 6.16879i 0.161389 0.279535i −0.773978 0.633213i \(-0.781736\pi\)
0.935367 + 0.353678i \(0.115069\pi\)
\(488\) 4.72680 8.18706i 0.213972 0.370611i
\(489\) 4.80776 0.217415
\(490\) 18.5885 32.1963i 0.839745 1.45448i
\(491\) 18.1231 + 31.3901i 0.817884 + 1.41662i 0.907238 + 0.420617i \(0.138186\pi\)
−0.0893539 + 0.996000i \(0.528480\pi\)
\(492\) −0.342329 0.592932i −0.0154334 0.0267314i
\(493\) −10.4384 −0.470124
\(494\) 0 0
\(495\) 7.12311 0.320160
\(496\) −6.00000 10.3923i −0.269408 0.466628i
\(497\) −3.93087 6.80847i −0.176324 0.305401i
\(498\) −0.684658 + 1.18586i −0.0306803 + 0.0531398i
\(499\) −4.49242 −0.201108 −0.100554 0.994932i \(-0.532062\pi\)
−0.100554 + 0.994932i \(0.532062\pi\)
\(500\) −2.09612 + 3.63058i −0.0937412 + 0.162365i
\(501\) 5.12311 8.87348i 0.228883 0.396438i
\(502\) 29.2614 1.30600
\(503\) 14.1231 24.4619i 0.629718 1.09070i −0.357890 0.933764i \(-0.616504\pi\)
0.987608 0.156940i \(-0.0501630\pi\)
\(504\) −0.684658 1.18586i −0.0304971 0.0528225i
\(505\) 13.4654 + 23.3228i 0.599204 + 1.03785i
\(506\) 6.24621 0.277678
\(507\) 0 0
\(508\) 2.38447 0.105794
\(509\) −6.90388 11.9579i −0.306009 0.530023i 0.671476 0.741026i \(-0.265660\pi\)
−0.977486 + 0.211003i \(0.932327\pi\)
\(510\) 4.34233 + 7.52113i 0.192282 + 0.333041i
\(511\) 2.84233 4.92306i 0.125737 0.217783i
\(512\) −11.4233 −0.504843
\(513\) 3.56155 6.16879i 0.157246 0.272359i
\(514\) −22.7808 + 39.4575i −1.00482 + 1.74039i
\(515\) −12.2462 −0.539633
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 8.24621 + 14.2829i 0.362668 + 0.628159i
\(518\) −3.31534 5.74234i −0.145668 0.252304i
\(519\) 20.2462 0.888710
\(520\) 0 0
\(521\) −9.06913 −0.397326 −0.198663 0.980068i \(-0.563660\pi\)
−0.198663 + 0.980068i \(0.563660\pi\)
\(522\) −5.21922 9.03996i −0.228439 0.395668i
\(523\) −16.9309 29.3251i −0.740335 1.28230i −0.952343 0.305030i \(-0.901333\pi\)
0.212007 0.977268i \(-0.432000\pi\)
\(524\) −1.61553 + 2.79818i −0.0705747 + 0.122239i
\(525\) −4.31534 −0.188337
\(526\) −7.31534 + 12.6705i −0.318964 + 0.552462i
\(527\) −2.00000 + 3.46410i −0.0871214 + 0.150899i
\(528\) −9.36932 −0.407747
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 1.90388 + 3.29762i 0.0826994 + 0.143239i
\(531\) −1.43845 2.49146i −0.0624233 0.108120i
\(532\) 1.75379 0.0760364
\(533\) 0 0
\(534\) −7.61553 −0.329556
\(535\) 14.6847 + 25.4346i 0.634873 + 1.09963i
\(536\) −5.56155 9.63289i −0.240222 0.416078i
\(537\) 2.43845 4.22351i 0.105227 0.182258i
\(538\) −33.3693 −1.43865
\(539\) 6.68466 11.5782i 0.287929 0.498707i
\(540\) −0.780776 + 1.35234i −0.0335993 + 0.0581956i
\(541\) −19.7386 −0.848630 −0.424315 0.905515i \(-0.639485\pi\)
−0.424315 + 0.905515i \(0.639485\pi\)
\(542\) −23.3693 + 40.4768i −1.00380 + 1.73863i
\(543\) 1.34233 + 2.32498i 0.0576049 + 0.0997745i
\(544\) −1.90388 3.29762i −0.0816283 0.141384i
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 3.93087 0.168072 0.0840359 0.996463i \(-0.473219\pi\)
0.0840359 + 0.996463i \(0.473219\pi\)
\(548\) −1.21922 2.11176i −0.0520827 0.0902098i
\(549\) −1.93845 3.35749i −0.0827309 0.143294i
\(550\) −12.0000 + 20.7846i −0.511682 + 0.886259i
\(551\) −47.6155 −2.02849
\(552\) 2.43845 4.22351i 0.103787 0.179765i
\(553\) 1.52699 2.64482i 0.0649341 0.112469i
\(554\) 8.30019 0.352641
\(555\) 13.4654 23.3228i 0.571576 0.989998i
\(556\) 3.93087 + 6.80847i 0.166706 + 0.288743i
\(557\) −21.4654 37.1792i −0.909520 1.57533i −0.814733 0.579837i \(-0.803116\pi\)
