Properties

Label 150.3.i.a.29.18
Level $150$
Weight $3$
Character 150.29
Analytic conductor $4.087$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [150,3,Mod(29,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.i (of order \(10\), degree \(4\), 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: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 29.18
Character \(\chi\) \(=\) 150.29
Dual form 150.3.i.a.119.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.437016 - 1.34500i) q^{2} +(1.66776 + 2.49371i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(1.13734 - 4.86893i) q^{5} +(4.08287 - 1.15333i) q^{6} -10.7444i q^{7} +(-2.28825 + 1.66251i) q^{8} +(-3.43719 + 8.31780i) q^{9} +O(q^{10})\) \(q+(0.437016 - 1.34500i) q^{2} +(1.66776 + 2.49371i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(1.13734 - 4.86893i) q^{5} +(4.08287 - 1.15333i) q^{6} -10.7444i q^{7} +(-2.28825 + 1.66251i) q^{8} +(-3.43719 + 8.31780i) q^{9} +(-6.05166 - 3.65752i) q^{10} +(5.39938 + 1.75436i) q^{11} +(0.233048 - 5.99547i) q^{12} +(17.4086 - 5.65639i) q^{13} +(-14.4512 - 4.69547i) q^{14} +(14.0385 - 5.28399i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-7.89674 + 5.73731i) q^{17} +(9.68531 + 8.25802i) q^{18} +(17.8734 - 12.9858i) q^{19} +(-7.56402 + 6.54107i) q^{20} +(26.7934 - 17.9190i) q^{21} +(4.71923 - 6.49546i) q^{22} +(-8.92126 + 27.4568i) q^{23} +(-7.96205 - 2.93357i) q^{24} +(-22.4129 - 11.0752i) q^{25} -25.8864i q^{26} +(-26.4746 + 5.30070i) q^{27} +(-12.6308 + 17.3848i) q^{28} +(-7.14969 + 9.84070i) q^{29} +(-0.971900 - 21.1909i) q^{30} +(-45.6777 + 33.1868i) q^{31} +5.65685 q^{32} +(4.62996 + 16.3903i) q^{33} +(4.26567 + 13.1284i) q^{34} +(-52.3137 - 12.2200i) q^{35} +(15.3396 - 9.41782i) q^{36} +(30.5541 - 9.92763i) q^{37} +(-9.65489 - 29.7147i) q^{38} +(43.1386 + 33.9785i) q^{39} +(5.49212 + 13.0321i) q^{40} +(15.7057 - 5.10308i) q^{41} +(-12.3919 - 43.8679i) q^{42} -4.27620i q^{43} +(-6.67400 - 9.18597i) q^{44} +(36.5895 + 26.1956i) q^{45} +(33.0306 + 23.9981i) q^{46} +(38.0423 + 27.6393i) q^{47} +(-7.42518 + 9.42691i) q^{48} -66.4420 q^{49} +(-24.6910 + 25.3053i) q^{50} +(-27.4770 - 10.1237i) q^{51} +(-34.8172 - 11.3128i) q^{52} +(46.4184 + 33.7249i) q^{53} +(-4.44038 + 37.9247i) q^{54} +(14.6828 - 24.2939i) q^{55} +(17.8626 + 24.5858i) q^{56} +(62.1913 + 22.9140i) q^{57} +(10.1112 + 13.9169i) q^{58} +(-108.045 + 35.1060i) q^{59} +(-28.9265 - 7.95357i) q^{60} +(13.2413 - 40.7526i) q^{61} +(24.6743 + 75.9396i) q^{62} +(89.3697 + 36.9305i) q^{63} +(2.47214 - 7.60845i) q^{64} +(-7.74113 - 91.1943i) q^{65} +(24.0683 + 0.935553i) q^{66} +(52.4788 + 72.2309i) q^{67} +19.5218 q^{68} +(-83.3478 + 23.5442i) q^{69} +(-39.2978 + 65.0214i) q^{70} +(-15.3975 + 21.1928i) q^{71} +(-5.96328 - 24.7475i) q^{72} +(-30.3947 - 9.87585i) q^{73} -45.4337i q^{74} +(-9.76085 - 74.3621i) q^{75} -44.1855 q^{76} +(18.8496 - 58.0130i) q^{77} +(64.5532 - 43.1722i) q^{78} +(81.0358 + 58.8759i) q^{79} +(19.9283 - 1.69164i) q^{80} +(-57.3715 - 57.1796i) q^{81} -23.3542i q^{82} +(-25.3592 + 18.4245i) q^{83} +(-64.4177 - 2.50396i) q^{84} +(18.9533 + 44.9739i) q^{85} +(-5.75148 - 1.86877i) q^{86} +(-36.4638 - 1.41737i) q^{87} +(-15.2717 + 4.96209i) q^{88} +(-29.3681 - 9.54229i) q^{89} +(51.2232 - 