Properties

Label 546.2.bn.e.173.13
Level $546$
Weight $2$
Character 546.173
Analytic conductor $4.360$
Analytic rank $0$
Dimension $34$
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] = [546,2,Mod(101,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bn (of order \(6\), degree \(2\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 173.13
Character \(\chi\) \(=\) 546.173
Dual form 546.2.bn.e.101.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.51226 - 0.844435i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.511132 + 0.295102i) q^{5} +(-1.48743 - 0.887438i) q^{6} +(1.57814 - 2.12355i) q^{7} +1.00000 q^{8} +(1.57386 - 2.55401i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.51226 - 0.844435i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.511132 + 0.295102i) q^{5} +(-1.48743 - 0.887438i) q^{6} +(1.57814 - 2.12355i) q^{7} +1.00000 q^{8} +(1.57386 - 2.55401i) q^{9} -0.590205i q^{10} +6.11042 q^{11} +(-0.0248275 + 1.73187i) q^{12} +(-1.86885 + 3.08341i) q^{13} +(-2.62812 - 0.304939i) q^{14} +(1.02216 + 0.0146533i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.82336 + 6.62225i) q^{17} +(-2.99877 - 0.0859963i) q^{18} -3.95103 q^{19} +(-0.511132 + 0.295102i) q^{20} +(0.593366 - 4.54400i) q^{21} +(-3.05521 - 5.29178i) q^{22} +(7.26252 - 4.19302i) q^{23} +(1.51226 - 0.844435i) q^{24} +(-2.32583 - 4.02845i) q^{25} +(3.60473 + 0.0767706i) q^{26} +(0.223387 - 5.19135i) q^{27} +(1.04997 + 2.42849i) q^{28} +(1.39183 + 0.803572i) q^{29} +(-0.498390 - 0.892543i) q^{30} +(-1.38966 - 2.40696i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(9.24054 - 5.15985i) q^{33} +7.64672 q^{34} +(1.43330 - 0.619700i) q^{35} +(1.42491 + 2.64001i) q^{36} +(-1.93040 + 1.11452i) q^{37} +(1.97552 + 3.42169i) q^{38} +(-0.222454 + 6.24103i) q^{39} +(0.511132 + 0.295102i) q^{40} +(1.36416 + 0.787598i) q^{41} +(-4.23190 + 1.75813i) q^{42} +(-2.90674 - 5.03462i) q^{43} +(-3.05521 + 5.29178i) q^{44} +(1.55814 - 0.840988i) q^{45} +(-7.26252 - 4.19302i) q^{46} +(-4.94554 - 2.85531i) q^{47} +(-1.48743 - 0.887438i) q^{48} +(-2.01892 - 6.70253i) q^{49} +(-2.32583 + 4.02845i) q^{50} +(-0.189849 + 13.2431i) q^{51} +(-1.73588 - 3.16018i) q^{52} +(-3.30431 + 1.90774i) q^{53} +(-4.60753 + 2.40222i) q^{54} +(3.12323 + 1.80320i) q^{55} +(1.57814 - 2.12355i) q^{56} +(-5.97499 + 3.33639i) q^{57} -1.60714i q^{58} +(3.88177 + 2.24114i) q^{59} +(-0.523770 + 0.877889i) q^{60} +0.100596i q^{61} +(-1.38966 + 2.40696i) q^{62} +(-2.93979 - 7.37276i) q^{63} +1.00000 q^{64} +(-1.86515 + 1.02453i) q^{65} +(-9.08883 - 5.42261i) q^{66} +10.3459i q^{67} +(-3.82336 - 6.62225i) q^{68} +(7.44209 - 12.4737i) q^{69} +(-1.25333 - 0.931429i) q^{70} +(-0.875991 - 1.51726i) q^{71} +(1.57386 - 2.55401i) q^{72} +(5.41081 + 9.37179i) q^{73} +(1.93040 + 1.11452i) q^{74} +(-6.91903 - 4.12806i) q^{75} +(1.97552 - 3.42169i) q^{76} +(9.64312 - 12.9758i) q^{77} +(5.51612 - 2.92787i) q^{78} +(-3.17751 + 5.50361i) q^{79} -0.590205i q^{80} +(-4.04594 - 8.03930i) q^{81} -1.57520i q^{82} +9.07449i q^{83} +(3.63853 + 2.78587i) q^{84} +(-3.90849 + 2.25657i) q^{85} +(-2.90674 + 5.03462i) q^{86} +(2.78337 + 0.0399014i) q^{87} +6.11042 q^{88} +(-3.56660 + 2.05918i) q^{89} +(-1.50739 - 0.928899i) q^{90} +(3.59844 + 8.83466i) q^{91} +8.38604i q^{92} +(-4.13405 - 2.46647i) q^{93} +5.71062i q^{94} +(-2.01950 - 1.16596i) q^{95} +(-0.0248275 + 1.73187i) q^{96} +(2.82580 + 4.89442i) q^{97} +(-4.79511 + 5.09970i) q^{98} +(9.61693 - 15.6061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 1.51226 0.844435i 0.873104 0.487535i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.511132 + 0.295102i 0.228585 + 0.131974i 0.609919 0.792464i \(-0.291202\pi\)
−0.381334 + 0.924437i \(0.624535\pi\)
\(6\) −1.48743 0.887438i −0.607242 0.362295i
\(7\) 1.57814 2.12355i 0.596483 0.802626i
\(8\) 1.00000 0.353553
\(9\) 1.57386 2.55401i 0.524620 0.851337i
\(10\) 0.590205i 0.186639i
\(11\) 6.11042 1.84236 0.921180 0.389137i \(-0.127227\pi\)
0.921180 + 0.389137i \(0.127227\pi\)
\(12\) −0.0248275 + 1.73187i −0.00716709 + 0.499949i
\(13\) −1.86885 + 3.08341i −0.518326 + 0.855183i
\(14\) −2.62812 0.304939i −0.702394 0.0814984i
\(15\) 1.02216 + 0.0146533i 0.263920 + 0.00378347i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.82336 + 6.62225i −0.927301 + 1.60613i −0.139483 + 0.990224i \(0.544544\pi\)
−0.787818 + 0.615908i \(0.788789\pi\)
\(18\) −2.99877 0.0859963i −0.706816 0.0202695i
\(19\) −3.95103 −0.906429 −0.453214 0.891401i \(-0.649723\pi\)
−0.453214 + 0.891401i \(0.649723\pi\)
\(20\) −0.511132 + 0.295102i −0.114293 + 0.0659869i
\(21\) 0.593366 4.54400i 0.129483 0.991582i
\(22\) −3.05521 5.29178i −0.651373 1.12821i
\(23\) 7.26252 4.19302i 1.51434 0.874305i 0.514482 0.857501i \(-0.327984\pi\)
0.999859 0.0168038i \(-0.00534907\pi\)
\(24\) 1.51226 0.844435i 0.308689 0.172370i
\(25\) −2.32583 4.02845i −0.465166 0.805691i
\(26\) 3.60473 + 0.0767706i 0.706946 + 0.0150560i
\(27\) 0.223387 5.19135i 0.0429908 0.999075i
\(28\) 1.04997 + 2.42849i 0.198427 + 0.458941i
\(29\) 1.39183 + 0.803572i 0.258456 + 0.149220i 0.623630 0.781720i \(-0.285657\pi\)
−0.365174 + 0.930939i \(0.618991\pi\)
\(30\) −0.498390 0.892543i −0.0909931 0.162955i
\(31\) −1.38966 2.40696i −0.249590 0.432303i 0.713822 0.700327i \(-0.246963\pi\)
−0.963412 + 0.268024i \(0.913629\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 9.24054 5.15985i 1.60857 0.898215i
\(34\) 7.64672 1.31140
\(35\) 1.43330 0.619700i 0.242273 0.104748i
\(36\) 1.42491 + 2.64001i 0.237485 + 0.440001i
\(37\) −1.93040 + 1.11452i −0.317356 + 0.183226i −0.650213 0.759752i \(-0.725321\pi\)
0.332857 + 0.942977i \(0.391987\pi\)
\(38\) 1.97552 + 3.42169i 0.320471 + 0.555072i
\(39\) −0.222454 + 6.24103i −0.0356211 + 0.999365i
\(40\) 0.511132 + 0.295102i 0.0808171 + 0.0466598i
\(41\) 1.36416 + 0.787598i 0.213046 + 0.123002i 0.602726 0.797948i \(-0.294081\pi\)
−0.389680 + 0.920950i \(0.627414\pi\)
\(42\) −4.23190 + 1.75813i −0.652996 + 0.271285i
\(43\) −2.90674 5.03462i −0.443274 0.767773i 0.554656 0.832080i \(-0.312850\pi\)
−0.997930 + 0.0643067i \(0.979516\pi\)
\(44\) −3.05521 + 5.29178i −0.460590 + 0.797765i
\(45\) 1.55814 0.840988i 0.232274 0.125367i
\(46\) −7.26252 4.19302i −1.07080 0.618227i
\(47\) −4.94554 2.85531i −0.721381 0.416489i 0.0938798 0.995584i \(-0.470073\pi\)
−0.815261 + 0.579094i \(0.803406\pi\)
\(48\) −1.48743 0.887438i −0.214692 0.128091i
\(49\) −2.01892 6.70253i −0.288417 0.957505i
\(50\) −2.32583 + 4.02845i −0.328922 + 0.569709i
\(51\) −0.189849 + 13.2431i −0.0265842 + 1.85441i
\(52\) −1.73588 3.16018i −0.240723 0.438238i
\(53\) −3.30431 + 1.90774i −0.453881 + 0.262049i −0.709468 0.704738i \(-0.751065\pi\)
0.255587 + 0.966786i \(0.417731\pi\)
\(54\) −4.60753 + 2.40222i −0.627006 + 0.326900i
\(55\) 3.12323 + 1.80320i 0.421136 + 0.243143i
\(56\) 1.57814 2.12355i 0.210888 0.283771i
\(57\) −5.97499 + 3.33639i −0.791406 + 0.441916i
\(58\) 1.60714i 0.211028i
\(59\) 3.88177 + 2.24114i 0.505363 + 0.291772i 0.730926 0.682457i \(-0.239089\pi\)
−0.225562 + 0.974229i \(0.572422\pi\)
\(60\) −0.523770 + 0.877889i −0.0676184 + 0.113335i
\(61\) 0.100596i 0.0128800i 0.999979 + 0.00644002i \(0.00204994\pi\)
−0.999979 + 0.00644002i \(0.997950\pi\)
\(62\) −1.38966 + 2.40696i −0.176487 + 0.305684i
\(63\) −2.93979 7.37276i −0.370379 0.928881i
\(64\) 1.00000 0.125000
\(65\) −1.86515 + 1.02453i −0.231344 + 0.127077i
\(66\) −9.08883 5.42261i −1.11876 0.667478i
\(67\) 10.3459i 1.26396i 0.774985 + 0.631979i \(0.217757\pi\)
−0.774985 + 0.631979i \(0.782243\pi\)
\(68\) −3.82336 6.62225i −0.463651 0.803066i