−0.0947869 0.995498i \(-0.530217\pi\)
\(558\) −4.00000 −0.169334
\(559\) 0 0
\(560\) 9.36932 0.395926
\(561\) 1.56155 + 2.70469i 0.0659288 + 0.114192i
\(562\) 13.9039 + 24.0822i 0.586500 + 1.01585i
\(563\) 11.6847 20.2384i 0.492450 0.852948i −0.507513 0.861644i \(-0.669435\pi\)
0.999962 + 0.00869657i \(0.00276824\pi\)
\(564\) −3.61553 −0.152241
\(565\) −10.3423 + 17.9134i −0.435105 + 0.753624i
\(566\) 10.6847 18.5064i 0.449110 0.777881i
\(567\) −0.561553 −0.0235830
\(568\) −17.0691 + 29.5646i −0.716205 + 1.24050i
\(569\) 4.36932 + 7.56788i 0.183171 + 0.317262i 0.942959 0.332910i \(-0.108030\pi\)
−0.759787 + 0.650171i \(0.774697\pi\)
\(570\) 19.8078 + 34.3081i 0.829656 + 1.43701i
\(571\) −5.36932 −0.224699 −0.112349 0.993669i \(-0.535838\pi\)
−0.112349 + 0.993669i \(0.535838\pi\)
\(572\) 0 0
\(573\) −9.12311 −0.381123
\(574\) 0.684658 + 1.18586i 0.0285771 + 0.0494970i
\(575\) −7.68466 13.3102i −0.320472 0.555074i
\(576\) −2.78078 + 4.81645i −0.115866 + 0.200685i
\(577\) 17.3153 0.720847 0.360424 0.932789i \(-0.382632\pi\)
0.360424 + 0.932789i \(0.382632\pi\)
\(578\) 11.3693 19.6922i 0.472901 0.819089i
\(579\) −6.74621 + 11.6848i −0.280363 + 0.485603i
\(580\) 10.4384 0.433433
\(581\) 0.246211 0.426450i 0.0102146 0.0176921i
\(582\) −6.68466 11.5782i −0.277088 0.479931i
\(583\) 0.684658 + 1.18586i 0.0283557 + 0.0491134i
\(584\) −24.6847 −1.02146
\(585\) 0 0
\(586\) −31.9157 −1.31843
\(587\) 19.6847 + 34.0948i 0.812473 + 1.40724i 0.911128 + 0.412123i \(0.135212\pi\)
−0.0986556 + 0.995122i \(0.531454\pi\)
\(588\) 1.46543 + 2.53821i 0.0604335 + 0.104674i
\(589\) −9.12311 + 15.8017i −0.375911 + 0.651097i
\(590\) 16.0000 0.658710
\(591\) 6.68466 11.5782i 0.274970 0.476262i
\(592\) −17.7116 + 30.6775i −0.727944 + 1.26084i
\(593\) 17.4233 0.715489 0.357744 0.933820i \(-0.383546\pi\)
0.357744 + 0.933820i \(0.383546\pi\)
\(594\) −1.56155 + 2.70469i −0.0640713 + 0.110975i
\(595\) −1.56155 2.70469i −0.0640174 0.110881i
\(596\) −0.534565 0.925894i −0.0218966 0.0379261i
\(597\) 22.1771 0.907648
\(598\) 0 0
\(599\) −41.6155 −1.70036 −0.850182 0.526489i \(-0.823508\pi\)
−0.850182 + 0.526489i \(0.823508\pi\)
\(600\) 9.36932 + 16.2281i 0.382501 + 0.662511i
\(601\) 3.53457 + 6.12205i 0.144178 + 0.249723i 0.929066 0.369914i \(-0.120613\pi\)
−0.784888 + 0.619638i \(0.787280\pi\)
\(602\) 2.00000 3.46410i 0.0815139 0.141186i
\(603\) −4.56155 −0.185761
\(604\) −2.05398 + 3.55759i −0.0835751 + 0.144756i
\(605\) 12.4654 21.5908i 0.506792 0.877789i
\(606\) −11.8078 −0.479658
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −8.68466 15.0423i −0.352209 0.610045i
\(609\) 1.87689 + 3.25088i 0.0760556 + 0.131732i
\(610\) 21.5616 0.873002
\(611\) 0 0
\(612\) −0.684658 −0.0276757
\(613\) −17.4309 30.1912i −0.704026 1.21941i −0.967042 0.254618i \(-0.918050\pi\)
0.263016 0.964792i \(-0.415283\pi\)
\(614\) 24.0540 + 41.6627i 0.970739 + 1.68137i
\(615\) −2.78078 + 4.81645i −0.112132 + 0.194218i
\(616\) 2.73863 0.110343
\(617\) 4.90388 8.49377i 0.197423 0.341946i −0.750269 0.661132i \(-0.770076\pi\)
0.947692 + 0.319186i \(0.103409\pi\)
\(618\) 2.68466 4.64996i 0.107993 0.187049i
\(619\) −29.3002 −1.17767 −0.588837 0.808252i \(-0.700414\pi\)
−0.588837 + 0.808252i \(0.700414\pi\)
\(620\) 2.00000 3.46410i 0.0803219 0.139122i
\(621\) −1.00000 1.73205i −0.0401286 0.0695048i
\(622\) 14.9309 + 25.8610i 0.598673 + 1.03693i
\(623\) 2.73863 0.109721