37.7649i) q^{90} +(-60.7745 - 187.045i) q^{91} +(46.7123 - 33.9385i) q^{92} +(-158.938 - 58.5596i) q^{93} +(53.7999 - 39.0879i) q^{94} +(-42.8988 - 101.794i) q^{95} +(9.43425 + 14.1066i) q^{96} +(30.6184 - 42.1426i) q^{97} +(-29.0362 + 89.3643i) q^{98} +(-33.1511 + 38.8808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 40 q^{4} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 40 q^{4} + 20 q^{9} + 16 q^{10} + 20 q^{12} + 32 q^{15} - 80 q^{16} + 60 q^{19} - 60 q^{21} + 40 q^{22} + 116 q^{25} - 210 q^{27} - 40 q^{28} - 68 q^{30} + 180 q^{31} - 50 q^{33} - 120 q^{34} + 40 q^{36} - 40 q^{37} + 220 q^{39} + 32 q^{40} + 468 q^{45} + 120 q^{46} - 40 q^{48} - 680 q^{49} + 20 q^{51} - 120 q^{54} - 272 q^{55} - 156 q^{60} - 200 q^{61} - 830 q^{63} - 160 q^{64} + 160 q^{66} + 500 q^{67} - 280 q^{69} - 584 q^{70} + 120 q^{73} - 138 q^{75} - 80 q^{76} + 620 q^{78} + 400 q^{79} - 420 q^{81} + 180 q^{84} + 1632 q^{85} + 750 q^{87} + 160 q^{88} + 472 q^{90} - 340 q^{91} + 160 q^{94} + 20 q^{97} - 260 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.437016 1.34500i 0.218508 0.672499i
\(3\) 1.66776 + 2.49371i 0.555918 + 0.831237i
\(4\) −1.61803 1.17557i −0.404508 0.293893i
\(5\) 1.13734 4.86893i 0.227468 0.973786i
\(6\) 4.08287 1.15333i 0.680478 0.192222i
\(7\) 10.7444i 1.53491i −0.641101 0.767457i \(-0.721522\pi\)
0.641101 0.767457i \(-0.278478\pi\)
\(8\) −2.28825 + 1.66251i −0.286031 + 0.207813i
\(9\) −3.43719 + 8.31780i −0.381910 + 0.924200i
\(10\) −6.05166 3.65752i −0.605166 0.365752i
\(11\) 5.39938 + 1.75436i 0.490852 + 0.159488i 0.543977 0.839100i \(-0.316918\pi\)
−0.0531243 + 0.998588i \(0.516918\pi\)
\(12\) 0.233048 5.99547i 0.0194207 0.499623i
\(13\) 17.4086 5.65639i 1.33912 0.435107i 0.450102 0.892977i \(-0.351388\pi\)
0.889019 + 0.457870i \(0.151388\pi\)
\(14\) −14.4512 4.69547i −1.03223 0.335391i
\(15\) 14.0385 5.28399i 0.935900 0.352266i
\(16\) 1.23607 + 3.80423i 0.0772542 + 0.237764i
\(17\) −7.89674 + 5.73731i −0.464514 + 0.337489i −0.795299 0.606217i \(-0.792686\pi\)
0.330785 + 0.943706i \(0.392686\pi\)
\(18\) 9.68531 + 8.25802i 0.538073 + 0.458779i
\(19\) 17.8734 12.9858i 0.940706 0.683463i −0.00788420 0.999969i \(-0.502510\pi\)
0.948591 + 0.316506i \(0.102510\pi\)
\(20\) −7.56402 + 6.54107i −0.378201 + 0.327054i
\(21\) 26.7934 17.9190i 1.27588 0.853286i
\(22\) 4.71923 6.49546i 0.214510 0.295248i
\(23\) −8.92126 + 27.4568i −0.387881 + 1.19377i 0.546488 + 0.837467i \(0.315964\pi\)
−0.934369 + 0.356307i \(0.884036\pi\)
\(24\) −7.96205 2.93357i −0.331752 0.122232i
\(25\) −22.4129 11.0752i −0.896517 0.443009i
\(26\) 25.8864i 0.995632i
\(27\) −26.4746 + 5.30070i −0.980539 + 0.196322i
\(28\) −12.6308 + 17.3848i −0.451100 + 0.620885i
\(29\) −7.14969 + 9.84070i −0.246541 + 0.339334i −0.914296 0.405046i \(-0.867255\pi\)
0.667755 + 0.744381i \(0.267255\pi\)
\(30\) −0.971900 21.1909i −0.0323967 0.706364i
\(31\) −45.6777 + 33.1868i −1.47348 + 1.07054i −0.493888 + 0.869526i \(0.664425\pi\)
−0.979588 + 0.201017i \(0.935575\pi\)
\(32\) 5.65685 0.176777
\(33\) 4.62996 + 16.3903i 0.140302 + 0.496677i
\(34\) 4.26567 + 13.1284i 0.125461 + 0.386129i
\(35\) −52.3137 12.2200i −1.49468 0.349143i
\(36\) 15.3396 9.41782i 0.426101 0.261606i
\(37\) 30.5541 9.92763i 0.825786 0.268314i 0.134517 0.990911i \(-0.457052\pi\)