\(69\) 7.44209 12.4737i 0.895922 1.50165i
\(70\) −1.25333 0.931429i −0.149801 0.111327i
\(71\) −0.875991 1.51726i −0.103961 0.180066i 0.809352 0.587324i \(-0.199818\pi\)
−0.913313 + 0.407258i \(0.866485\pi\)
\(72\) 1.57386 2.55401i 0.185481 0.300993i
\(73\) 5.41081 + 9.37179i 0.633287 + 1.09689i 0.986875 + 0.161484i \(0.0516280\pi\)
−0.353588 + 0.935401i \(0.615039\pi\)
\(74\) 1.93040 + 1.11452i 0.224405 + 0.129560i
\(75\) −6.91903 4.12806i −0.798940 0.476667i
\(76\) 1.97552 3.42169i 0.226607 0.392495i
\(77\) 9.64312 12.9758i 1.09894 1.47873i
\(78\) 5.51612 2.92787i 0.624578 0.331516i
\(79\) −3.17751 + 5.50361i −0.357498 + 0.619205i −0.987542 0.157355i \(-0.949703\pi\)
0.630044 + 0.776559i \(0.283037\pi\)
\(80\) 0.590205i 0.0659869i
\(81\) −4.04594 8.03930i −0.449549 0.893256i
\(82\) 1.57520i 0.173951i
\(83\) 9.07449i 0.996055i 0.867161 + 0.498027i \(0.165942\pi\)
−0.867161 + 0.498027i \(0.834058\pi\)
\(84\) 3.63853 + 2.78587i 0.396997 + 0.303963i
\(85\) −3.90849 + 2.25657i −0.423935 + 0.244759i
\(86\) −2.90674 + 5.03462i −0.313442 + 0.542897i
\(87\) 2.78337 + 0.0399014i 0.298408 + 0.00427788i
\(88\) 6.11042 0.651373
\(89\) −3.56660 + 2.05918i −0.378059 + 0.218272i −0.676973 0.736008i \(-0.736709\pi\)
0.298915 + 0.954280i \(0.403375\pi\)
\(90\) −1.50739 0.928899i −0.158893 0.0979145i
\(91\) 3.59844 + 8.83466i 0.377219 + 0.926124i
\(92\) 8.38604i 0.874305i
\(93\) −4.13405 2.46647i −0.428681 0.255761i
\(94\) 5.71062i 0.589005i
\(95\) −2.01950 1.16596i −0.207196 0.119625i
\(96\) −0.0248275 + 1.73187i −0.00253395 + 0.176759i
\(97\) 2.82580 + 4.89442i 0.286916 + 0.496953i 0.973072 0.230501i \(-0.0740365\pi\)
−0.686156 + 0.727455i \(0.740703\pi\)
\(98\) −4.79511 + 5.09970i −0.484379 + 0.515148i
\(99\) 9.61693 15.6061i 0.966538 1.56847i
\(100\) 4.65166 0.465166
\(101\) −11.8216 −1.17629 −0.588144 0.808756i \(-0.700141\pi\)
−0.588144 + 0.808756i \(0.700141\pi\)
\(102\) 11.5638 6.45716i 1.14499 0.639354i
\(103\) −3.76608 2.17435i −0.371083 0.214245i 0.302848 0.953039i \(-0.402062\pi\)
−0.673932 + 0.738794i \(0.735396\pi\)
\(104\) −1.86885 + 3.08341i −0.183256 + 0.302353i
\(105\) 1.64423 2.14748i 0.160461 0.209573i
\(106\) 3.30431 + 1.90774i 0.320943 + 0.185296i
\(107\) −7.65622 + 4.42032i −0.740154 + 0.427328i −0.822125 0.569306i \(-0.807212\pi\)
0.0819711 + 0.996635i \(0.473878\pi\)
\(108\) 4.38415 + 2.78913i 0.421865 + 0.268384i
\(109\) −14.8949 + 8.59957i −1.42667 + 0.823690i −0.996857 0.0792270i \(-0.974755\pi\)
−0.429816 + 0.902917i \(0.641421\pi\)
\(110\) 3.60640i 0.343856i
\(111\) −1.97813 + 3.31554i −0.187756 + 0.314697i
\(112\) −2.62812 0.304939i −0.248334 0.0288141i
\(113\) 13.5393 7.81690i 1.27367 0.735353i 0.297992 0.954568i \(-0.403683\pi\)
0.975676 + 0.219216i \(0.0703499\pi\)
\(114\) 5.87689 + 3.50630i 0.550421 + 0.328395i
\(115\) 4.94948 0.461541
\(116\) −1.39183 + 0.803572i −0.129228 + 0.0746098i
\(117\) 4.93374 + 9.62591i 0.456125 + 0.889916i
\(118\) 4.48228i 0.412627i
\(119\) 8.02886 + 18.5700i 0.736005 + 1.70231i
\(120\) 1.02216 + 0.0146533i 0.0933100 + 0.00133766i
\(121\) 26.3372 2.39429
\(122\) 0.0871190 0.0502982i 0.00788738 0.00455378i
\(123\) 2.72804 + 0.0391082i 0.245979 + 0.00352627i
\(124\) 2.77932 0.249590
\(125\) 5.69645i 0.509506i
\(126\) −4.91511 + 6.23231i −0.437872 + 0.555219i
\(127\) 2.99064 5.17994i 0.265377 0.459646i −0.702286 0.711895i \(-0.747837\pi\)
0.967662 + 0.252250i \(0.0811704\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −8.64716 5.15910i −0.761340 0.454234i
\(130\) 1.81984 + 1.10301i 0.159611 + 0.0967400i
\(131\) −2.79856 + 4.84725i −0.244511 + 0.423506i −0.961994 0.273070i \(-0.911961\pi\)
0.717483 + 0.696576i \(0.245294\pi\)
\(132\) −0.151707 + 10.5825i −0.0132044 + 0.921085i
\(133\) −6.23530 + 8.39021i −0.540669 + 0.727523i
\(134\) 8.95985 5.17297i 0.774013 0.446877i
\(135\) 1.64616 2.58754i 0.141679 0.222700i
\(136\) −3.82336 + 6.62225i −0.327850 + 0.567854i
\(137\) −10.5736 + 18.3140i −0.903363 + 1.56467i −0.0802641 + 0.996774i \(0.525576\pi\)
−0.823099 + 0.567898i \(0.807757\pi\)
\(138\) −14.5236 0.208205i −1.23633 0.0177236i
\(139\) 9.34314 5.39426i 0.792475 0.457535i −0.0483583 0.998830i \(-0.515399\pi\)
0.840833 + 0.541295i \(0.182066\pi\)
\(140\) −0.179977 + 1.55113i −0.0152108 + 0.131094i
\(141\) −9.89006 0.141781i −0.832893 0.0119401i
\(142\) −0.875991 + 1.51726i −0.0735115 + 0.127326i
\(143\) −11.4195 + 18.8409i −0.954944 + 1.57555i
\(144\) −2.99877 0.0859963i −0.249897 0.00716636i
\(145\) 0.474272 + 0.821463i 0.0393861 + 0.0682188i
\(146\) 5.41081 9.37179i 0.447801 0.775615i
\(147\) −8.71298 8.43113i −0.718635 0.695388i
\(148\) 2.22904i 0.183226i
\(149\) −8.02218 −0.657203 −0.328601 0.944469i \(-0.606577\pi\)
−0.328601 + 0.944469i \(0.606577\pi\)
\(150\) −0.115489 + 8.05608i −0.00942966 + 0.657776i
\(151\) 7.60834 4.39268i 0.619158 0.357471i −0.157383 0.987538i \(-0.550306\pi\)
0.776541 + 0.630066i \(0.216972\pi\)
\(152\) −3.95103 −0.320471
\(153\) 10.8959 + 20.1874i 0.880880 + 1.63205i
\(154\) −16.0589 1.86331i −1.29406 0.150149i
\(155\) 1.64037i 0.131758i
\(156\) −5.29367 3.31317i −0.423833 0.265266i
\(157\) 2.49489 1.44042i 0.199114 0.114958i −0.397128 0.917763i \(-0.629993\pi\)
0.596242 + 0.802805i \(0.296660\pi\)
\(158\) 6.35503 0.505579
\(159\) −3.38600 + 5.67527i −0.268528 + 0.450078i
\(160\) −0.511132 + 0.295102i −0.0404086 + 0.0233299i
\(161\) 2.55723 22.0395i 0.201538 1.73696i
\(162\) −4.93927 + 7.52354i −0.388066 + 0.591105i
\(163\) 5.37931i 0.421340i 0.977557 + 0.210670i \(0.0675646\pi\)
−0.977557 + 0.210670i \(0.932435\pi\)
\(164\) −1.36416 + 0.787598i −0.106523 + 0.0615011i
\(165\) 6.24582 + 0.0895380i 0.486237 + 0.00697052i
\(166\) 7.85874 4.53725i 0.609957 0.352159i
\(167\) 14.1115 + 8.14728i 1.09198 + 0.630455i 0.934103 0.357003i \(-0.116202\pi\)
0.157878 + 0.987459i \(0.449535\pi\)
\(168\) 0.593366 4.54400i 0.0457792 0.350577i
\(169\) −6.01478 11.5249i −0.462676 0.886528i
\(170\) 3.90849 + 2.25657i 0.299767 + 0.173071i
\(171\) −6.21837 + 10.0910i −0.475530 + 0.771676i
\(172\) 5.81348 0.443274
\(173\) 14.4001 1.09482 0.547408 0.836866i \(-0.315615\pi\)
0.547408 + 0.836866i \(0.315615\pi\)
\(174\) −1.35713 2.43042i −0.102884 0.184250i
\(175\) −12.2251 1.41847i −0.924132 0.107227i
\(176\) −3.05521 5.29178i −0.230295 0.398883i
\(177\) 7.76274 + 0.111284i 0.583483 + 0.00836462i
\(178\) 3.56660 + 2.05918i 0.267328 + 0.154342i
\(179\) 11.4696i 0.857281i 0.903475 + 0.428641i \(0.141007\pi\)
−0.903475 + 0.428641i \(0.858993\pi\)
\(180\) −0.0507554 + 1.76989i −0.00378309 + 0.131920i
\(181\) 14.7039i 1.09293i −0.837482 0.546465i \(-0.815973\pi\)
0.837482 0.546465i \(-0.184027\pi\)
\(182\) 5.85182 7.53367i 0.433766 0.558433i
\(183\) 0.0849471 + 0.152128i 0.00627947 + 0.0112456i
\(184\) 7.26252 4.19302i 0.535400 0.309114i
\(185\) −1.31559 −0.0967239
\(186\) −0.0690037 + 4.81343i −0.00505960 + 0.352938i
\(187\) −23.3623 + 40.4647i −1.70842 + 2.95907i
\(188\) 4.94554 2.85531i 0.360690 0.208245i
\(189\) −10.6715 8.66707i −0.776241 0.630437i
\(190\) 2.33192i 0.169175i
\(191\) 10.8591i 0.785739i −0.919594 0.392870i \(-0.871482\pi\)
0.919594 0.392870i \(-0.128518\pi\)
\(192\) 1.51226 0.844435i 0.109138 0.0609419i
\(193\) 19.2440i 1.38521i 0.721315 + 0.692607i \(0.243538\pi\)
−0.721315 + 0.692607i \(0.756462\pi\)
\(194\) 2.82580 4.89442i 0.202880 0.351399i
\(195\) −1.95545 + 3.12435i −0.140032 + 0.223739i
\(196\) 6.81402 + 1.60283i 0.486716 + 0.114488i
\(197\) 3.97307 6.88156i 0.283070 0.490291i −0.689070 0.724695i \(-0.741981\pi\)
0.972139 + 0.234404i \(0.0753139\pi\)
\(198\) −18.3237 0.525473i −1.30221 0.0373438i