\(624\) 0 0
\(625\) −4.36932 −0.174773
\(626\) 10.6847 + 18.5064i 0.427045 + 0.739663i
\(627\) 7.12311 + 12.3376i 0.284469 + 0.492716i
\(628\) −4.46543 + 7.73436i −0.178190 + 0.308635i
\(629\) 11.8078 0.470806
\(630\) 1.56155 2.70469i 0.0622138 0.107757i
\(631\) −9.28078 + 16.0748i −0.369462 + 0.639927i −0.989481 0.144660i \(-0.953791\pi\)
0.620020 + 0.784586i \(0.287125\pi\)
\(632\) −13.2614 −0.527509
\(633\) −9.84233 + 17.0474i −0.391197 + 0.677574i
\(634\) 10.9730 + 19.0058i 0.435794 + 0.754817i
\(635\) −9.68466 16.7743i −0.384324 0.665669i
\(636\) −0.300187 −0.0119032
\(637\) 0 0
\(638\) 20.8769 0.826524
\(639\) 7.00000 + 12.1244i 0.276916 + 0.479632i
\(640\) −24.1501 41.8292i −0.954616 1.65344i
\(641\) 9.58854 16.6078i 0.378725 0.655970i −0.612152 0.790740i \(-0.709696\pi\)
0.990877 + 0.134770i \(0.0430294\pi\)
\(642\) −12.8769 −0.508210
\(643\) −15.7732 + 27.3200i −0.622034 + 1.07739i 0.367072 + 0.930192i \(0.380360\pi\)
−0.989106 + 0.147202i \(0.952973\pi\)
\(644\) 0.246211 0.426450i 0.00970208 0.0168045i
\(645\) 16.2462 0.639694
\(646\) −8.68466 + 15.0423i −0.341693 + 0.591830i
\(647\) 3.19224 + 5.52911i 0.125500 + 0.217372i 0.921928 0.387361i \(-0.126613\pi\)
−0.796428 + 0.604733i \(0.793280\pi\)
\(648\) 1.21922 + 2.11176i 0.0478956 + 0.0829577i
\(649\) 5.75379 0.225856
\(650\) 0 0
\(651\) 1.43845 0.0563772
\(652\) −1.05398 1.82554i −0.0412769 0.0714936i
\(653\) −11.5616 20.0252i −0.452439 0.783647i 0.546098 0.837721i \(-0.316112\pi\)
−0.998537 + 0.0540745i \(0.982779\pi\)
\(654\) −2.19224 + 3.79706i −0.0857232 + 0.148477i
\(655\) 26.2462 1.02552
\(656\) 3.65767 6.33527i 0.142808 0.247351i
\(657\) −5.06155 + 8.76687i −0.197470 + 0.342028i
\(658\) 7.23106 0.281896
\(659\) 1.12311 1.94528i 0.0437500 0.0757772i −0.843321 0.537410i \(-0.819403\pi\)
0.887071 + 0.461633i \(0.152736\pi\)
\(660\) −1.56155 2.70469i −0.0607834 0.105280i
\(661\) 2.81534 + 4.87631i 0.109504 + 0.189667i 0.915569 0.402160i \(-0.131740\pi\)
−0.806065 + 0.591827i \(0.798407\pi\)
\(662\) 4.98485 0.193742
\(663\) 0 0
\(664\) −2.13826 −0.0829806
\(665\) −7.12311 12.3376i −0.276222 0.478431i
\(666\) 5.90388 + 10.2258i 0.228771 + 0.396243i
\(667\) −6.68466 + 11.5782i −0.258831 + 0.448308i
\(668\) −4.49242 −0.173817
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) 12.6847 21.9705i 0.490051 0.848793i
\(671\) 7.75379 0.299332
\(672\) −0.684658 + 1.18586i −0.0264113 + 0.0457457i
\(673\) 11.6231 + 20.1318i 0.448038 + 0.776024i 0.998258 0.0589952i \(-0.0187897\pi\)
−0.550220 + 0.835019i \(0.685456\pi\)
\(674\) 4.78078 + 8.28055i 0.184149 + 0.318955i
\(675\) 7.68466 0.295783
\(676\) 0 0
\(677\) −15.6155 −0.600153 −0.300077 0.953915i \(-0.597012\pi\)
−0.300077 + 0.953915i \(0.597012\pi\)
\(678\) −4.53457 7.85410i −0.174149 0.301635i
\(679\) 2.40388 + 4.16365i 0.0922525 + 0.159786i
\(680\) −6.78078 + 11.7446i −0.260031 + 0.450387i
\(681\) −7.12311 −0.272958
\(682\) 4.00000 6.92820i 0.153168 0.265295i
\(683\) −19.0540 + 33.0025i −0.729080 + 1.26280i 0.228192 + 0.973616i \(0.426719\pi\)
−0.957272 + 0.289188i \(0.906615\pi\)
\(684\) −3.12311 −0.119415
\(685\) −9.90388 + 17.1540i −0.378408 + 0.655422i
\(686\) −6.00000 10.3923i −0.229081 0.396780i
\(687\) −8.12311 14.0696i −0.309916 0.536790i
\(688\) −21.3693 −0.814698
\(689\) 0 0
\(690\) 11.1231 0.423449
\(691\) −25.6501 44.4273i −0.975776 1.69009i −0.677352 0.735659i \(-0.736872\pi\)
−0.298424 0.954433i \(-0.596461\pi\)