0.691269 + 0.722597i \(0.257052\pi\)
\(38\) −9.65489 29.7147i −0.254076 0.781966i
\(39\) 43.1386 + 33.9785i 1.10612 + 0.871243i
\(40\) 5.49212 + 13.0321i 0.137303 + 0.325803i
\(41\) 15.7057 5.10308i 0.383065 0.124465i −0.111153 0.993803i \(-0.535454\pi\)
0.494218 + 0.869338i \(0.335454\pi\)
\(42\) −12.3919 43.8679i −0.295045 1.04447i
\(43\) 4.27620i 0.0994465i −0.998763 0.0497233i \(-0.984166\pi\)
0.998763 0.0497233i \(-0.0158339\pi\)
\(44\) −6.67400 9.18597i −0.151682 0.208772i
\(45\) 36.5895 + 26.1956i 0.813100 + 0.582123i
\(46\) 33.0306 + 23.9981i 0.718056 + 0.521699i
\(47\) 38.0423 + 27.6393i 0.809410 + 0.588071i 0.913659 0.406481i \(-0.133244\pi\)
−0.104250 + 0.994551i \(0.533244\pi\)
\(48\) −7.42518 + 9.42691i −0.154691 + 0.196394i
\(49\) −66.4420 −1.35596
\(50\) −24.6910 + 25.3053i −0.493819 + 0.506105i
\(51\) −27.4770 10.1237i −0.538765 0.198505i
\(52\) −34.8172 11.3128i −0.669561 0.217553i
\(53\) 46.4184 + 33.7249i 0.875818 + 0.636319i 0.932142 0.362093i \(-0.117938\pi\)
−0.0563236 + 0.998413i \(0.517938\pi\)
\(54\) −4.44038 + 37.9247i −0.0822293 + 0.702309i
\(55\) 14.6828 24.2939i 0.266960 0.441707i
\(56\) 17.8626 + 24.5858i 0.318976 + 0.439032i
\(57\) 62.1913 + 22.9140i 1.09108 + 0.402000i
\(58\) 10.1112 + 13.9169i 0.174331 + 0.239946i
\(59\) −108.045 + 35.1060i −1.83128 + 0.595018i −0.832092 + 0.554638i \(0.812857\pi\)
−0.999184 + 0.0403794i \(0.987143\pi\)
\(60\) −28.9265 7.95357i −0.482108 0.132560i
\(61\) 13.2413 40.7526i 0.217071 0.668076i −0.781929 0.623367i \(-0.785764\pi\)
0.999000 0.0447083i \(-0.0142358\pi\)
\(62\) 24.6743 + 75.9396i 0.397972 + 1.22483i
\(63\) 89.3697 + 36.9305i 1.41857 + 0.586198i
\(64\) 2.47214 7.60845i 0.0386271 0.118882i
\(65\) −7.74113 91.1943i −0.119094 1.40299i
\(66\) 24.0683 + 0.935553i 0.364671 + 0.0141750i
\(67\) 52.4788 + 72.2309i 0.783266 + 1.07807i 0.994914 + 0.100727i \(0.0321169\pi\)
−0.211648 + 0.977346i \(0.567883\pi\)
\(68\) 19.5218 0.287085
\(69\) −83.3478 + 23.5442i −1.20794 + 0.341220i
\(70\) −39.2978 + 65.0214i −0.561397 + 0.928877i
\(71\) −15.3975 + 21.1928i −0.216866 + 0.298490i −0.903565 0.428452i \(-0.859059\pi\)
0.686699 + 0.726942i \(0.259059\pi\)
\(72\) −5.96328 24.7475i −0.0828233 0.343715i
\(73\) −30.3947 9.87585i −0.416366 0.135286i 0.0933396 0.995634i \(-0.470246\pi\)
−0.509706 + 0.860349i \(0.670246\pi\)
\(74\) 45.4337i 0.613969i
\(75\) −9.76085 74.3621i −0.130145 0.991495i
\(76\) −44.1855 −0.581389
\(77\) 18.8496 58.0130i 0.244800 0.753416i
\(78\) 64.5532 43.1722i 0.827606 0.553490i
\(79\) 81.0358 + 58.8759i 1.02577 + 0.745265i 0.967458 0.253033i \(-0.0814282\pi\)
0.0583119 + 0.998298i \(0.481428\pi\)
\(80\) 19.9283 1.69164i 0.249104 0.0211455i
\(81\) −57.3715 57.1796i −0.708290 0.705921i
\(82\) 23.3542i 0.284807i
\(83\) −25.3592 + 18.4245i −0.305533 + 0.221983i −0.729977 0.683471i \(-0.760469\pi\)
0.424445 + 0.905454i \(0.360469\pi\)
\(84\) −64.4177 2.50396i −0.766877 0.0298091i
\(85\) 18.9533 + 44.9739i 0.222980 + 0.529105i
\(86\) −5.75148 1.86877i −0.0668776 0.0217299i
\(87\) −36.4638 1.41737i −0.419124 0.0162917i
\(88\) −15.2717 + 4.96209i −0.173543 + 0.0563874i
\(89\) −29.3681 9.54229i −0.329979 0.107217i 0.139342 0.990244i \(-0.455501\pi\)
−0.469321 + 0.883028i \(0.655501\pi\)
\(90\) 51.2232 37.7649i 0.569146 0.419610i