\(199\) −16.2970 9.40910i −1.15527 0.666993i −0.205101 0.978741i \(-0.565752\pi\)
−0.950165 + 0.311748i \(0.899086\pi\)
\(200\) −2.32583 4.02845i −0.164461 0.284855i
\(201\) 8.73648 + 15.6458i 0.616224 + 1.10357i
\(202\) 5.91078 + 10.2378i 0.415881 + 0.720327i
\(203\) 3.90293 1.68746i 0.273932 0.118436i
\(204\) −11.3740 6.78599i −0.796338 0.475114i
\(205\) 0.464844 + 0.805133i 0.0324661 + 0.0562330i
\(206\) 4.34870i 0.302988i
\(207\) 0.721168 25.1478i 0.0501247 1.74789i
\(208\) 3.60473 + 0.0767706i 0.249943 + 0.00532309i
\(209\) −24.1425 −1.66997
\(210\) −2.68189 0.350207i −0.185068 0.0241666i
\(211\) 1.28361 2.22329i 0.0883677 0.153057i −0.818454 0.574573i \(-0.805168\pi\)
0.906821 + 0.421515i \(0.138502\pi\)
\(212\) 3.81548i 0.262049i
\(213\) −2.60595 1.55477i −0.178557 0.106531i
\(214\) 7.65622 + 4.42032i 0.523368 + 0.302167i
\(215\) 3.43114i 0.234002i
\(216\) 0.223387 5.19135i 0.0151995 0.353227i
\(217\) −7.30439 0.847524i −0.495854 0.0575337i
\(218\) 14.8949 + 8.59957i 1.00881 + 0.582437i
\(219\) 16.0964 + 9.60351i 1.08769 + 0.648945i
\(220\) −3.12323 + 1.80320i −0.210568 + 0.121572i
\(221\) −13.2738 24.1650i −0.892893 1.62551i
\(222\) 3.86041 + 0.0553415i 0.259093 + 0.00371428i
\(223\) −1.78923 + 3.09905i −0.119816 + 0.207527i −0.919695 0.392634i \(-0.871564\pi\)
0.799879 + 0.600162i \(0.204897\pi\)
\(224\) 1.04997 + 2.42849i 0.0701544 + 0.162260i
\(225\) −13.9492 0.400025i −0.929949 0.0266684i
\(226\) −13.5393 7.81690i −0.900619 0.519973i
\(227\) 10.3697 + 5.98695i 0.688261 + 0.397368i 0.802960 0.596033i \(-0.203257\pi\)
−0.114699 + 0.993400i \(0.536590\pi\)
\(228\) 0.0980944 6.84269i 0.00649646 0.453168i
\(229\) −5.57509 + 9.65634i −0.368412 + 0.638109i −0.989318 0.145777i \(-0.953432\pi\)
0.620905 + 0.783886i \(0.286765\pi\)
\(230\) −2.47474 4.28638i −0.163180 0.282635i
\(231\) 3.62571 27.7657i 0.238554 1.82685i
\(232\) 1.39183 + 0.803572i 0.0913779 + 0.0527571i
\(233\) 13.8355 + 7.98795i 0.906396 + 0.523308i 0.879270 0.476324i \(-0.158031\pi\)
0.0271263 + 0.999632i \(0.491364\pi\)
\(234\) 5.86941 9.08570i 0.383696 0.593951i
\(235\) −1.68522 2.91888i −0.109931 0.190407i
\(236\) −3.88177 + 2.24114i −0.252682 + 0.145886i
\(237\) −0.157780 + 11.0061i −0.0102489 + 0.714923i
\(238\) 12.0676 16.2382i 0.782229 1.05257i
\(239\) −17.6869 −1.14407 −0.572034 0.820230i \(-0.693846\pi\)
−0.572034 + 0.820230i \(0.693846\pi\)
\(240\) −0.498390 0.892543i −0.0321709 0.0576134i
\(241\) 12.0836 20.9293i 0.778370 1.34818i −0.154510 0.987991i \(-0.549380\pi\)
0.932881 0.360186i \(-0.117287\pi\)
\(242\) −13.1686 22.8087i −0.846510 1.46620i
\(243\) −12.9072 8.74098i −0.827996 0.560734i
\(244\) −0.0871190 0.0502982i −0.00557722 0.00322001i
\(245\) 0.946000 4.02167i 0.0604377 0.256935i
\(246\) −1.33015 2.38210i −0.0848073 0.151877i
\(247\) 7.38390 12.1826i 0.469826 0.775163i
\(248\) −1.38966 2.40696i −0.0882435 0.152842i
\(249\) 7.66282 + 13.7230i 0.485612 + 0.869659i
\(250\) −4.93327 + 2.84823i −0.312008 + 0.180138i
\(251\) 1.60381 + 2.77787i 0.101231 + 0.175338i 0.912192 0.409763i \(-0.134388\pi\)
−0.810961 + 0.585100i \(0.801055\pi\)
\(252\) 7.85489 + 1.14045i 0.494812 + 0.0718416i
\(253\) 44.3770 25.6211i 2.78996 1.61078i
\(254\) −5.98128 −0.375299
\(255\) −4.00512 + 6.71298i −0.250811 + 0.420383i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.591663 1.02479i −0.0369069 0.0639246i 0.846982 0.531622i \(-0.178417\pi\)
−0.883889 + 0.467697i \(0.845084\pi\)
\(258\) −0.144334 + 10.0682i −0.00898587 + 0.626819i
\(259\) −0.679720 + 5.85817i −0.0422358 + 0.364009i
\(260\) 0.0453104 2.12753i 0.00281003 0.131944i
\(261\) 4.24287 2.29003i 0.262627 0.141749i
\(262\) 5.59712 0.345791
\(263\) 1.34212i 0.0827589i 0.999144 + 0.0413794i \(0.0131752\pi\)
−0.999144 + 0.0413794i \(0.986825\pi\)
\(264\) 9.24054 5.15985i 0.568716 0.317567i
\(265\) −2.25192 −0.138334
\(266\) 10.3838 + 1.20482i 0.636671 + 0.0738726i
\(267\) −3.65478 + 6.12577i −0.223669 + 0.374891i
\(268\) −8.95985 5.17297i −0.547310 0.315990i
\(269\) 3.23296 5.59965i 0.197117 0.341417i −0.750476 0.660898i \(-0.770175\pi\)
0.947592 + 0.319482i \(0.103509\pi\)
\(270\) −3.06396 0.131844i −0.186467 0.00802376i
\(271\) −9.61794 16.6588i −0.584249 1.01195i −0.994969 0.100187i \(-0.968056\pi\)
0.410720 0.911761i \(-0.365277\pi\)
\(272\) 7.64672 0.463651
\(273\) 12.9021 + 10.3216i 0.780869 + 0.624695i
\(274\) 21.1472 1.27755
\(275\) −14.2118 24.6155i −0.857003 1.48437i
\(276\) 7.08147 + 12.6819i 0.426254 + 0.763359i
\(277\) 5.88112 10.1864i 0.353362 0.612042i −0.633474 0.773764i \(-0.718372\pi\)
0.986836 + 0.161722i \(0.0517049\pi\)
\(278\) −9.34314 5.39426i −0.560364 0.323526i
\(279\) −8.33453 0.239011i −0.498976 0.0143092i
\(280\) 1.43330 0.619700i 0.0856564 0.0370342i
\(281\) 21.9950 1.31211 0.656057 0.754711i \(-0.272223\pi\)
0.656057 + 0.754711i \(0.272223\pi\)
\(282\) 4.82224 + 8.63593i 0.287160 + 0.514262i
\(283\) 12.8485i 0.763761i 0.924212 + 0.381881i \(0.124723\pi\)
−0.924212 + 0.381881i \(0.875277\pi\)
\(284\) 1.75198 0.103961
\(285\) −4.03859 0.0578958i −0.239225 0.00342945i
\(286\) 22.0264 + 0.469101i 1.30245 + 0.0277385i
\(287\) 3.82534 1.65392i 0.225803 0.0976275i
\(288\) 1.42491 + 2.64001i 0.0839635 + 0.155564i
\(289\) −20.7362 35.9161i −1.21977 2.11271i
\(290\) 0.474272 0.821463i 0.0278502 0.0482380i
\(291\) 8.40636 + 5.01544i 0.492790 + 0.294010i
\(292\) −10.8216 −0.633287
\(293\) 0.344829 0.199087i 0.0201451 0.0116308i −0.489894 0.871782i \(-0.662964\pi\)
0.510039 + 0.860151i \(0.329631\pi\)
\(294\) −2.94508 + 11.7612i −0.171761 + 0.685929i
\(295\) 1.32273 + 2.29104i 0.0770124 + 0.133389i
\(296\) −1.93040 + 1.11452i −0.112202 + 0.0647800i
\(297\) 1.36499 31.7213i 0.0792045 1.84066i
\(298\) 4.01109 + 6.94741i 0.232356 + 0.402453i
\(299\) −0.643802 + 30.2294i −0.0372320 + 1.74821i
\(300\) 7.03452 3.92802i 0.406138 0.226785i
\(301\) −15.2785 1.77276i −0.880640 0.102180i
\(302\) −7.60834 4.39268i −0.437811 0.252770i
\(303\) −17.8773 + 9.98254i −1.02702 + 0.573482i
\(304\) 1.97552 + 3.42169i 0.113304 + 0.196248i
\(305\) −0.0296862 + 0.0514180i −0.00169983 + 0.00294419i
\(306\) 12.0349 19.5298i 0.687987 1.11644i
\(307\) −10.2738 −0.586356 −0.293178 0.956058i \(-0.594713\pi\)
−0.293178 + 0.956058i \(0.594713\pi\)
\(308\) 6.41578 + 14.8391i 0.365573 + 0.845535i
\(309\) −7.53139 0.107968i −0.428446 0.00614206i
\(310\) −1.42060 + 0.820184i −0.0806847 + 0.0465833i
\(311\) 1.05163 + 1.82148i 0.0596325 + 0.103287i 0.894300 0.447467i \(-0.147674\pi\)
−0.834668 + 0.550754i \(0.814340\pi\)
\(312\) −0.222454 + 6.24103i −0.0125940 + 0.353329i
\(313\) −9.44084 5.45067i −0.533628 0.308090i 0.208865 0.977945i \(-0.433023\pi\)
−0.742492 + 0.669854i \(0.766356\pi\)
\(314\) −2.49489 1.44042i −0.140795 0.0812878i
\(315\) 0.673099 4.63600i 0.0379248 0.261209i
\(316\) −3.17751 5.50361i −0.178749 0.309602i
\(317\) 5.27267 9.13253i 0.296143 0.512934i −0.679107 0.734039i \(-0.737633\pi\)
0.975250 + 0.221105i \(0.0709663\pi\)
\(318\) 6.60793 + 0.0947291i 0.370555 + 0.00531214i
\(319\) 8.50465 + 4.91016i 0.476169 + 0.274916i
\(320\) 0.511132 + 0.295102i 0.0285732 + 0.0164967i
\(321\) −7.84551 + 13.1498i −0.437894 + 0.733953i
\(322\) −20.3654 + 8.80513i −1.13492 + 0.490691i
\(323\) 15.1062 26.1647i 0.840533 1.45585i
\(324\) 8.98521 + 0.515766i 0.499178 + 0.0286537i
\(325\) 16.7680 + 0.357111i 0.930121 + 0.0198089i
\(326\) 4.65862 2.68966i 0.258017 0.148966i
\(327\) −15.2632 + 25.5826i −0.844055 + 1.41472i
\(328\) 1.36416 + 0.787598i 0.0753231 + 0.0434878i
\(329\) −13.8682 + 5.99600i −0.764576 + 0.330570i
\(330\) −3.04537 5.45381i −0.167642 0.300222i