\(692\) −4.43845 7.68762i −0.168724 0.292239i
\(693\) 0.561553 0.972638i 0.0213316 0.0369475i
\(694\) 43.1231 1.63693
\(695\) 31.9309 55.3059i 1.21121 2.09787i
\(696\) 8.15009 14.1164i 0.308928 0.535080i
\(697\) −2.43845 −0.0923628
\(698\) 5.31534 9.20644i 0.201189 0.348469i
\(699\) −13.0000 22.5167i −0.491705 0.851658i
\(700\) 0.946025 + 1.63856i 0.0357564 + 0.0619319i
\(701\) −5.36932 −0.202796 −0.101398 0.994846i \(-0.532332\pi\)
−0.101398 + 0.994846i \(0.532332\pi\)
\(702\) 0 0
\(703\) 53.8617 2.03143
\(704\) −5.56155 9.63289i −0.209609 0.363053i
\(705\) 14.6847 + 25.4346i 0.553056 + 0.957921i
\(706\) 4.15009 7.18817i 0.156191 0.270530i
\(707\) 4.24621 0.159695
\(708\) −0.630683 + 1.09238i −0.0237025 + 0.0410540i
\(709\) −3.74621 + 6.48863i −0.140692 + 0.243686i −0.927757 0.373184i \(-0.878266\pi\)
0.787065 + 0.616869i \(0.211599\pi\)
\(710\) −77.8617 −2.92210
\(711\) −2.71922 + 4.70983i −0.101979 + 0.176633i
\(712\) −5.94602 10.2988i −0.222837 0.385964i
\(713\) 2.56155 + 4.43674i 0.0959309 + 0.166157i
\(714\) 1.36932 0.0512454
\(715\) 0 0
\(716\) −2.13826 −0.0799106
\(717\) −12.6847 21.9705i −0.473717 0.820502i
\(718\) −7.31534 12.6705i −0.273006 0.472860i
\(719\) 11.6847 20.2384i 0.435764 0.754766i −0.561593 0.827413i \(-0.689811\pi\)
0.997358 + 0.0726475i \(0.0231448\pi\)
\(720\) −16.6847 −0.621801
\(721\) −0.965435 + 1.67218i −0.0359547 + 0.0622753i
\(722\) −24.7808 + 42.9216i −0.922245 + 1.59738i
\(723\) 17.8078 0.662278
\(724\) 0.588540 1.01938i 0.0218729 0.0378850i
\(725\) −25.6847 44.4871i −0.953904 1.65221i
\(726\) 5.46543 + 9.46641i 0.202841 + 0.351331i
\(727\) −38.6695 −1.43417 −0.717086 0.696984i \(-0.754525\pi\)
−0.717086 + 0.696984i \(0.754525\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −28.1501 48.7574i −1.04188 1.80459i
\(731\) 3.56155 + 6.16879i 0.131729 + 0.228161i
\(732\) −0.849907 + 1.47208i −0.0314135 + 0.0544097i
\(733\) −20.5076 −0.757465 −0.378732 0.925506i \(-0.623640\pi\)
−0.378732 + 0.925506i \(0.623640\pi\)
\(734\) 13.3153 23.0628i 0.491478 0.851265i
\(735\) 11.9039 20.6181i 0.439081 0.760511i
\(736\) −4.87689 −0.179765
\(737\) 4.56155 7.90084i 0.168027 0.291031i
\(738\) −1.21922 2.11176i −0.0448802 0.0777349i
\(739\) 5.12311 + 8.87348i 0.188456 + 0.326416i 0.944736 0.327833i \(-0.106318\pi\)
−0.756279 + 0.654249i \(0.772985\pi\)
\(740\) −11.8078 −0.434062
\(741\) 0 0
\(742\) 0.600373 0.0220404
\(743\) −6.31534 10.9385i −0.231687 0.401294i 0.726617 0.687042i \(-0.241091\pi\)
−0.958305 + 0.285748i \(0.907758\pi\)
\(744\) −3.12311 5.40938i −0.114499 0.198317i
\(745\) −4.34233 + 7.52113i −0.159091 + 0.275553i
\(746\) 44.3002 1.62195
\(747\) −0.438447 + 0.759413i −0.0160419 + 0.0277855i
\(748\) 0.684658 1.18586i 0.0250336 0.0433595i
\(749\) 4.63068 0.169201
\(750\) −7.46543 + 12.9305i −0.272599 + 0.472156i
\(751\) −22.0540 38.1986i −0.804761 1.39389i −0.916452 0.400144i \(-0.868960\pi\)
0.111691 0.993743i \(-0.464373\pi\)
\(752\) −19.3153 33.4552i −0.704358 1.21998i
\(753\) 18.7386 0.682874
\(754\) 0 0
\(755\) 33.3693 1.21443
\(756\) 0.123106 + 0.213225i 0.00447731 + 0.00775493i
\(757\) −15.0000 25.9808i −0.545184 0.944287i −0.998595 0.0529853i \(-0.983126\pi\)
0.453411 0.891302i \(-0.350207\pi\)
\(758\) 18.4924 32.0298i 0.671675 1.16338i
\(759\) 4.00000 0.145191
\(760\) −30.9309 + 53.5738i −1.12198 + 1.94333i
\(761\) 4.68466 8.11407i 0.169819 0.294135i −0.768537 0.639805i \(-0.779015\pi\)