\(91\) −60.7745 187.045i −0.667851 2.05544i
\(92\) 46.7123 33.9385i 0.507743 0.368897i
\(93\) −158.938 58.5596i −1.70901 0.629673i
\(94\) 53.7999 39.0879i 0.572339 0.415829i
\(95\) −42.8988 101.794i −0.451567 1.07151i
\(96\) 9.43425 + 14.1066i 0.0982734 + 0.146943i
\(97\) 30.6184 42.1426i 0.315654 0.434460i −0.621480 0.783430i \(-0.713468\pi\)
0.937134 + 0.348970i \(0.113468\pi\)
\(98\) −29.0362 + 89.3643i −0.296288 + 0.911880i
\(99\) −33.1511 + 38.8808i −0.334860 + 0.392736i
\(100\) 23.2452 + 44.2681i 0.232452 + 0.442681i
\(101\) 47.2486i 0.467808i −0.972260 0.233904i \(-0.924850\pi\)
0.972260 0.233904i \(-0.0751501\pi\)
\(102\) −25.6243 + 32.5323i −0.251219 + 0.318944i
\(103\) 14.1633 19.4940i 0.137507 0.189263i −0.734710 0.678382i \(-0.762682\pi\)
0.872217 + 0.489119i \(0.162682\pi\)
\(104\) −30.4313 + 41.8851i −0.292609 + 0.402741i
\(105\) −56.7733 150.835i −0.540698 1.43653i
\(106\) 65.6455 47.6942i 0.619297 0.449946i
\(107\) 180.539 1.68728 0.843638 0.536913i \(-0.180409\pi\)
0.843638 + 0.536913i \(0.180409\pi\)
\(108\) 49.0681 + 22.5460i 0.454334 + 0.208759i
\(109\) 9.24039 + 28.4390i 0.0847742 + 0.260908i 0.984454 0.175642i \(-0.0562001\pi\)
−0.899680 + 0.436550i \(0.856200\pi\)
\(110\) −26.2586 30.3651i −0.238714 0.276047i
\(111\) 75.7134 + 59.6362i 0.682102 + 0.537263i
\(112\) 40.8741 13.2808i 0.364947 0.118579i
\(113\) −30.2461 93.0880i −0.267665 0.823788i −0.991067 0.133361i \(-0.957423\pi\)
0.723403 0.690426i \(-0.242577\pi\)
\(114\) 57.9979 73.6334i 0.508753 0.645907i
\(115\) 123.539 + 74.6646i 1.07425 + 0.649258i
\(116\) 23.1369 7.51763i 0.199456 0.0648071i
\(117\) −12.7878 + 164.243i −0.109298 + 1.40379i
\(118\) 160.662i 1.36155i
\(119\) 61.6440 + 84.8456i 0.518016 + 0.712989i
\(120\) −23.3389 + 35.4302i −0.194491 + 0.295251i
\(121\) −71.8156 52.1771i −0.593517 0.431215i
\(122\) −49.0255 35.6191i −0.401848 0.291960i
\(123\) 38.9188 + 30.6547i 0.316413 + 0.249225i
\(124\) 112.922 0.910658
\(125\) −79.4156 + 96.5307i −0.635325 + 0.772245i
\(126\) 88.7274 104.063i 0.704185 0.825895i
\(127\) 42.5592 + 13.8283i 0.335112 + 0.108885i 0.471739 0.881738i \(-0.343626\pi\)
−0.136627 + 0.990623i \(0.543626\pi\)
\(128\) −9.15298 6.65003i −0.0715077 0.0519534i
\(129\) 10.6636 7.13165i 0.0826636 0.0552841i
\(130\) −126.039 29.4416i −0.969532 0.226474i
\(131\) −40.6958 56.0130i −0.310655 0.427580i 0.624930 0.780681i \(-0.285127\pi\)
−0.935585 + 0.353100i \(0.885127\pi\)
\(132\) 11.7766 31.9630i 0.0892163 0.242144i
\(133\) −139.525 192.039i −1.04906 1.44390i
\(134\) 120.084 39.0178i 0.896152 0.291178i
\(135\) −4.30179 + 134.931i −0.0318651 + 0.999492i
\(136\) 8.53134 26.2568i 0.0627305 0.193064i
\(137\) 22.5835 + 69.5049i 0.164843 + 0.507335i 0.999025 0.0441551i \(-0.0140596\pi\)
−0.834182 + 0.551490i \(0.814060\pi\)
\(138\) −4.75746 + 122.392i −0.0344743 + 0.886897i
\(139\) 31.6022 97.2614i 0.227354 0.699723i −0.770691 0.637210i \(-0.780089\pi\)
0.998044 0.0625129i \(-0.0199115\pi\)
\(140\) 70.2798 + 81.2708i 0.501999 + 0.580506i
\(141\) −5.47929 + 140.962i −0.0388602 + 0.999730i
\(142\) 21.7753 + 29.9711i 0.153347 + 0.211064i
\(143\) 103.919 0.726705
\(144\) −35.8914 2.79447i −0.249246 0.0194060i
\(145\) 39.7821 + 46.0035i 0.274359 + 0.317266i
\(146\) −26.5660 + 36.5649i −0.181959 + 0.250445i