\(331\) 14.5681i 0.800733i 0.916355 + 0.400366i \(0.131117\pi\)
−0.916355 + 0.400366i \(0.868883\pi\)
\(332\) −7.85874 4.53725i −0.431304 0.249014i
\(333\) −0.191689 + 6.68436i −0.0105045 + 0.366301i
\(334\) 16.2946i 0.891599i
\(335\) −3.05311 + 5.28815i −0.166809 + 0.288922i
\(336\) −4.23190 + 1.75813i −0.230869 + 0.0959138i
\(337\) −31.0830 −1.69320 −0.846599 0.532231i \(-0.821354\pi\)
−0.846599 + 0.532231i \(0.821354\pi\)
\(338\) −6.97343 + 10.9714i −0.379305 + 0.596765i
\(339\) 13.8740 23.2542i 0.753534 1.26300i
\(340\) 4.51313i 0.244759i
\(341\) −8.49140 14.7075i −0.459835 0.796458i
\(342\) 11.8482 + 0.339774i 0.640679 + 0.0183729i
\(343\) −17.4193 6.29030i −0.940554 0.339644i
\(344\) −2.90674 5.03462i −0.156721 0.271449i
\(345\) 7.48490 4.17951i 0.402973 0.225018i
\(346\) −7.20003 12.4708i −0.387076 0.670435i
\(347\) −21.3630 12.3339i −1.14682 0.662119i −0.198713 0.980058i \(-0.563676\pi\)
−0.948111 + 0.317938i \(0.897009\pi\)
\(348\) −1.42624 + 2.39052i −0.0764545 + 0.128145i
\(349\) 16.5800 28.7175i 0.887509 1.53721i 0.0446981 0.999001i \(-0.485767\pi\)
0.842811 0.538210i \(-0.180899\pi\)
\(350\) 4.88412 + 11.2965i 0.261067 + 0.603823i
\(351\) 15.5896 + 10.3907i 0.832109 + 0.554612i
\(352\) −3.05521 + 5.29178i −0.162843 + 0.282053i
\(353\) 14.4690i 0.770108i −0.922894 0.385054i \(-0.874183\pi\)
0.922894 0.385054i \(-0.125817\pi\)
\(354\) −3.78499 6.77837i −0.201170 0.360266i
\(355\) 1.03403i 0.0548805i
\(356\) 4.11835i 0.218272i
\(357\) 27.8229 + 21.3028i 1.47254 + 1.12746i
\(358\) 9.93300 5.73482i 0.524975 0.303095i
\(359\) 7.00098 12.1261i 0.369498 0.639989i −0.619989 0.784610i \(-0.712863\pi\)
0.989487 + 0.144621i \(0.0461964\pi\)
\(360\) 1.55814 0.840988i 0.0821214 0.0443239i
\(361\) −3.38934 −0.178386
\(362\) −12.7339 + 7.35194i −0.669281 + 0.386409i
\(363\) 39.8287 22.2401i 2.09046 1.16730i
\(364\) −9.45026 1.30099i −0.495328 0.0681903i
\(365\) 6.38697i 0.334309i
\(366\) 0.0892730 0.149630i 0.00466637 0.00782130i
\(367\) 14.7332i 0.769065i 0.923111 + 0.384533i \(0.125637\pi\)
−0.923111 + 0.384533i \(0.874363\pi\)
\(368\) −7.26252 4.19302i −0.378585 0.218576i
\(369\) 4.15853 2.24451i 0.216484 0.116845i
\(370\) 0.657794 + 1.13933i 0.0341971 + 0.0592310i
\(371\) −1.16349 + 10.0275i −0.0604054 + 0.520604i
\(372\) 4.20305 2.34696i 0.217918 0.121684i
\(373\) 15.8300 0.819645 0.409822 0.912165i \(-0.365591\pi\)
0.409822 + 0.912165i \(0.365591\pi\)
\(374\) 46.7247 2.41607
\(375\) −4.81029 8.61452i −0.248402 0.444852i
\(376\) −4.94554 2.85531i −0.255047 0.147251i
\(377\) −5.07886 + 2.78981i −0.261575 + 0.143683i
\(378\) −2.17013 + 13.5754i −0.111620 + 0.698241i
\(379\) −11.2444 6.49193i −0.577584 0.333468i 0.182589 0.983189i \(-0.441552\pi\)
−0.760173 + 0.649721i \(0.774886\pi\)
\(380\) 2.01950 1.16596i 0.103598 0.0598124i
\(381\) 0.148501 10.3588i 0.00760791 0.530698i
\(382\) −9.40428 + 5.42957i −0.481165 + 0.277801i
\(383\) 4.18573i 0.213881i 0.994265 + 0.106940i \(0.0341054\pi\)
−0.994265 + 0.106940i \(0.965895\pi\)
\(384\) −1.48743 0.887438i −0.0759052 0.0452869i
\(385\) 8.75809 3.78663i 0.446354 0.192984i
\(386\) 16.6658 9.62200i 0.848267 0.489747i
\(387\) −17.4333 0.499938i −0.886183 0.0254133i
\(388\) −5.65159 −0.286916
\(389\) −19.0201 + 10.9812i −0.964356 + 0.556771i −0.897511 0.440992i \(-0.854627\pi\)
−0.0668451 + 0.997763i \(0.521293\pi\)
\(390\) 3.68349 + 0.131293i 0.186521 + 0.00664829i
\(391\) 64.1257i 3.24298i
\(392\) −2.01892 6.70253i −0.101971 0.338529i
\(393\) −0.138963 + 9.69349i −0.00700974 + 0.488972i
\(394\) −7.94614 −0.400321
\(395\) −3.24826 + 1.87538i −0.163438 + 0.0943608i
\(396\) 8.70679 + 16.1315i 0.437532 + 0.810641i
\(397\) −33.1213 −1.66231 −0.831156 0.556039i \(-0.812320\pi\)
−0.831156 + 0.556039i \(0.812320\pi\)
\(398\) 18.8182i 0.943271i
\(399\) −2.34441 + 17.9535i −0.117367 + 0.898798i
\(400\) −2.32583 + 4.02845i −0.116291 + 0.201423i
\(401\) −3.47187 6.01346i −0.173377 0.300298i 0.766221 0.642577i \(-0.222135\pi\)
−0.939598 + 0.342279i \(0.888801\pi\)
\(402\) 9.18138 15.3889i 0.457926 0.767528i
\(403\) 10.0187 + 0.213370i 0.499067 + 0.0106287i
\(404\) 5.91078 10.2378i 0.294072 0.509348i
\(405\) 0.304407 5.30311i 0.0151261 0.263514i
\(406\) −3.41285 2.53631i −0.169377 0.125875i
\(407\) −11.7956 + 6.81017i −0.584684 + 0.337568i
\(408\) −0.189849 + 13.2431i −0.00939894 + 0.655634i
\(409\) −0.151773 + 0.262878i −0.00750467 + 0.0129985i −0.869753 0.493487i \(-0.835722\pi\)
0.862249 + 0.506485i \(0.169056\pi\)
\(410\) 0.464844 0.805133i 0.0229570 0.0397627i
\(411\) −0.525033 + 36.6243i −0.0258980 + 1.80654i
\(412\) 3.76608 2.17435i 0.185542 0.107123i
\(413\) 10.8852 4.70628i 0.535624 0.231581i
\(414\) −22.1392 + 11.9493i −1.08808 + 0.587278i
\(415\) −2.67790 + 4.63827i −0.131453 + 0.227684i
\(416\) −1.73588 3.16018i −0.0851086 0.154940i
\(417\) 9.57415 16.0472i 0.468848 0.785835i
\(418\) 12.0712 + 20.9080i 0.590423 + 1.02264i
\(419\) 2.85725 4.94891i 0.139586 0.241770i −0.787754 0.615990i \(-0.788756\pi\)
0.927340 + 0.374220i \(0.122089\pi\)
\(420\) 1.03766 + 2.49769i 0.0506324 + 0.121875i
\(421\) 9.25537i 0.451079i 0.974234 + 0.225540i \(0.0724145\pi\)
−0.974234 + 0.225540i \(0.927585\pi\)
\(422\) −2.56723 −0.124971
\(423\) −15.0761 + 8.13711i −0.733023 + 0.395640i
\(424\) −3.30431 + 1.90774i −0.160471 + 0.0926481i
\(425\) 35.5699 1.72540
\(426\) −0.0434974 + 3.03421i −0.00210746 + 0.147008i
\(427\) 0.213621 + 0.158756i 0.0103379 + 0.00768272i
\(428\) 8.84064i 0.427328i
\(429\) −1.35928 + 38.1353i −0.0656269 + 1.84119i
\(430\) −2.97146 + 1.71557i −0.143296 + 0.0827322i
\(431\) −10.1057 −0.486773 −0.243386 0.969929i \(-0.578258\pi\)
−0.243386 + 0.969929i \(0.578258\pi\)
\(432\) −4.60753 + 2.40222i −0.221680 + 0.115577i
\(433\) −32.8655 + 18.9749i −1.57942 + 0.911877i −0.584476 + 0.811411i \(0.698700\pi\)
−0.994941 + 0.100466i \(0.967967\pi\)
\(434\) 2.91822 + 6.74955i 0.140079 + 0.323989i
\(435\) 1.41089 + 0.841774i 0.0676472 + 0.0403600i
\(436\) 17.1991i 0.823690i
\(437\) −28.6945 + 16.5668i −1.37264 + 0.792495i
\(438\) 0.268674 18.7417i 0.0128377 0.895511i
\(439\) 24.6369 14.2241i 1.17586 0.678881i 0.220805 0.975318i \(-0.429132\pi\)
0.955052 + 0.296437i \(0.0957984\pi\)
\(440\) 3.12323 + 1.80320i 0.148894 + 0.0859641i
\(441\) −20.2958 5.39251i −0.966468 0.256786i
\(442\) −14.2906 + 23.5779i −0.679734 + 1.12149i
\(443\) 18.7651 + 10.8340i 0.891555 + 0.514740i 0.874451 0.485114i \(-0.161222\pi\)
0.0171043 + 0.999854i \(0.494555\pi\)
\(444\) −1.88228 3.37088i −0.0893289 0.159975i
\(445\) −2.43067 −0.115225
\(446\) 3.57847 0.169445
\(447\) −12.1316 + 6.77421i −0.573806 + 0.320409i
\(448\) 1.57814 2.12355i 0.0745603 0.100328i
\(449\) 6.23704 + 10.8029i 0.294344 + 0.509819i 0.974832 0.222940i \(-0.0715656\pi\)
−0.680488 + 0.732759i \(0.738232\pi\)
\(450\) 6.62819 + 12.2804i 0.312456 + 0.578904i
\(451\) 8.33558 + 4.81255i 0.392507 + 0.226614i
\(452\) 15.6338i 0.735353i
\(453\) 7.79646 13.0676i 0.366310 0.613971i
\(454\) 11.9739i 0.561963i
\(455\) −0.767849 + 5.57759i −0.0359973 + 0.261481i
\(456\) −5.97499 + 3.33639i −0.279804 + 0.156241i
\(457\) 8.30703 4.79607i 0.388587 0.224351i −0.292961 0.956124i \(-0.594641\pi\)
0.681548 + 0.731774i \(0.261307\pi\)
\(458\) 11.1502 0.521014
\(459\) 33.5243 + 21.3277i 1.56478 + 0.995493i
\(460\) −2.47474 + 4.28638i −0.115385 + 0.199853i
\(461\) −4.17780 + 2.41206i −0.194580 + 0.112341i −0.594125 0.804373i \(-0.702501\pi\)
0.399545 + 0.916714i \(0.369168\pi\)
\(462\) −25.8587 + 10.7429i −1.20305 + 0.499805i
\(463\) 3.08747i 0.143487i 0.997423 + 0.0717434i \(0.0228563\pi\)
−0.997423 + 0.0717434i \(0.977144\pi\)