0.938356 + 0.345670i \(0.112348\pi\)
\(762\) 8.49242 0.307648
\(763\) 0.788354 1.36547i 0.0285403 0.0494333i
\(764\) 2.00000 + 3.46410i 0.0723575 + 0.125327i
\(765\) 2.78078 + 4.81645i 0.100539 + 0.174139i
\(766\) 35.5076 1.28294
\(767\) 0 0
\(768\) 10.0540 0.362792
\(769\) −9.00000 15.5885i −0.324548 0.562134i 0.656873 0.754002i \(-0.271879\pi\)
−0.981421 + 0.191867i \(0.938546\pi\)
\(770\) 3.12311 + 5.40938i 0.112549 + 0.194940i
\(771\) −14.5885 + 25.2681i −0.525393 + 0.910008i
\(772\) 5.91571 0.212911
\(773\) −12.1231 + 20.9978i −0.436038 + 0.755240i −0.997380 0.0723444i \(-0.976952\pi\)
0.561342 + 0.827584i \(0.310285\pi\)
\(774\) −3.56155 + 6.16879i −0.128017 + 0.221733i
\(775\) −19.6847 −0.707094
\(776\) 10.4384 18.0799i 0.374718 0.649031i
\(777\) −2.12311 3.67733i −0.0761660 0.131923i
\(778\) −26.5885 46.0527i −0.953245 1.65107i
\(779\) −11.1231 −0.398527
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) 2.43845 + 4.22351i 0.0871987 + 0.151033i
\(783\) −3.34233 5.78908i −0.119445 0.206885i
\(784\) −15.6577 + 27.1199i −0.559203 + 0.968567i
\(785\) 72.5464 2.58929
\(786\) −5.75379 + 9.96585i −0.205231 + 0.355470i
\(787\) 22.0885 38.2585i 0.787371 1.36377i −0.140201 0.990123i \(-0.544775\pi\)
0.927572 0.373644i \(-0.121892\pi\)
\(788\) −5.86174 −0.208816
\(789\) −4.68466 + 8.11407i −0.166778 + 0.288868i
\(790\) −15.1231 26.1940i −0.538056 0.931940i
\(791\) 1.63068 + 2.82443i 0.0579804 + 0.100425i
\(792\) −4.87689 −0.173293
\(793\) 0 0
\(794\) −39.1231 −1.38843
\(795\) 1.21922 + 2.11176i 0.0432414 + 0.0748963i
\(796\) −4.86174 8.42078i −0.172320 0.298467i
\(797\) 0.192236 0.332962i 0.00680935 0.0117941i −0.862601 0.505885i \(-0.831166\pi\)
0.869410 + 0.494091i \(0.164499\pi\)
\(798\) 6.24621 0.221113
\(799\) −6.43845 + 11.1517i −0.227776 + 0.394519i
\(800\) 9.36932 16.2281i 0.331255 0.573751i
\(801\) −4.87689 −0.172317
\(802\) 11.2732 19.5258i 0.398070 0.689478i
\(803\) −10.1231 17.5337i −0.357237 0.618752i
\(804\) 1.00000 + 1.73205i 0.0352673 + 0.0610847i
\(805\) −4.00000 −0.140981
\(806\) 0 0
\(807\) −21.3693 −0.752236
\(808\) −9.21922 15.9682i −0.324331 0.561758i
\(809\) 8.15009 + 14.1164i 0.286542 + 0.496305i 0.972982 0.230881i \(-0.0741609\pi\)
−0.686440 + 0.727187i \(0.740828\pi\)
\(810\) −2.78078 + 4.81645i −0.0977065 + 0.169233i
\(811\) −2.56155 −0.0899483 −0.0449741 0.998988i \(-0.514321\pi\)
−0.0449741 + 0.998988i \(0.514321\pi\)
\(812\) 0.822919 1.42534i 0.0288788 0.0500195i
\(813\) −14.9654 + 25.9209i −0.524861 + 0.909085i
\(814\) −23.6155 −0.827724
\(815\) −8.56155 + 14.8290i −0.299898 + 0.519439i
\(816\) −3.65767 6.33527i −0.128044 0.221779i
\(817\) 16.2462 + 28.1393i 0.568383 + 0.984468i
\(818\) −9.94602 −0.347755
\(819\) 0 0
\(820\) 2.43845 0.0851543
\(821\) 3.24621 + 5.62260i 0.113294 + 0.196230i 0.917096 0.398666i \(-0.130527\pi\)
−0.803803 + 0.594896i \(0.797193\pi\)
\(822\) −4.34233 7.52113i −0.151456 0.262330i
\(823\) −4.00000 + 6.92820i −0.139431 + 0.241502i −0.927281 0.374365i \(-0.877861\pi\)
0.787850 + 0.615867i \(0.211194\pi\)
\(824\) 8.38447 0.292087
\(825\) −7.68466 + 13.3102i −0.267545 + 0.463402i
\(826\) 1.26137 2.18475i 0.0438885 0.0760172i
\(827\) 14.7386 0.512513 0.256256 0.966609i \(-0.417511\pi\)
0.256256 + 0.966609i \(0.417511\pi\)
\(828\) −0.438447 + 0.759413i −0.0152371 + 0.0263914i
\(829\) −6.74621 11.6848i −0.234306 0.405829i 0.724765 0.688996i \(-0.241948\pi\)