\(147\) −110.809 165.687i −0.753802 1.12712i
\(148\) −61.1082 19.8553i −0.412893 0.134157i
\(149\) 243.028i 1.63106i −0.578712 0.815532i \(-0.696445\pi\)
0.578712 0.815532i \(-0.303555\pi\)
\(150\) −104.282 19.3691i −0.695217 0.129128i
\(151\) −206.162 −1.36531 −0.682654 0.730742i \(-0.739174\pi\)
−0.682654 + 0.730742i \(0.739174\pi\)
\(152\) −19.3098 + 59.4294i −0.127038 + 0.390983i
\(153\) −20.5793 85.4037i −0.134505 0.558194i
\(154\) −69.7898 50.7052i −0.453180 0.329255i
\(155\) 109.633 + 260.146i 0.707311 + 1.67836i
\(156\) −29.8557 105.691i −0.191383 0.677506i
\(157\) 53.5181i 0.340880i 0.985368 + 0.170440i \(0.0545189\pi\)
−0.985368 + 0.170440i \(0.945481\pi\)
\(158\) 114.602 83.2632i 0.725329 0.526982i
\(159\) −6.68572 + 171.999i −0.0420486 + 1.08175i
\(160\) 6.43375 27.5428i 0.0402110 0.172143i
\(161\) 295.007 + 95.8535i 1.83234 + 0.595363i
\(162\) −101.979 + 52.1761i −0.629498 + 0.322075i
\(163\) −240.196 + 78.0445i −1.47360 + 0.478801i −0.932193 0.361962i \(-0.882107\pi\)
−0.541404 + 0.840762i \(0.682107\pi\)
\(164\) −31.4113 10.2062i −0.191532 0.0622327i
\(165\) 85.0692 3.90161i 0.515571 0.0236461i
\(166\) 13.6986 + 42.1599i 0.0825216 + 0.253975i
\(167\) 98.6670 71.6858i 0.590820 0.429256i −0.251788 0.967782i \(-0.581019\pi\)
0.842609 + 0.538526i \(0.181019\pi\)
\(168\) −31.5194 + 85.5474i −0.187615 + 0.509210i
\(169\) 134.340 97.6037i 0.794911 0.577537i
\(170\) 68.7727 5.83784i 0.404545 0.0343402i
\(171\) 46.5790 + 193.302i 0.272392 + 1.13042i
\(172\) −5.02697 + 6.91904i −0.0292266 + 0.0402270i
\(173\) −6.05485 + 18.6349i −0.0349991 + 0.107716i −0.967030 0.254663i \(-0.918035\pi\)
0.932031 + 0.362379i \(0.118035\pi\)
\(174\) −17.8416 + 48.4243i −0.102538 + 0.278300i
\(175\) −118.997 + 240.813i −0.679981 + 1.37608i
\(176\) 22.7090i 0.129028i
\(177\) −267.737 210.885i −1.51264 1.19144i
\(178\) −25.6687 + 35.3299i −0.144206 + 0.198483i
\(179\) −21.4825 + 29.5681i −0.120014 + 0.165185i −0.864797 0.502122i \(-0.832553\pi\)
0.744783 + 0.667307i \(0.232553\pi\)
\(180\) −28.4084 85.3989i −0.157824 0.474438i
\(181\) 257.579 187.142i 1.42309 1.03393i 0.431835 0.901953i \(-0.357866\pi\)
0.991252 0.131981i \(-0.0421338\pi\)
\(182\) −278.134 −1.52821
\(183\) 123.709 34.9453i 0.676003 0.190958i
\(184\) −25.2331 77.6596i −0.137137 0.422063i
\(185\) −13.5866 160.057i −0.0734410 0.865172i
\(186\) −148.221 + 188.179i −0.796886 + 1.01172i
\(187\) −52.7028 + 17.1242i −0.281833 + 0.0915731i
\(188\) −29.0617 89.4427i −0.154583 0.475759i
\(189\) 56.9528 + 284.453i 0.301338 + 1.50504i
\(190\) −155.660 + 13.2133i −0.819261 + 0.0695438i
\(191\) −229.392 + 74.5340i −1.20101 + 0.390230i −0.840131 0.542384i \(-0.817522\pi\)
−0.360875 + 0.932614i \(0.617522\pi\)
\(192\) 23.0962 6.52424i 0.120293 0.0339804i
\(193\) 52.0777i 0.269833i 0.990857 + 0.134916i \(0.0430765\pi\)
−0.990857 + 0.134916i \(0.956923\pi\)
\(194\) −43.3010 59.5987i −0.223201 0.307210i
\(195\) 214.502 171.394i 1.10001 0.878943i
\(196\) 107.505 + 78.1072i 0.548497 + 0.398506i
\(197\) −82.7097 60.0921i −0.419846 0.305036i 0.357730 0.933825i \(-0.383551\pi\)
−0.777576 + 0.628789i \(0.783551\pi\)
\(198\) 37.8071 + 61.5797i 0.190945 + 0.311009i
\(199\) −230.058 −1.15607 −0.578036 0.816011i \(-0.696181\pi\)
−0.578036 + 0.816011i \(0.696181\pi\)