\(464\) 1.60714i 0.0746098i
\(465\) −1.38518 2.48066i −0.0642364 0.115038i
\(466\) 15.9759i 0.740069i
\(467\) 4.16237 7.20943i 0.192611 0.333613i −0.753504 0.657444i \(-0.771638\pi\)
0.946115 + 0.323831i \(0.104971\pi\)
\(468\) −10.8032 0.540211i −0.499376 0.0249713i
\(469\) 21.9701 + 16.3274i 1.01449 + 0.753929i
\(470\) −1.68522 + 2.91888i −0.0777332 + 0.134638i
\(471\) 2.55657 4.28506i 0.117801 0.197445i
\(472\) 3.88177 + 2.24114i 0.178673 + 0.103157i
\(473\) −17.7614 30.7636i −0.816670 1.41451i
\(474\) 9.61045 5.36641i 0.441422 0.246487i
\(475\) 9.18943 + 15.9166i 0.421640 + 0.730302i
\(476\) −20.0965 2.33179i −0.921121 0.106877i
\(477\) −0.328118 + 11.4417i −0.0150235 + 0.523882i
\(478\) 8.84344 + 15.3173i 0.404489 + 0.700596i
\(479\) 12.0776i 0.551839i −0.961181 0.275920i \(-0.911018\pi\)
0.961181 0.275920i \(-0.0889824\pi\)
\(480\) −0.523770 + 0.877889i −0.0239067 + 0.0400700i
\(481\) 0.171124 8.03508i 0.00780260 0.366368i
\(482\) −24.1671 −1.10078
\(483\) −14.7437 35.4889i −0.670863 1.61480i
\(484\) −13.1686 + 22.8087i −0.598573 + 1.03676i
\(485\) 3.33560i 0.151462i
\(486\) −1.11632 + 15.5484i −0.0506374 + 0.705291i
\(487\) 4.84833 + 2.79918i 0.219699 + 0.126843i 0.605811 0.795609i \(-0.292849\pi\)
−0.386112 + 0.922452i \(0.626182\pi\)
\(488\) 0.100596i 0.00455378i
\(489\) 4.54248 + 8.13492i 0.205418 + 0.367874i
\(490\) −3.95587 + 1.19157i −0.178708 + 0.0538299i
\(491\) 0.451495 + 0.260671i 0.0203757 + 0.0117639i 0.510153 0.860084i \(-0.329589\pi\)
−0.489778 + 0.871847i \(0.662922\pi\)
\(492\) −1.39789 + 2.34300i −0.0630217 + 0.105630i
\(493\) −10.6429 + 6.14469i −0.479333 + 0.276743i
\(494\) −14.2424 0.303323i −0.640797 0.0136472i
\(495\) 9.52091 5.13879i 0.427933 0.230971i
\(496\) −1.38966 + 2.40696i −0.0623976 + 0.108076i
\(497\) −4.60442 0.534248i −0.206536 0.0239643i
\(498\) 8.05305 13.4977i 0.360866 0.604846i
\(499\) 28.9603 + 16.7202i 1.29644 + 0.748501i 0.979788 0.200041i \(-0.0641074\pi\)
0.316654 + 0.948541i \(0.397441\pi\)
\(500\) 4.93327 + 2.84823i 0.220623 + 0.127377i
\(501\) 28.2201 + 0.404554i 1.26078 + 0.0180741i
\(502\) 1.60381 2.77787i 0.0715814 0.123983i
\(503\) −9.16509 15.8744i −0.408651 0.707805i 0.586088 0.810248i \(-0.300667\pi\)
−0.994739 + 0.102443i \(0.967334\pi\)
\(504\) −2.93979 7.37276i −0.130949 0.328409i
\(505\) −6.04238 3.48857i −0.268882 0.155239i
\(506\) −44.3770 25.6211i −1.97280 1.13900i
\(507\) −18.8279 12.3495i −0.836177 0.548460i
\(508\) 2.99064 + 5.17994i 0.132688 + 0.229823i
\(509\) 30.2332 17.4552i 1.34006 0.773686i 0.353248 0.935530i \(-0.385077\pi\)
0.986816 + 0.161843i \(0.0517439\pi\)
\(510\) 7.81617 + 0.112050i 0.346106 + 0.00496166i
\(511\) 28.4405 + 3.29993i 1.25813 + 0.145980i
\(512\) 1.00000 0.0441942
\(513\) −0.882608 + 20.5112i −0.0389681 + 0.905591i
\(514\) −0.591663 + 1.02479i −0.0260971 + 0.0452015i
\(515\) −1.28331 2.22276i −0.0565495 0.0979465i
\(516\) 8.79149 4.90911i 0.387024 0.216111i
\(517\) −30.2193 17.4471i −1.32904 0.767324i
\(518\) 5.41319 2.34043i 0.237842 0.102833i
\(519\) 21.7766 12.1599i 0.955888 0.533761i
\(520\) −1.86515 + 1.02453i −0.0817923 + 0.0449284i
\(521\) 15.3561 + 26.5976i 0.672763 + 1.16526i 0.977117 + 0.212701i \(0.0682260\pi\)
−0.304354 + 0.952559i \(0.598441\pi\)
\(522\) −4.10466 2.52942i −0.179656 0.110710i
\(523\) 27.1317 15.6645i 1.18639 0.684960i 0.228902 0.973449i \(-0.426486\pi\)
0.957483 + 0.288490i \(0.0931531\pi\)
\(524\) −2.79856 4.84725i −0.122256 0.211753i
\(525\) −19.6854 + 8.17822i −0.859139 + 0.356927i
\(526\) 1.16231 0.671062i 0.0506793 0.0292597i
\(527\) 21.2527 0.925782
\(528\) −9.08883 5.42261i −0.395541 0.235989i
\(529\) 23.6628 40.9852i 1.02882 1.78197i
\(530\) 1.12596 + 1.95022i 0.0489085 + 0.0847120i
\(531\) 11.8332 6.38684i 0.513519 0.277165i
\(532\) −4.14848 9.59503i −0.179860 0.415997i
\(533\) −4.97790 + 2.73435i −0.215617 + 0.118438i
\(534\) 7.13246 + 0.102249i 0.308652 + 0.00442473i
\(535\) −5.21779 −0.225585
\(536\) 10.3459i 0.446877i
\(537\) 9.68537 + 17.3451i 0.417954 + 0.748495i
\(538\) −6.46592 −0.278765
\(539\) −12.3364 40.9553i −0.531368 1.76407i
\(540\) 1.41780 + 2.71939i 0.0610124 + 0.117024i
\(541\) 18.3221 + 10.5782i 0.787726 + 0.454794i 0.839162 0.543882i \(-0.183046\pi\)
−0.0514351 + 0.998676i \(0.516380\pi\)
\(542\) −9.61794 + 16.6588i −0.413126 + 0.715555i
\(543\) −12.4165 22.2361i −0.532842 0.954241i
\(544\) −3.82336 6.62225i −0.163925 0.283927i
\(545\) −10.1510 −0.434822
\(546\) 2.48777 16.3344i 0.106467 0.699046i
\(547\) −2.57133 −0.109942 −0.0549710 0.998488i \(-0.517507\pi\)
−0.0549710 + 0.998488i \(0.517507\pi\)
\(548\) −10.5736 18.3140i −0.451682 0.782336i
\(549\) 0.256924 + 0.158324i 0.0109653 + 0.00675712i
\(550\) −14.2118 + 24.6155i −0.605993 + 1.04961i
\(551\) −5.49916 3.17494i −0.234272 0.135257i
\(552\) 7.44209 12.4737i 0.316756 0.530914i
\(553\) 6.67261 + 15.4331i 0.283748 + 0.656282i
\(554\) −11.7622 −0.499730
\(555\) −1.98951 + 1.11093i −0.0844500 + 0.0471563i
\(556\) 10.7885i 0.457535i
\(557\) 15.1289 0.641031 0.320515 0.947243i \(-0.396144\pi\)
0.320515 + 0.947243i \(0.396144\pi\)
\(558\) 3.96028 + 7.33742i 0.167652 + 0.310618i
\(559\) 20.9561 + 0.446305i 0.886347 + 0.0188767i
\(560\) −1.25333 0.931429i −0.0529628 0.0393600i
\(561\) −1.16006 + 80.9212i −0.0489777 + 3.41649i
\(562\) −10.9975 19.0483i −0.463902 0.803503i
\(563\) −2.91404 + 5.04726i −0.122812 + 0.212717i −0.920876 0.389857i \(-0.872525\pi\)
0.798064 + 0.602573i \(0.205858\pi\)
\(564\) 5.06782 8.49415i 0.213394 0.357668i
\(565\) 9.22715 0.388189
\(566\) 11.1271 6.42423i 0.467706 0.270030i
\(567\) −23.4569 4.09544i −0.985098 0.171992i
\(568\) −0.875991 1.51726i −0.0367558 0.0636628i
\(569\) −20.0259 + 11.5620i −0.839530 + 0.484703i −0.857104 0.515143i \(-0.827739\pi\)
0.0175747 + 0.999846i \(0.494406\pi\)
\(570\) 1.96915 + 3.52647i 0.0824788 + 0.147707i
\(571\) −17.1315 29.6727i −0.716933 1.24176i −0.962209 0.272311i \(-0.912212\pi\)
0.245277 0.969453i \(-0.421121\pi\)
\(572\) −10.6070 19.3100i −0.443499 0.807392i
\(573\) −9.16983 16.4218i −0.383075 0.686032i
\(574\) −3.34500 2.48589i −0.139618 0.103759i
\(575\) −33.7828 19.5045i −1.40884 0.813394i
\(576\) 1.57386 2.55401i 0.0655774 0.106417i
\(577\) 7.81628 + 13.5382i 0.325396 + 0.563602i 0.981592 0.190988i \(-0.0611691\pi\)
−0.656196 + 0.754590i \(0.727836\pi\)
\(578\) −20.7362 + 35.9161i −0.862511 + 1.49391i
\(579\) 16.2503 + 29.1019i 0.675340 + 1.20944i
\(580\) −0.948544 −0.0393861
\(581\) 19.2701 + 14.3209i 0.799460 + 0.594130i
\(582\) 0.140315 9.78784i 0.00581625 0.405719i
\(583\) −20.1907 + 11.6571i −0.836213 + 0.482788i
\(584\) 5.41081 + 9.37179i 0.223901 + 0.387807i
\(585\) −0.318835 + 6.37607i −0.0131822 + 0.263618i
\(586\) −0.344829 0.199087i −0.0142448 0.00822421i
\(587\) 25.9699 + 14.9937i 1.07189 + 0.618856i 0.928697 0.370838i \(-0.120930\pi\)
0.143193 + 0.989695i \(0.454263\pi\)
\(588\) 11.6581 3.33010i 0.480770 0.137331i
\(589\) 5.49059 + 9.50998i 0.226236 + 0.391852i
\(590\) 1.32273 2.29104i 0.0544560 0.0943205i
\(591\) 0.197283 13.7617i 0.00811514 0.566081i
\(592\) 1.93040 + 1.11452i 0.0793390 + 0.0458064i
\(593\) 12.0409 + 6.95181i 0.494460 + 0.285477i 0.726423 0.687248i \(-0.241181\pi\)
−0.231963 + 0.972725i \(0.574515\pi\)
\(594\) −28.1539 + 14.6785i −1.15517 + 0.602268i
\(595\) −1.37623 + 11.8610i −0.0564200 + 0.486256i
\(596\) 4.01109 6.94741i 0.164301 0.284577i
\(597\) −32.5907 0.467210i −1.33385 0.0191216i
\(598\) 26.5014 14.5572i 1.08372 0.595287i
\(599\) 5.85303 3.37925i 0.239148 0.138072i −0.375637 0.926767i \(-0.622576\pi\)
0.614785 + 0.788695i \(0.289243\pi\)