−0.959071 + 0.283167i \(0.908615\pi\)
\(830\) −2.43845 4.22351i −0.0846397 0.146600i
\(831\) 5.31534 0.184387
\(832\) 0 0
\(833\) 10.4384 0.361671
\(834\) 14.0000 + 24.2487i 0.484780 + 0.839664i
\(835\) 18.2462 + 31.6034i 0.631436 + 1.09368i
\(836\) 3.12311 5.40938i 0.108015 0.187087i
\(837\) −2.56155 −0.0885402
\(838\) 26.7386 46.3127i 0.923671 1.59984i
\(839\) 10.8078 18.7196i 0.373125 0.646272i −0.616919 0.787027i \(-0.711619\pi\)
0.990045 + 0.140754i \(0.0449528\pi\)
\(840\) 4.87689 0.168269
\(841\) −7.84233 + 13.5833i −0.270425 + 0.468390i
\(842\) 24.3963 + 42.2556i 0.840752 + 1.45623i
\(843\) 8.90388 + 15.4220i 0.306666 + 0.531161i
\(844\) 8.63068 0.297080
\(845\) 0 0
\(846\) −12.8769 −0.442717
\(847\) −1.96543 3.40423i −0.0675331 0.116971i
\(848\) −1.60370 2.77768i −0.0550711 0.0953860i
\(849\) 6.84233 11.8513i 0.234828 0.406734i
\(850\) −18.7386 −0.642730
\(851\) 7.56155 13.0970i 0.259207 0.448959i
\(852\) 3.06913 5.31589i 0.105147 0.182119i
\(853\) −2.12311 −0.0726938 −0.0363469 0.999339i \(-0.511572\pi\)
−0.0363469 + 0.999339i \(0.511572\pi\)
\(854\) 1.69981 2.94416i 0.0581664 0.100747i
\(855\) 12.6847 + 21.9705i 0.433806 + 0.751374i
\(856\) −10.0540 17.4140i −0.343638 0.595198i
\(857\) 35.5616 1.21476 0.607380 0.794412i \(-0.292221\pi\)
0.607380 + 0.794412i \(0.292221\pi\)
\(858\) 0 0
\(859\) 24.5616 0.838029 0.419015 0.907979i \(-0.362376\pi\)
0.419015 + 0.907979i \(0.362376\pi\)
\(860\) −3.56155 6.16879i −0.121448 0.210354i
\(861\) 0.438447 + 0.759413i 0.0149422 + 0.0258807i
\(862\) −8.68466 + 15.0423i −0.295801 + 0.512342i
\(863\) −30.4924 −1.03797 −0.518987 0.854782i \(-0.673691\pi\)
−0.518987 + 0.854782i \(0.673691\pi\)
\(864\) 1.21922 2.11176i 0.0414788 0.0718434i
\(865\) −36.0540 + 62.4473i −1.22587 + 2.12327i
\(866\) 13.6695 0.464509
\(867\) 7.28078 12.6107i 0.247268 0.428281i
\(868\) −0.315342 0.546188i −0.0107034 0.0185388i
\(869\) −5.43845 9.41967i −0.184487 0.319540i
\(870\) 37.1771 1.26042
\(871\) 0 0
\(872\) −6.84658 −0.231855
\(873\) −4.28078 7.41452i −0.144882 0.250944i
\(874\) 11.1231 + 19.2658i 0.376245 + 0.651675i
\(875\) 2.68466 4.64996i 0.0907580 0.157198i
\(876\) 4.43845 0.149961
\(877\) 11.7808 20.4049i 0.397809 0.689025i −0.595647 0.803247i \(-0.703104\pi\)
0.993455 + 0.114222i \(0.0364375\pi\)
\(878\) 10.6847 18.5064i 0.360590 0.624560i
\(879\) −20.4384 −0.689372
\(880\) 16.6847 28.8987i 0.562440 0.974174i
\(881\) 4.53457 + 7.85410i 0.152773 + 0.264611i 0.932246 0.361825i \(-0.117846\pi\)
−0.779473 + 0.626436i \(0.784513\pi\)
\(882\) 5.21922 + 9.03996i 0.175740 + 0.304391i
\(883\) 8.80776 0.296405 0.148202 0.988957i \(-0.452651\pi\)
0.148202 + 0.988957i \(0.452651\pi\)
\(884\) 0 0
\(885\) 10.2462 0.344423
\(886\) 27.1231 + 46.9786i 0.911219 + 1.57828i
\(887\) −12.3153 21.3308i −0.413509 0.716218i 0.581762 0.813359i \(-0.302364\pi\)
−0.995271 + 0.0971410i \(0.969030\pi\)
\(888\) −9.21922 + 15.9682i −0.309377 + 0.535856i
\(889\) −3.05398 −0.102427
\(890\) 13.5616 23.4893i 0.454584 0.787363i
\(891\) −1.00000 + 1.73205i −0.0335013 + 0.0580259i
\(892\) −3.50758 −0.117442
\(893\) −29.3693 + 50.8691i −0.982807 + 1.70227i
\(894\) −1.90388 3.29762i −0.0636753 0.110289i
\(895\) 8.68466 + 15.0423i 0.290296 + 0.502808i
\(896\) −7.61553 −0.254417
\(897\) 0 0
\(898\) 12.8769 0.429708
\(899\) 8.56155 + 14.8290i 0.285544 + 0.494576i
\(900\) −1.68466 2.91791i −0.0561553 0.0972638i