\(200\) 69.6989 11.9188i 0.348495 0.0595941i
\(201\) −92.6011 + 251.330i −0.460702 + 1.25040i
\(202\) −63.5492 20.6484i −0.314600 0.102220i
\(203\) 105.732 + 76.8190i 0.520849 + 0.378419i
\(204\) 32.5576 + 48.6817i 0.159596 + 0.238636i
\(205\) −6.98388 82.2736i −0.0340677 0.401335i
\(206\) −20.0299 27.5687i −0.0972324 0.133829i
\(207\) −197.716 168.579i −0.955151 0.814393i
\(208\) 43.0364 + 59.2345i 0.206906 + 0.284781i
\(209\) 119.287 38.7587i 0.570752 0.185449i
\(210\) −227.684 + 10.4425i −1.08421 + 0.0497261i
\(211\) −112.652 + 346.708i −0.533897 + 1.64317i 0.212123 + 0.977243i \(0.431962\pi\)
−0.746020 + 0.665923i \(0.768038\pi\)
\(212\) −35.4605 109.136i −0.167266 0.514793i
\(213\) −78.5279 3.05244i −0.368676 0.0143307i
\(214\) 78.8982 242.824i 0.368683 1.13469i
\(215\) −20.8205 4.86348i −0.0968396 0.0226209i
\(216\) 51.7678 56.1435i 0.239666 0.259923i
\(217\) 356.572 + 490.780i 1.64319 + 2.26166i
\(218\) 42.2886 0.193984
\(219\) −26.0635 92.2662i −0.119011 0.421307i
\(220\) −52.3164 + 22.0477i −0.237802 + 0.100217i
\(221\) −105.018 + 144.546i −0.475197 + 0.654052i
\(222\) 113.298 75.7723i 0.510354 0.341317i
\(223\) 199.645 + 64.8685i 0.895268 + 0.290890i 0.720283 0.693681i \(-0.244012\pi\)
0.174986 + 0.984571i \(0.444012\pi\)
\(224\) 60.7795i 0.271337i
\(225\) 169.159 148.359i 0.751817 0.659371i
\(226\) −138.421 −0.612483
\(227\) −34.4887 + 106.145i −0.151933 + 0.467600i −0.997837 0.0657339i \(-0.979061\pi\)
0.845905 + 0.533334i \(0.179061\pi\)
\(228\) −73.6906 110.186i −0.323205 0.483272i
\(229\) 11.0271 + 8.01164i 0.0481532 + 0.0349853i 0.611601 0.791166i \(-0.290526\pi\)
−0.563448 + 0.826151i \(0.690526\pi\)
\(230\) 154.412 133.530i 0.671357 0.580564i
\(231\) 176.104 49.7461i 0.762356 0.215351i
\(232\) 34.4044i 0.148295i
\(233\) −2.07945 + 1.51081i −0.00892468 + 0.00648416i −0.592239 0.805763i \(-0.701756\pi\)
0.583314 + 0.812247i \(0.301756\pi\)
\(234\) 215.318 + 88.9764i 0.920162 + 0.380241i
\(235\) 177.841 153.790i 0.756769 0.654425i
\(236\) 216.091 + 70.2121i 0.915638 + 0.297509i
\(237\) −11.6717 + 300.270i −0.0492478 + 1.26696i
\(238\) 141.057 45.8320i 0.592674 0.192572i
\(239\) 147.333 + 47.8714i 0.616456 + 0.200299i 0.600566 0.799575i \(-0.294942\pi\)
0.0158898 + 0.999874i \(0.494942\pi\)
\(240\) 37.4540 + 46.8743i 0.156058 + 0.195309i
\(241\) −57.8325 177.990i −0.239969 0.738548i −0.996423 0.0845018i \(-0.973070\pi\)
0.756454 0.654046i \(-0.226930\pi\)
\(242\) −101.563 + 73.7895i −0.419680 + 0.304915i
\(243\) 46.9078 238.430i 0.193036 0.981192i
\(244\) −69.3325 + 50.3730i −0.284150 + 0.206447i
\(245\) −75.5670 + 323.501i −0.308437 + 1.32041i
\(246\) 58.2386 38.9491i 0.236742 0.158330i
\(247\) 237.698 327.163i 0.962341 1.32455i
\(248\) 49.3485 151.879i 0.198986 0.612416i
\(249\) −88.2385 32.5109i −0.354371 0.130566i
\(250\) 95.1276 + 148.999i 0.380510 + 0.595997i
\(251\) 125.493i 0.499972i −0.968249 0.249986i \(-0.919574\pi\)
0.968249 0.249986i \(-0.0804260\pi\)
\(252\) −101.189 164.815i −0.401543 0.654028i
\(253\) −96.3385 + 132.599i −0.380785 + 0.524105i
\(254\) 37.1981 51.1988i 0.146449 0.201570i
\(255\) −80.5424 + 122.270i −0.315853 + 0.479488i
\(256\) −12.9443 + 9.40456i −0.0505636 + 0.0367366i
\(257\) −135.710 −0.528053 −0.264026 0.964515i \(-0.585051\pi\)