\(600\) −6.91903 4.12806i −0.282468 0.168527i
\(601\) −11.3845 6.57283i −0.464382 0.268111i 0.249503 0.968374i \(-0.419733\pi\)
−0.713885 + 0.700263i \(0.753066\pi\)
\(602\) 6.10401 + 14.1180i 0.248781 + 0.575405i
\(603\) 26.4236 + 16.2831i 1.07605 + 0.663097i
\(604\) 8.78536i 0.357471i
\(605\) 13.4618 + 7.77217i 0.547300 + 0.315984i
\(606\) 17.5838 + 10.4909i 0.714291 + 0.426163i
\(607\) 30.5177i 1.23867i −0.785125 0.619337i \(-0.787401\pi\)
0.785125 0.619337i \(-0.212599\pi\)
\(608\) 1.97552 3.42169i 0.0801178 0.138768i
\(609\) 4.47729 5.84765i 0.181429 0.236959i
\(610\) 0.0593724 0.00240392
\(611\) 18.0466 9.91295i 0.730085 0.401035i
\(612\) −22.9307 0.657590i −0.926920 0.0265815i
\(613\) 3.63396i 0.146774i 0.997304 + 0.0733872i \(0.0233809\pi\)
−0.997304 + 0.0733872i \(0.976619\pi\)
\(614\) 5.13689 + 8.89736i 0.207308 + 0.359068i
\(615\) 1.38285 + 0.825040i 0.0557618 + 0.0332688i
\(616\) 9.64312 12.9758i 0.388533 0.522809i
\(617\) −17.7255 30.7015i −0.713603 1.23600i −0.963496 0.267723i \(-0.913729\pi\)
0.249893 0.968273i \(-0.419605\pi\)
\(618\) 3.67219 + 6.57636i 0.147717 + 0.264540i
\(619\) −21.7709 37.7083i −0.875046 1.51562i −0.856713 0.515793i \(-0.827497\pi\)
−0.0183329 0.999832i \(-0.505836\pi\)
\(620\) 1.42060 + 0.820184i 0.0570527 + 0.0329394i
\(621\) −20.1451 38.6390i −0.808394 1.55053i
\(622\) 1.05163 1.82148i 0.0421666 0.0730347i
\(623\) −1.25585 + 10.8235i −0.0503144 + 0.433635i
\(624\) 5.51612 2.92787i 0.220822 0.117208i
\(625\) −9.94811 + 17.2306i −0.397924 + 0.689225i
\(626\) 10.9013i 0.435705i
\(627\) −36.5097 + 20.3867i −1.45806 + 0.814168i
\(628\) 2.88085i 0.114958i
\(629\) 17.0448i 0.679621i
\(630\) −4.35144 + 1.73508i −0.173366 + 0.0691271i
\(631\) −21.1471 + 12.2093i −0.841854 + 0.486045i −0.857894 0.513827i \(-0.828227\pi\)
0.0160399 + 0.999871i \(0.494894\pi\)
\(632\) −3.17751 + 5.50361i −0.126395 + 0.218922i
\(633\) 0.0637380 4.44611i 0.00253336 0.176717i
\(634\) −10.5453 −0.418809
\(635\) 3.05723 1.76509i 0.121322 0.0700455i
\(636\) −3.22193 5.77000i −0.127758 0.228795i
\(637\) 24.4397 + 6.30091i 0.968336 + 0.249651i
\(638\) 9.82032i 0.388790i
\(639\) −5.25379 0.150664i −0.207837 0.00596017i
\(640\) 0.590205i 0.0233299i
\(641\) 16.6886 + 9.63517i 0.659160 + 0.380566i 0.791957 0.610577i \(-0.209062\pi\)
−0.132797 + 0.991143i \(0.542396\pi\)
\(642\) 15.3109 + 0.219491i 0.604271 + 0.00866263i
\(643\) −15.0498 26.0670i −0.593505 1.02798i −0.993756 0.111575i \(-0.964410\pi\)
0.400251 0.916405i \(-0.368923\pi\)
\(644\) 17.8082 + 13.2344i 0.701740 + 0.521508i
\(645\) −2.89738 5.18878i −0.114084 0.204308i
\(646\) −30.2124 −1.18869
\(647\) −28.6708 −1.12716 −0.563582 0.826060i \(-0.690577\pi\)
−0.563582 + 0.826060i \(0.690577\pi\)
\(648\) −4.04594 8.03930i −0.158939 0.315814i
\(649\) 23.7192 + 13.6943i 0.931061 + 0.537548i
\(650\) −8.07473 14.7001i −0.316717 0.576584i
\(651\) −11.7618 + 4.88640i −0.460982 + 0.191513i
\(652\) −4.65862 2.68966i −0.182446 0.105335i
\(653\) 23.9099 13.8044i 0.935666 0.540207i 0.0470671 0.998892i \(-0.485013\pi\)
0.888599 + 0.458685i \(0.151679\pi\)
\(654\) 29.7867 + 0.427013i 1.16475 + 0.0166975i
\(655\) −2.86087 + 1.65172i −0.111783 + 0.0645381i
\(656\) 1.57520i 0.0615011i
\(657\) 32.4515 + 0.930619i 1.26605 + 0.0363069i
\(658\) 12.1268 + 9.01218i 0.472751 + 0.351331i
\(659\) 28.9405 16.7088i 1.12736 0.650884i 0.184093 0.982909i \(-0.441065\pi\)
0.943270 + 0.332025i \(0.107732\pi\)
\(660\) −3.20045 + 5.36427i −0.124577 + 0.208804i
\(661\) 10.4140 0.405058 0.202529 0.979276i \(-0.435084\pi\)
0.202529 + 0.979276i \(0.435084\pi\)
\(662\) 12.6163 7.28403i 0.490347 0.283102i
\(663\) −40.4792 25.3349i −1.57208 0.983925i
\(664\) 9.07449i 0.352159i
\(665\) −5.66303 + 2.44845i −0.219603 + 0.0949470i
\(666\) 5.88467 3.17617i 0.228026 0.123074i
\(667\) 13.4776 0.521854
\(668\) −14.1115 + 8.14728i −0.545990 + 0.315228i
\(669\) −0.0888446 + 6.19745i −0.00343493 + 0.239607i
\(670\) 6.10622 0.235904
\(671\) 0.614686i 0.0237297i
\(672\) 3.63853 + 2.78587i 0.140360 + 0.107467i
\(673\) −0.105584 + 0.182877i −0.00406998 + 0.00704941i −0.868053 0.496471i \(-0.834629\pi\)
0.863983 + 0.503521i \(0.167962\pi\)
\(674\) 15.5415 + 26.9187i 0.598636 + 1.03687i
\(675\) −21.4327 + 11.1743i −0.824944 + 0.430098i
\(676\) 12.9882 + 0.553475i 0.499547 + 0.0212875i
\(677\) −11.7820 + 20.4071i −0.452820 + 0.784307i −0.998560 0.0536474i \(-0.982915\pi\)
0.545740 + 0.837955i \(0.316249\pi\)
\(678\) −27.0758 0.388149i −1.03984 0.0149068i
\(679\) 14.8531 + 1.72339i 0.570008 + 0.0661377i
\(680\) −3.90849 + 2.25657i −0.149884 + 0.0865353i
\(681\) 20.7373 + 0.297282i 0.794654 + 0.0113919i
\(682\) −8.49140 + 14.7075i −0.325153 + 0.563181i
\(683\) −0.694198 + 1.20239i −0.0265627 + 0.0460080i −0.879001 0.476820i \(-0.841790\pi\)
0.852438 + 0.522828i \(0.175123\pi\)
\(684\) −5.62986 10.4308i −0.215263 0.398830i
\(685\) −10.8090 + 6.24059i −0.412991 + 0.238441i
\(686\) 3.26209 + 18.2307i 0.124547 + 0.696052i
\(687\) −0.276832 + 19.3107i −0.0105618 + 0.736749i
\(688\) −2.90674 + 5.03462i −0.110818 + 0.191943i
\(689\) 0.292917 13.7538i 0.0111593 0.523978i
\(690\) −7.36202 4.39236i −0.280267 0.167214i
\(691\) 13.1244 + 22.7321i 0.499276 + 0.864771i 1.00000 0.000835740i \(-0.000266024\pi\)
−0.500724 + 0.865607i \(0.666933\pi\)
\(692\) −7.20003 + 12.4708i −0.273704 + 0.474069i
\(693\) −17.9633 45.0507i −0.682371 1.71133i
\(694\) 24.6678i 0.936378i
\(695\) 6.36744 0.241531
\(696\) 2.78337 + 0.0399014i 0.105503 + 0.00151246i
\(697\) −10.4313 + 6.02254i −0.395115 + 0.228120i
\(698\) −33.1601 −1.25513
\(699\) 27.6682 + 0.396642i 1.04651 + 0.0150024i
\(700\) 7.34099 9.87802i 0.277463 0.373354i
\(701\) 35.5148i 1.34137i 0.741740 + 0.670687i \(0.234001\pi\)
−0.741740 + 0.670687i \(0.765999\pi\)
\(702\) 1.20379 18.6963i 0.0454342 0.705646i
\(703\) 7.62708 4.40350i 0.287661 0.166081i
\(704\) 6.11042 0.230295
\(705\) −5.01329 2.99105i −0.188811 0.112649i
\(706\) −12.5305 + 7.23450i −0.471593 + 0.272274i
\(707\) −18.6561 + 25.1036i −0.701636 + 0.944120i
\(708\) −3.97774 + 6.66709i −0.149493 + 0.250564i
\(709\) 21.6989i 0.814918i −0.913224 0.407459i \(-0.866415\pi\)
0.913224 0.407459i \(-0.133585\pi\)
\(710\) −0.895494 + 0.517014i −0.0336073 + 0.0194032i
\(711\) 9.05533 + 16.7773i 0.339601 + 0.629198i
\(712\) −3.56660 + 2.05918i −0.133664 + 0.0771709i
\(713\) −20.1849 11.6537i −0.755930 0.436436i
\(714\) 4.53730 34.7467i 0.169804 1.30036i
\(715\) −11.3969 + 6.26028i −0.426218 + 0.234121i
\(716\) −9.93300 5.73482i −0.371214 0.214320i
\(717\) −26.7471 + 14.9354i −0.998890 + 0.557773i
\(718\) −14.0020 −0.522549
\(719\) −29.4841 −1.09957 −0.549785 0.835306i \(-0.685290\pi\)
−0.549785 + 0.835306i \(0.685290\pi\)
\(720\) −1.50739 0.928899i −0.0561771 0.0346180i
\(721\) −10.5608 + 4.56602i −0.393303 + 0.170048i
\(722\) 1.69467 + 2.93526i 0.0630691 + 0.109239i
\(723\) 0.600010 41.8544i 0.0223146 1.55658i
\(724\) 12.7339 + 7.35194i 0.473253 + 0.273233i
\(725\) 7.47588i 0.277647i
\(726\) −39.1748 23.3726i −1.45391 0.867439i
\(727\) 7.96128i 0.295268i −0.989042 0.147634i \(-0.952834\pi\)
0.989042 0.147634i \(-0.0471657\pi\)
\(728\) 3.59844 + 8.83466i 0.133367 + 0.327434i
\(729\) −26.9002 2.31936i −0.996304 0.0859021i
\(730\) 5.53127 3.19348i 0.204722 0.118196i
\(731\) 44.4541 1.64419
\(732\) −0.174220 0.00249756i −0.00643936 9.23125e-5i
\(733\) 23.6265 40.9223i 0.872665 1.51150i 0.0134348 0.999910i \(-0.495723\pi\)
0.859230 0.511590i \(-0.170943\pi\)
\(734\) 12.7593 7.36659i 0.470954 0.271906i
\(735\) −1.96544 6.88064i −0.0724964 0.253796i
\(736\) 8.38604i 0.309114i
\(737\) 63.2180i 2.32867i