\(901\) −0.534565 + 0.925894i −0.0178089 + 0.0308460i
\(902\) 4.87689 0.162383
\(903\) 1.28078 2.21837i 0.0426216 0.0738227i
\(904\) 7.08096 12.2646i 0.235509 0.407914i
\(905\) −9.56155 −0.317837
\(906\) −7.31534 + 12.6705i −0.243036 + 0.420951i
\(907\) −14.0000 24.2487i −0.464862 0.805165i 0.534333 0.845274i \(-0.320563\pi\)
−0.999195 + 0.0401089i \(0.987230\pi\)
\(908\) 1.56155 + 2.70469i 0.0518220 + 0.0897583i
\(909\) −7.56155 −0.250801
\(910\) 0 0
\(911\) 38.7386 1.28347 0.641734 0.766927i \(-0.278215\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(912\) −16.6847 28.8987i −0.552484 0.956931i
\(913\) −0.876894 1.51883i −0.0290210 0.0502658i
\(914\) 9.84991 17.0605i 0.325806 0.564312i
\(915\) 13.8078 0.456471
\(916\) −3.56155 + 6.16879i −0.117677 + 0.203823i
\(917\) 2.06913 3.58384i 0.0683287 0.118349i
\(918\) −2.43845 −0.0804807
\(919\) −5.75379 + 9.96585i −0.189800 + 0.328743i −0.945183 0.326540i \(-0.894117\pi\)
0.755383 + 0.655283i \(0.227451\pi\)
\(920\) 8.68466 + 15.0423i 0.286325 + 0.495929i
\(921\) 15.4039 + 26.6803i 0.507575 + 0.879146i
\(922\) 25.2850 0.832718
\(923\) 0 0
\(924\) −0.492423 −0.0161995
\(925\) 29.0540 + 50.3230i 0.955289 + 1.65461i
\(926\) −11.1771 19.3593i −0.367302 0.636185i
\(927\) 1.71922 2.97778i 0.0564667 0.0978032i
\(928\) −16.3002 −0.535080
\(929\) −3.90388 + 6.76172i −0.128082 + 0.221845i −0.922934 0.384959i \(-0.874215\pi\)
0.794851 + 0.606804i \(0.207549\pi\)
\(930\) 7.12311 12.3376i 0.233576 0.404565i
\(931\) 47.6155 1.56054
\(932\) −5.69981 + 9.87237i −0.186704 + 0.323380i
\(933\) 9.56155 + 16.5611i 0.313031 + 0.542186i
\(934\) 20.3002 + 35.1610i 0.664242 + 1.15050i
\(935\) −11.1231 −0.363764
\(936\) 0 0
\(937\) −7.56155 −0.247025 −0.123513 0.992343i \(-0.539416\pi\)
−0.123513 + 0.992343i \(0.539416\pi\)
\(938\) −2.00000 3.46410i −0.0653023 0.113107i
\(939\) 6.84233 + 11.8513i 0.223291 + 0.386751i
\(940\) 6.43845 11.1517i 0.209999 0.363729i
\(941\) −30.4924 −0.994025 −0.497012 0.867744i \(-0.665570\pi\)
−0.497012 + 0.867744i \(0.665570\pi\)
\(942\) −15.9039 + 27.5463i −0.518176 + 0.897508i
\(943\) −1.56155 + 2.70469i −0.0508512 + 0.0880768i
\(944\) −13.4773 −0.438648
\(945\) 1.00000 1.73205i 0.0325300 0.0563436i
\(946\) −7.12311 12.3376i −0.231592 0.401129i
\(947\) −19.3693 33.5486i −0.629418 1.09018i −0.987669 0.156559i \(-0.949960\pi\)
0.358250 0.933626i \(-0.383373\pi\)
\(948\) 2.38447 0.0774440
\(949\) 0 0
\(950\) −85.4773 −2.77325
\(951\) 7.02699 + 12.1711i 0.227866 + 0.394675i
\(952\) 1.06913 + 1.85179i 0.0346507 + 0.0600168i
\(953\) −15.4924 + 26.8337i −0.501849 + 0.869228i 0.498149 + 0.867091i \(0.334013\pi\)
−0.999998 + 0.00213612i \(0.999320\pi\)
\(954\) −1.06913 −0.0346144
\(955\) 16.2462 28.1393i 0.525715 0.910565i
\(956\) −5.56155 + 9.63289i −0.179873 + 0.311550i
\(957\) 13.3693 0.432169
\(958\) 8.00000 13.8564i 0.258468 0.447680i
\(959\) 1.56155 + 2.70469i 0.0504252 + 0.0873390i
\(960\) −9.90388 17.1540i −0.319646 0.553644i
\(961\) −24.4384 −0.788337
\(962\) 0 0
\(963\) −8.24621 −0.265730
\(964\) −3.90388 6.76172i −0.125736 0.217780i
\(965\) −24.0270 41.6160i −0.773456 1.33967i
\(966\) 0.876894 1.51883i 0.0282136 0.0488674i
\(967\) 0.876894 0.0281990 0.0140995 0.999901i \(-0.495512\pi\)
0.0140995 + 0.999901i \(0.495512\pi\)
\(968\) −8.53457 + 14.7823i −0.274311 + 0.475121i
\(969\) −5.56155 + 9.63289i −0.178663 + 0.309453i
\(970\) 47.6155 1.52884
\(971\) 6.49242 11.2452i 0.208352 0.360876i −0.742844 0.669465i \(-0.766523\pi\)