−0.264026 + 0.964515i \(0.585051\pi\)
\(258\) −4.93189 17.4592i −0.0191158 0.0676712i
\(259\) −106.666 328.285i −0.411839 1.26751i
\(260\) −94.6800 + 156.656i −0.364154 + 0.602522i
\(261\) −57.2781 93.2940i −0.219456 0.357448i
\(262\) −93.1221 + 30.2572i −0.355428 + 0.115485i
\(263\) −133.102 409.647i −0.506093 1.55759i −0.798926 0.601430i \(-0.794598\pi\)
0.292833 0.956164i \(-0.405402\pi\)
\(264\) −37.8435 29.8078i −0.143347 0.112908i
\(265\) 216.998 187.651i 0.818859 0.708117i
\(266\) −319.266 + 103.736i −1.20025 + 0.389985i
\(267\) −25.1832 89.1498i −0.0943189 0.333894i
\(268\) 178.565i 0.666286i
\(269\) 210.481 + 289.702i 0.782457 + 1.07696i 0.995007 + 0.0998098i \(0.0318234\pi\)
−0.212549 + 0.977150i \(0.568177\pi\)
\(270\) 179.602 + 64.7531i 0.665194 + 0.239826i
\(271\) 77.1071 + 56.0216i 0.284528 + 0.206722i 0.720890 0.693049i \(-0.243733\pi\)
−0.436362 + 0.899771i \(0.643733\pi\)
\(272\) −31.5869 22.9493i −0.116128 0.0843723i
\(273\) 365.078 463.499i 1.33728 1.69780i
\(274\) 103.353 0.377201
\(275\) −101.586 99.1198i −0.369403 0.360436i
\(276\) 162.537 + 59.8859i 0.588904 + 0.216978i
\(277\) −61.1400 19.8656i −0.220722 0.0717170i 0.196568 0.980490i \(-0.437020\pi\)
−0.417291 + 0.908773i \(0.637020\pi\)
\(278\) −117.006 85.0096i −0.420884 0.305790i
\(279\) −119.038 494.008i −0.426661 1.77064i
\(280\) 140.022 59.0095i 0.500080 0.210748i
\(281\) −82.6559 113.766i −0.294149 0.404861i 0.636207 0.771518i \(-0.280502\pi\)
−0.930356 + 0.366657i \(0.880502\pi\)
\(282\) 187.199 + 68.9723i 0.663826 + 0.244583i
\(283\) −110.380 151.924i −0.390034 0.536835i 0.568174 0.822908i \(-0.307650\pi\)
−0.958208 + 0.286073i \(0.907650\pi\)
\(284\) 49.8272 16.1899i 0.175448 0.0570065i
\(285\) 182.299 276.744i 0.639646 0.971032i
\(286\) 45.4142 139.771i 0.158791 0.488708i
\(287\) −54.8295 168.748i −0.191043 0.587971i
\(288\) −19.4437 + 47.0526i −0.0675127 + 0.163377i
\(289\) −59.8642 + 184.243i −0.207143 + 0.637520i
\(290\) 79.2600 33.4025i 0.273310 0.115181i
\(291\) 156.156 + 6.06988i 0.536617 + 0.0208587i
\(292\) 37.5700 + 51.7106i 0.128664 + 0.177091i
\(293\) −498.902 −1.70274 −0.851368 0.524569i \(-0.824226\pi\)
−0.851368 + 0.524569i \(0.824226\pi\)
\(294\) −271.274 + 76.6298i −0.922700 + 0.260646i
\(295\) 48.0448 + 565.992i 0.162864 + 1.91862i
\(296\) −53.4105 + 73.5133i −0.180441 + 0.248356i
\(297\) −152.246 17.8255i −0.512611 0.0600186i
\(298\) −326.873 106.207i −1.09689 0.356400i
\(299\) 528.446i 1.76738i
\(300\) −71.6245 + 131.795i −0.238748 + 0.439317i
\(301\) −45.9452 −0.152642
\(302\) −90.0959 + 277.287i −0.298331 + 0.918168i
\(303\) 117.824 78.7991i 0.388859 0.260063i
\(304\) 71.4937 + 51.9432i 0.235177 + 0.170866i
\(305\) −183.362 110.821i −0.601186 0.363346i
\(306\) −123.861 9.64372i −0.404775 0.0315154i
\(307\) 281.408i 0.916638i 0.888788 + 0.458319i \(0.151548\pi\)
−0.888788 + 0.458319i \(0.848452\pi\)
\(308\) −98.6977 + 71.7080i −0.320447 + 0.232818i
\(309\) 72.2333 + 2.80776i 0.233765 + 0.00908661i
\(310\) 397.807 33.7683i 1.28325 0.108930i
\(311\) −172.030 55.8960i −0.553151 0.179730i 0.0190860 0.999818i \(-0.493924\pi\)
−0.572237 + 0.820088i \(0.693924\pi\)
\(312\) −155.201 6.03279i −0.497440 0.0193359i
\(313\) 216.891 70.4723i 0.692943 0.225151i 0.0586901 0.998276i \(-0.481308\pi\)