\(738\) −4.02307 2.47914i −0.148091 0.0912582i
\(739\) 21.8654i 0.804332i 0.915567 + 0.402166i \(0.131742\pi\)
−0.915567 + 0.402166i \(0.868258\pi\)
\(740\) 0.657794 1.13933i 0.0241810 0.0418827i
\(741\) 0.878922 24.6585i 0.0322880 0.905854i
\(742\) 9.26586 4.00616i 0.340160 0.147071i
\(743\) 5.23639 9.06969i 0.192104 0.332735i −0.753843 0.657055i \(-0.771802\pi\)
0.945947 + 0.324320i \(0.105135\pi\)
\(744\) −4.13405 2.46647i −0.151562 0.0904253i
\(745\) −4.10040 2.36736i −0.150227 0.0867335i
\(746\) −7.91499 13.7092i −0.289788 0.501928i
\(747\) 23.1763 + 14.2820i 0.847978 + 0.522550i
\(748\) −23.3623 40.4647i −0.854211 1.47954i
\(749\) −2.69586 + 23.2342i −0.0985045 + 0.848961i
\(750\) −5.05525 + 8.47309i −0.184592 + 0.309393i
\(751\) −17.3269 30.0111i −0.632268 1.09512i −0.987087 0.160185i \(-0.948791\pi\)
0.354819 0.934935i \(-0.384542\pi\)
\(752\) 5.71062i 0.208245i
\(753\) 4.77111 + 2.84656i 0.173869 + 0.103734i
\(754\) 4.95548 + 3.00351i 0.180468 + 0.109382i
\(755\) 5.18516 0.188707
\(756\) 12.8417 4.90829i 0.467047 0.178513i
\(757\) −12.1846 + 21.1043i −0.442856 + 0.767050i −0.997900 0.0647715i \(-0.979368\pi\)
0.555044 + 0.831821i \(0.312701\pi\)
\(758\) 12.9839i 0.471595i
\(759\) 45.4743 76.2193i 1.65061 2.76659i
\(760\) −2.01950 1.16596i −0.0732550 0.0422938i
\(761\) 6.69934i 0.242851i −0.992601 0.121426i \(-0.961253\pi\)
0.992601 0.121426i \(-0.0387466\pi\)
\(762\) −9.04525 + 5.05081i −0.327675 + 0.182971i
\(763\) −5.24469 + 45.2014i −0.189871 + 1.63640i
\(764\) 9.40428 + 5.42957i 0.340235 + 0.196435i
\(765\) −0.388113 + 13.5338i −0.0140322 + 0.489317i
\(766\) 3.62494 2.09286i 0.130975 0.0756182i
\(767\) −14.1648 + 7.78071i −0.511461 + 0.280945i
\(768\) −0.0248275 + 1.73187i −0.000895887 + 0.0624936i
\(769\) 3.97005 6.87633i 0.143164 0.247967i −0.785523 0.618833i \(-0.787606\pi\)
0.928686 + 0.370866i \(0.120939\pi\)
\(770\) −7.65836 5.69142i −0.275988 0.205104i
\(771\) −1.76012 1.05013i −0.0633890 0.0378194i
\(772\) −16.6658 9.62200i −0.599815 0.346304i
\(773\) −12.9640 7.48477i −0.466283 0.269208i 0.248400 0.968658i \(-0.420095\pi\)
−0.714682 + 0.699449i \(0.753429\pi\)
\(774\) 8.28368 + 15.3476i 0.297751 + 0.551659i
\(775\) −6.46422 + 11.1964i −0.232202 + 0.402185i
\(776\) 2.82580 + 4.89442i 0.101440 + 0.175700i
\(777\) 3.91893 + 9.43306i 0.140591 + 0.338409i
\(778\) 19.0201 + 10.9812i 0.681903 + 0.393697i
\(779\) −5.38984 3.11182i −0.193111 0.111493i
\(780\) −1.72804 3.25564i −0.0618738 0.116571i
\(781\) −5.35267 9.27110i −0.191534 0.331746i
\(782\) 55.5345 32.0629i 1.98591 1.14657i
\(783\) 4.48254 7.04595i 0.160193 0.251802i
\(784\) −4.79511 + 5.09970i −0.171254 + 0.182132i
\(785\) 1.70029 0.0606859
\(786\) 8.46429 4.72640i 0.301911 0.168585i
\(787\) −8.80556 + 15.2517i −0.313884 + 0.543664i −0.979200 0.202899i \(-0.934964\pi\)
0.665315 + 0.746562i \(0.268297\pi\)
\(788\) 3.97307 + 6.88156i 0.141535 + 0.245145i
\(789\) 1.13334 + 2.02964i 0.0403478 + 0.0722571i
\(790\) 3.24826 + 1.87538i 0.115568 + 0.0667231i
\(791\) 4.76736 41.0875i 0.169508 1.46090i
\(792\) 9.61693 15.6061i 0.341723 0.554538i
\(793\) −0.310179 0.188000i −0.0110148 0.00667606i
\(794\) 16.5607 + 28.6839i 0.587716 + 1.01795i
\(795\) −3.40548 + 1.90160i −0.120780 + 0.0674427i
\(796\) 16.2970 9.40910i 0.577633 0.333497i
\(797\) −0.00976904 0.0169205i −0.000346037 0.000599354i 0.865852 0.500300i \(-0.166777\pi\)
−0.866198 + 0.499700i \(0.833443\pi\)
\(798\) 16.7204 6.94642i 0.591895 0.245901i
\(799\) 37.8172 21.8337i 1.33787 0.772422i
\(800\) 4.65166 0.164461
\(801\) −0.354163 + 12.3500i −0.0125137 + 0.436365i
\(802\) −3.47187 + 6.01346i −0.122596 + 0.212343i
\(803\) 33.0623 + 57.2656i 1.16674 + 2.02086i
\(804\) −17.9179 0.256864i −0.631914 0.00905891i
\(805\) 7.81100 10.5105i 0.275301 0.370445i
\(806\) −4.82457 8.78314i −0.169938 0.309373i
\(807\) 0.160533 11.1981i 0.00565102 0.394193i
\(808\) −11.8216 −0.415881
\(809\) 6.51658i 0.229111i 0.993417 + 0.114555i \(0.0365443\pi\)
−0.993417 + 0.114555i \(0.963456\pi\)
\(810\) −4.74483 + 2.38793i −0.166716 + 0.0839034i
\(811\) −7.01415 −0.246300 −0.123150 0.992388i \(-0.539300\pi\)
−0.123150 + 0.992388i \(0.539300\pi\)
\(812\) −0.490081 + 4.22377i −0.0171985 + 0.148225i
\(813\) −28.6121 17.0707i −1.00347 0.598694i
\(814\) 11.7956 + 6.81017i 0.413434 + 0.238696i
\(815\) −1.58745 + 2.74954i −0.0556059 + 0.0963122i
\(816\) 11.5638 6.45716i 0.404815 0.226046i
\(817\) 11.4846 + 19.8920i 0.401796 + 0.695932i
\(818\) 0.303545 0.0106132
\(819\) 28.2273 + 4.71405i 0.986340 + 0.164722i
\(820\) −0.929688 −0.0324661
\(821\) 6.32403 + 10.9535i 0.220710 + 0.382281i 0.955024 0.296529i \(-0.0958292\pi\)
−0.734314 + 0.678810i \(0.762496\pi\)
\(822\) 31.9800 17.8574i 1.11543 0.622850i
\(823\) 21.7868 37.7359i 0.759441 1.31539i −0.183694 0.982983i \(-0.558806\pi\)
0.943136 0.332408i \(-0.107861\pi\)
\(824\) −3.76608 2.17435i −0.131198 0.0757471i
\(825\) −42.2781 25.2242i −1.47194 0.878192i
\(826\) −9.51834 7.07369i −0.331185 0.246125i
\(827\) 25.1546 0.874712 0.437356 0.899288i \(-0.355915\pi\)
0.437356 + 0.899288i \(0.355915\pi\)
\(828\) 21.4180 + 13.1984i 0.744328 + 0.458677i
\(829\) 48.6579i 1.68996i −0.534799 0.844979i \(-0.679613\pi\)
0.534799 0.844979i \(-0.320387\pi\)
\(830\) 5.35581 0.185903
\(831\) 0.292028 20.3707i 0.0101303 0.706652i
\(832\) −1.86885 + 3.08341i −0.0647908 + 0.106898i
\(833\) 52.1049 + 12.2564i 1.80533 + 0.424660i
\(834\) −18.6844 0.267853i −0.646986 0.00927498i
\(835\) 4.80856 + 8.32867i 0.166407 + 0.288226i
\(836\) 12.0712 20.9080i 0.417492 0.723118i
\(837\) −12.8058 + 6.67653i −0.442634 + 0.230775i
\(838\) −5.71451 −0.197404
\(839\) −18.3244 + 10.5796i −0.632630 + 0.365249i −0.781770 0.623567i \(-0.785683\pi\)
0.149140 + 0.988816i \(0.452350\pi\)
\(840\) 1.64423 2.14748i 0.0567314 0.0740951i
\(841\) −13.2085 22.8779i −0.455467 0.788892i
\(842\) 8.01539 4.62769i 0.276229 0.159481i
\(843\) 33.2622 18.5734i 1.14561 0.639701i
\(844\) 1.28361 + 2.22329i 0.0441838 + 0.0765286i
\(845\) 0.326664 7.66570i 0.0112376 0.263708i
\(846\) 14.5850 + 8.98770i 0.501442 + 0.309004i
\(847\) 41.5639 55.9283i 1.42815 1.92172i
\(848\) 3.30431 + 1.90774i 0.113470 + 0.0655121i
\(849\) 10.8497 + 19.4302i 0.372360 + 0.666843i
\(850\) −17.7850 30.8045i −0.610019 1.05658i
\(851\) −9.34639 + 16.1884i −0.320390 + 0.554932i
\(852\) 2.64945 1.47944i 0.0907687 0.0506846i
\(853\) −53.6426 −1.83669 −0.918344 0.395782i \(-0.870473\pi\)
−0.918344 + 0.395782i \(0.870473\pi\)
\(854\) 0.0306758 0.264379i 0.00104970 0.00904687i
\(855\) −6.15628 + 3.32277i −0.210540 + 0.113636i
\(856\) −7.65622 + 4.42032i −0.261684 + 0.151083i
\(857\) 12.3135 + 21.3277i 0.420623 + 0.728540i 0.996000 0.0893479i \(-0.0284783\pi\)
−0.575378 + 0.817888i \(0.695145\pi\)
\(858\) 33.7058 17.8905i 1.15070 0.610771i
\(859\) 1.35293 + 0.781117i 0.0461615 + 0.0266514i 0.522903 0.852392i \(-0.324849\pi\)
−0.476742 + 0.879043i \(0.658182\pi\)
\(860\) 2.97146 + 1.71557i 0.101326 + 0.0585005i
\(861\) 4.38829 5.73140i 0.149552 0.195326i
\(862\) 5.05283 + 8.75176i 0.172100 + 0.298086i
\(863\) 13.1821 22.8320i 0.448723 0.777210i −0.549581 0.835441i \(-0.685212\pi\)
0.998303 + 0.0582303i \(0.0185458\pi\)
\(864\) 4.38415 + 2.78913i 0.149152 + 0.0948882i
\(865\) 7.36033 + 4.24949i 0.250259 + 0.144487i
\(866\) 32.8655 + 18.9749i 1.11682 + 0.644794i
\(867\) −61.6873 36.8041i −2.09501 1.24993i
\(868\) 4.38617 5.90202i 0.148876 0.200328i
\(869\) −19.4159 + 33.6294i −0.658640 + 1.14080i
\(870\) 0.0235500 1.64276i 0.000798420 0.0556947i
\(871\) −31.9007 19.3350i −1.08092 0.655143i
\(872\) −14.8949 + 8.59957i −0.504405 + 0.291218i