0.951195 + 0.308589i \(0.0998568\pi\)
\(972\) −0.219224 0.379706i −0.00703160 0.0121791i
\(973\) −5.03457 8.72012i −0.161401 0.279554i
\(974\) −11.1231 −0.356407
\(975\) 0 0
\(976\) −18.1619 −0.581349
\(977\) 30.5885 + 52.9809i 0.978614 + 1.69501i 0.667453 + 0.744652i \(0.267385\pi\)
0.311162 + 0.950357i \(0.399282\pi\)
\(978\) −3.75379 6.50175i −0.120033 0.207903i
\(979\) 4.87689 8.44703i 0.155866 0.269968i
\(980\) −10.4384 −0.333444
\(981\) −1.40388 + 2.43160i −0.0448225 + 0.0776349i
\(982\) 28.3002 49.0174i 0.903095 1.56421i
\(983\) −13.6155 −0.434268 −0.217134 0.976142i \(-0.569671\pi\)
−0.217134 + 0.976142i \(0.569671\pi\)
\(984\) 1.90388 3.29762i 0.0606935 0.105124i
\(985\) 23.8078 + 41.2363i 0.758578 + 1.31390i
\(986\) 8.15009 + 14.1164i 0.259552 + 0.449557i
\(987\) 4.63068 0.147396
\(988\) 0 0
\(989\) 9.12311 0.290098
\(990\) −5.56155 9.63289i −0.176758 0.306153i
\(991\) 25.1771 + 43.6080i 0.799776 + 1.38525i 0.919762 + 0.392478i \(0.128382\pi\)
−0.119985 + 0.992776i \(0.538285\pi\)
\(992\) −3.12311 + 5.40938i −0.0991587 + 0.171748i
\(993\) 3.19224 0.101303
\(994\) −6.13826 + 10.6318i −0.194694 + 0.337220i
\(995\) −39.4924 + 68.4029i −1.25199 + 2.16852i
\(996\) 0.384472 0.0121825
\(997\) 10.3078 17.8536i 0.326450 0.565428i −0.655355 0.755321i \(-0.727481\pi\)
0.981805 + 0.189893i \(0.0608141\pi\)
\(998\) 3.50758 + 6.07530i 0.111030 + 0.192310i
\(999\) 3.78078 + 6.54850i 0.119618 + 0.207185i
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 507.2.e.g.484.1 4
13.2 odd 12 507.2.b.d.337.2 4
13.3 even 3 507.2.a.d.1.2 2
13.4 even 6 39.2.e.b.22.2 yes 4
13.5 odd 4 507.2.j.g.361.2 8
13.6 odd 12 507.2.j.g.316.3 8
13.7 odd 12 507.2.j.g.316.2 8
13.8 odd 4 507.2.j.g.361.3 8
13.9 even 3 inner 507.2.e.g.22.1 4
13.10 even 6 507.2.a.g.1.1 2
13.11 odd 12 507.2.b.d.337.3 4
13.12 even 2 39.2.e.b.16.2 4
39.2 even 12 1521.2.b.h.1351.3 4
39.11 even 12 1521.2.b.h.1351.2 4
39.17 odd 6 117.2.g.c.100.1 4
39.23 odd 6 1521.2.a.g.1.2 2
39.29 odd 6 1521.2.a.m.1.1 2
39.38 odd 2 117.2.g.c.55.1 4
52.3 odd 6 8112.2.a.bo.1.2 2
52.23 odd 6 8112.2.a.bk.1.1 2
52.43 odd 6 624.2.q.h.529.1 4
52.51 odd 2 624.2.q.h.289.1 4
65.4 even 6 975.2.i.k.451.1 4
65.12 odd 4 975.2.bb.i.874.2 8
65.17 odd 12 975.2.bb.i.724.3 8
65.38 odd 4 975.2.bb.i.874.3 8
65.43 odd 12 975.2.bb.i.724.2 8
65.64 even 2 975.2.i.k.601.1 4
156.95 even 6 1872.2.t.r.1153.2 4
156.155 even 2 1872.2.t.r.289.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.e.b.16.2 4 13.12 even 2
39.2.e.b.22.2 yes 4 13.4 even 6
117.2.g.c.55.1 4 39.38 odd 2
117.2.g.c.100.1 4 39.17 odd 6
507.2.a.d.1.2 2 13.3 even 3
507.2.a.g.1.1 2 13.10 even 6
507.2.b.d.337.2 4 13.2 odd 12
507.2.b.d.337.3 4 13.11 odd 12
507.2.e.g.22.1 4 13.9 even 3 inner
507.2.e.g.484.1 4 1.1 even 1 trivial
507.2.j.g.316.2 8 13.7 odd 12
507.2.j.g.316.3 8 13.6 odd 12
507.2.j.g.361.2 8 13.5 odd 4
507.2.j.g.361.3 8 13.8 odd 4
624.2.q.h.289.1 4 52.51 odd 2
624.2.q.h.529.1 4 52.43 odd 6
975.2.i.k.451.1 4 65.4 even 6
975.2.i.k.601.1 4 65.64 even 2
975.2.bb.i.724.2 8 65.43 odd 12
975.2.bb.i.724.3 8 65.17 odd 12
975.2.bb.i.874.2 8 65.12 odd 4
975.2.bb.i.874.3 8 65.38 odd 4
1521.2.a.g.1.2 2 39.23 odd 6
1521.2.a.m.1.1 2 39.29 odd 6
1521.2.b.h.1351.2 4 39.11 even 12
1521.2.b.h.1351.3 4 39.2 even 12
1872.2.t.r.289.2 4 156.155 even 2
1872.2.t.r.1153.2 4 156.95 even 6
8112.2.a.bk.1.1 2 52.23 odd 6
8112.2.a.bo.1.2 2 52.3 odd 6