\(873\) 16.9478 + 0.486016i 0.573597 + 0.0164492i
\(874\) 28.6945 + 16.5668i 0.970605 + 0.560379i
\(875\) −12.0967 8.98983i −0.408943 0.303912i
\(876\) −16.3651 + 9.13815i −0.552925 + 0.308749i
\(877\) 23.3161i 0.787328i 0.919254 + 0.393664i \(0.128793\pi\)
−0.919254 + 0.393664i \(0.871207\pi\)
\(878\) −24.6369 14.2241i −0.831456 0.480042i
\(879\) 0.353355 0.592257i 0.0119184 0.0199763i
\(880\) 3.60640i 0.121572i
\(881\) 7.67467 13.2929i 0.258566 0.447850i −0.707292 0.706922i \(-0.750083\pi\)
0.965858 + 0.259072i \(0.0834167\pi\)
\(882\) 5.47787 + 20.2730i 0.184449 + 0.682626i
\(883\) 34.2457 1.15246 0.576230 0.817287i \(-0.304523\pi\)
0.576230 + 0.817287i \(0.304523\pi\)
\(884\) 27.5644 + 0.587044i 0.927091 + 0.0197444i
\(885\) 3.93495 + 2.34768i 0.132272 + 0.0789165i
\(886\) 21.6680i 0.727952i
\(887\) −21.8340 37.8177i −0.733116 1.26979i −0.955545 0.294845i \(-0.904732\pi\)
0.222430 0.974949i \(-0.428601\pi\)
\(888\) −1.97813 + 3.31554i −0.0663817 + 0.111262i
\(889\) −6.28019 14.5255i −0.210631 0.487169i
\(890\) 1.21534 + 2.10502i 0.0407381 + 0.0705605i
\(891\) −24.7224 49.1235i −0.828231 1.64570i
\(892\) −1.78923 3.09905i −0.0599080 0.103764i
\(893\) 19.5400 + 11.2814i 0.653881 + 0.377518i
\(894\) 11.9324 + 7.11919i 0.399081 + 0.238101i
\(895\) −3.38472 + 5.86250i −0.113139 + 0.195962i
\(896\) −2.62812 0.304939i −0.0877993 0.0101873i
\(897\) 24.5532 + 46.2584i 0.819808 + 1.54452i
\(898\) 6.23704 10.8029i 0.208133 0.360496i
\(899\) 4.46677i 0.148975i
\(900\) 7.32105 11.8804i 0.244035 0.396013i
\(901\) 29.1759i 0.971992i
\(902\) 9.62510i 0.320481i
\(903\) −24.6021 + 10.2209i −0.818706 + 0.340129i
\(904\) 13.5393 7.81690i 0.450310 0.259986i
\(905\) 4.33915 7.51563i 0.144238 0.249828i
\(906\) −15.2151 0.218119i −0.505489 0.00724651i
\(907\) 23.3018 0.773723 0.386861 0.922138i \(-0.373559\pi\)
0.386861 + 0.922138i \(0.373559\pi\)
\(908\) −10.3697 + 5.98695i −0.344131 + 0.198684i
\(909\) −18.6055 + 30.1924i −0.617104 + 1.00142i
\(910\) 5.21426 2.12382i 0.172851 0.0704039i
\(911\) 48.4817i 1.60627i −0.595796 0.803136i \(-0.703163\pi\)
0.595796 0.803136i \(-0.296837\pi\)
\(912\) 5.87689 + 3.50630i 0.194603 + 0.116105i
\(913\) 55.4489i 1.83509i
\(914\) −8.30703 4.79607i −0.274772 0.158640i
\(915\) −0.00147407 + 0.102825i −4.87313e−5 + 0.00339931i
\(916\) −5.57509 9.65634i −0.184206 0.319054i
\(917\) 5.87683 + 13.5925i 0.194070 + 0.448865i
\(918\) 1.70818 39.6968i 0.0563782 1.31019i
\(919\) 2.50142 0.0825141 0.0412570 0.999149i \(-0.486864\pi\)
0.0412570 + 0.999149i \(0.486864\pi\)
\(920\) 4.94948 0.163180
\(921\) −15.5366 + 8.67554i −0.511949 + 0.285869i
\(922\) 4.17780 + 2.41206i 0.137589 + 0.0794368i
\(923\) 6.31543 + 0.134501i 0.207875 + 0.00442715i
\(924\) 22.2330 + 17.0228i 0.731411 + 0.560010i
\(925\) 8.97957 + 5.18436i 0.295246 + 0.170461i
\(926\) 2.67382 1.54373i 0.0878673 0.0507302i
\(927\) −11.4806 + 6.19650i −0.377072 + 0.203520i
\(928\) −1.39183 + 0.803572i −0.0456890 + 0.0263785i
\(929\) 29.5977i 0.971069i −0.874217 0.485535i \(-0.838625\pi\)
0.874217 0.485535i \(-0.161375\pi\)
\(930\) −1.45572 + 2.43994i −0.0477351 + 0.0800086i
\(931\) 7.97681 + 26.4819i 0.261429 + 0.867910i
\(932\) −13.8355 + 7.98795i −0.453198 + 0.261654i
\(933\) 3.12846 + 1.86651i 0.102421 + 0.0611070i
\(934\) −8.32473 −0.272394
\(935\) −23.8825 + 13.7886i −0.781041 + 0.450934i
\(936\) 4.93374 + 9.62591i 0.161264 + 0.314633i
\(937\) 27.0251i 0.882873i −0.897293 0.441436i \(-0.854469\pi\)
0.897293 0.441436i \(-0.145531\pi\)
\(938\) 3.15488 27.1904i 0.103011 0.887797i
\(939\) −18.8797 0.270654i −0.616117 0.00883244i
\(940\) 3.37043 0.109931
\(941\) −32.5113 + 18.7704i −1.05984 + 0.611898i −0.925387 0.379022i \(-0.876260\pi\)
−0.134451 + 0.990920i \(0.542927\pi\)
\(942\) −4.98926 0.0715243i −0.162559 0.00233039i
\(943\) 13.2097 0.430165
\(944\) 4.48228i 0.145886i
\(945\) −2.89690 7.57922i −0.0942361 0.246552i
\(946\) −17.7614 + 30.7636i −0.577473 + 1.00021i
\(947\) −15.7164 27.2216i −0.510714 0.884583i −0.999923 0.0124164i \(-0.996048\pi\)
0.489209 0.872167i \(-0.337286\pi\)
\(948\) −9.45267 5.63969i −0.307008 0.183169i
\(949\) −39.0090 0.830782i −1.26629 0.0269683i
\(950\) 9.18943 15.9166i 0.298144 0.516401i
\(951\) 0.261815 18.2632i 0.00848993 0.592224i
\(952\) 8.02886 + 18.5700i 0.260217 + 0.601856i
\(953\) −47.5409 + 27.4478i −1.54000 + 0.889120i −0.541163 + 0.840918i \(0.682016\pi\)
−0.998838 + 0.0482023i \(0.984651\pi\)
\(954\) 10.0729 5.43672i 0.326122 0.176020i
\(955\) 3.20456 5.55045i 0.103697 0.179608i
\(956\) 8.84344 15.3173i 0.286017 0.495396i
\(957\) 17.0075 + 0.243814i 0.549776 + 0.00788140i
\(958\) −10.4595 + 6.03880i −0.337931 + 0.195105i
\(959\) 22.2040 + 51.3557i 0.717005 + 1.65836i
\(960\) 1.02216 + 0.0146533i 0.0329901 + 0.000472934i
\(961\) 11.6377 20.1571i 0.375409 0.650228i
\(962\) −7.04415 + 3.86934i −0.227112 + 0.124753i
\(963\) −0.760262 + 26.5110i −0.0244991 + 0.854305i
\(964\) 12.0836 + 20.9293i 0.389185 + 0.674088i
\(965\) −5.67895 + 9.83623i −0.182812 + 0.316640i
\(966\) −23.3624 + 30.5129i −0.751673 + 0.981736i
\(967\) 11.5256i 0.370639i 0.982678 + 0.185320i \(0.0593321\pi\)
−0.982678 + 0.185320i \(0.940668\pi\)
\(968\) 26.3372 0.846510
\(969\) 0.750101 52.3241i 0.0240967 1.68089i
\(970\) 2.88871 1.66780i 0.0927509 0.0535498i
\(971\) 49.9796 1.60392 0.801962 0.597376i \(-0.203790\pi\)
0.801962 + 0.597376i \(0.203790\pi\)
\(972\) 14.0235 6.80745i 0.449804 0.218349i
\(973\) 3.28985 28.3535i 0.105468 0.908973i
\(974\) 5.59837i 0.179383i
\(975\) 25.6591 13.6194i 0.821749 0.436171i
\(976\) 0.0871190 0.0502982i 0.00278861 0.00161000i
\(977\) −4.37679 −0.140026 −0.0700129 0.997546i \(-0.522304\pi\)
−0.0700129 + 0.997546i \(0.522304\pi\)
\(978\) 4.77381 8.00136i 0.152649 0.255855i
\(979\) −21.7934 + 12.5824i −0.696520 + 0.402136i
\(980\) 3.00987 + 2.83009i 0.0961467 + 0.0904041i
\(981\) −1.47906 + 51.5762i −0.0472228 + 1.64670i
\(982\) 0.521341i 0.0166367i
\(983\) −22.4448 + 12.9585i −0.715879 + 0.413313i −0.813234 0.581937i \(-0.802295\pi\)
0.0973553 + 0.995250i \(0.468962\pi\)
\(984\) 2.72804 + 0.0391082i 0.0869667 + 0.00124673i
\(985\) 4.06153 2.34492i 0.129411 0.0747155i
\(986\) 10.6429 + 6.14469i 0.338940 + 0.195687i
\(987\) −15.9090 + 20.7783i −0.506390 + 0.661380i
\(988\) 6.85852 + 12.4860i 0.218199 + 0.397231i
\(989\) −42.2205 24.3760i −1.34254 0.775113i
\(990\) −9.21078 5.67596i −0.292738 0.180394i
\(991\) 23.1574 0.735620 0.367810 0.929901i \(-0.380108\pi\)
0.367810 + 0.929901i \(0.380108\pi\)
\(992\) 2.77932 0.0882435
\(993\) 12.3018 + 22.0307i 0.390385 + 0.699123i
\(994\) 1.83954 + 4.25467i 0.0583466 + 0.134950i
\(995\) −5.55329 9.61859i −0.176051 0.304930i
\(996\) −15.7159 0.225297i −0.497976 0.00713882i
\(997\) 8.34585 + 4.81848i 0.264316 + 0.152603i 0.626302 0.779581i \(-0.284568\pi\)
−0.361986 + 0.932184i \(0.617901\pi\)
\(998\) 33.4405i 1.05854i
\(999\) 5.35462 + 10.2704i 0.169413 + 0.324940i
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 546.2.bn.e.173.13 yes 34
3.2 odd 2 546.2.bn.f.173.5 yes 34
7.3 odd 6 546.2.bi.f.17.14 yes 34
13.10 even 6 546.2.bi.e.257.9 yes 34
21.17 even 6 546.2.bi.e.17.9 34
39.23 odd 6 546.2.bi.f.257.14 yes 34
91.10 odd 6 546.2.bn.f.101.5 yes 34
273.101 even 6 inner 546.2.bn.e.101.13 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bi.e.17.9 34 21.17 even 6
546.2.bi.e.257.9 yes 34 13.10 even 6
546.2.bi.f.17.14 yes 34 7.3 odd 6
546.2.bi.f.257.14 yes 34 39.23 odd 6
546.2.bn.e.101.13 yes 34 273.101 even 6 inner
546.2.bn.e.173.13 yes 34 1.1 even 1 trivial
546.2.bn.f.101.5 yes 34 91.10 odd 6
546.2.bn.f.173.5 yes 34 3.2 odd 2