0.634253 + 0.773125i \(0.281308\pi\)
\(314\) 71.9817 + 23.3883i 0.229241 + 0.0744849i
\(315\) 281.455 393.132i 0.893509 1.24804i
\(316\) −61.9058 190.527i −0.195905 0.602932i
\(317\) 104.200 75.7055i 0.328706 0.238819i −0.411176 0.911556i \(-0.634882\pi\)
0.739881 + 0.672738i \(0.234882\pi\)
\(318\) 228.416 + 84.1585i 0.718290 + 0.264649i
\(319\) −55.8680 + 40.5905i −0.175135 + 0.127243i
\(320\) −34.2334 20.6900i −0.106979 0.0646563i
\(321\) 301.094 + 450.211i 0.937988 + 1.40253i
\(322\) 257.845 354.894i 0.800762 1.10215i
\(323\) −66.6381 + 205.091i −0.206310 + 0.634956i
\(324\) 25.6104 + 159.963i 0.0790443 + 0.493712i
\(325\) −452.823 66.0278i −1.39330 0.203162i
\(326\) 357.170i 1.09561i
\(327\) −55.5079 + 70.4721i −0.169749 + 0.215511i
\(328\) −27.4545 + 37.7879i −0.0837027 + 0.115207i
\(329\) 296.968 408.741i 0.902637 1.24237i
\(330\) 31.9289 116.123i 0.0967544 0.351887i
\(331\) −235.296 + 170.953i −0.710864 + 0.516473i −0.883452 0.468521i \(-0.844787\pi\)
0.172588 + 0.984994i \(0.444787\pi\)
\(332\) 62.6914 0.188830
\(333\) −22.4441 + 288.266i −0.0673997 + 0.865663i
\(334\) −53.2981 164.035i −0.159575 0.491122i
\(335\) 411.373 173.365i 1.22798 0.517506i
\(336\) 101.286 + 79.7791i 0.301448 + 0.237438i
\(337\) −541.009 + 175.784i −1.60537 + 0.521616i −0.968427 0.249297i \(-0.919800\pi\)
−0.636941 + 0.770913i \(0.719800\pi\)
\(338\) −72.5680 223.341i −0.214698 0.660773i
\(339\) 181.691 230.673i 0.535963 0.680452i
\(340\) 22.2029 95.0503i 0.0653026 0.279560i
\(341\) −304.853 + 99.0528i −0.893998 + 0.290477i
\(342\) 280.347 + 21.8275i 0.819727 + 0.0638232i
\(343\) 187.403i 0.546366i
\(344\) 7.10922 + 9.78500i 0.0206663 + 0.0284448i
\(345\) 19.8404 + 432.592i 0.0575084 + 1.25389i
\(346\) 22.4178 + 16.2875i 0.0647914 + 0.0470737i
\(347\) −531.211 385.948i −1.53087 1.11224i −0.955754 0.294168i \(-0.904957\pi\)
−0.575115 0.818073i \(-0.695043\pi\)
\(348\) 57.3334 + 45.1591i 0.164751 + 0.129768i
\(349\) 580.681 1.66384 0.831921 0.554894i \(-0.187241\pi\)
0.831921 + 0.554894i \(0.187241\pi\)
\(350\) 271.890 + 265.289i 0.776828 + 0.757970i
\(351\) −430.902 + 242.028i −1.22764 + 0.689539i
\(352\) 30.5435 + 9.92418i 0.0867713 + 0.0281937i
\(353\) 379.891 + 276.007i 1.07618 + 0.781889i 0.977013 0.213182i \(-0.0683827\pi\)
0.0991655 + 0.995071i \(0.468383\pi\)
\(354\) −400.646 + 267.946i −1.13177 + 0.756909i
\(355\) 85.6741 + 99.0725i 0.241335 + 0.279078i
\(356\) 36.3010 + 49.9641i 0.101969 + 0.140348i
\(357\) −108.773 + 295.224i −0.304687 + 0.826958i
\(358\) 30.3808 + 41.8156i 0.0848626 + 0.116803i
\(359\) −555.853 + 180.608i −1.54834 + 0.503085i −0.953662 0.300880i \(-0.902720\pi\)
−0.594676 + 0.803966i \(0.702720\pi\)
\(360\) −127.276 + 0.888490i −0.353545 + 0.00246803i
\(361\) 39.2730 120.870i 0.108790 0.334820i
\(362\) −139.139 428.227i −0.384363 1.18295i
\(363\) 10.3437 266.106i 0.0284951 0.733074i
\(364\) −121.549 + 374.089i −0.333926 + 1.02772i
\(365\) −82.6539 + 136.758i −0.226449 + 0.374678i
\(366\) 7.06123 181.659i 0.0192930 0.496337i
\(367\) −80.2646 110.475i −0.218705 0.301021i 0.685541 0.728034i \(-0.259566\pi\)
−0.904245 + 0.427013i \(0.859566\pi\)
\(368\) −115.479 −0.313802
\(369\) −11.5369 + 148.177i −0.0312653 + 0.401563i
\(370\) −221.213 51.6734i −0.597874 0.139658i
\(371\) 362.354 498.737i 0.976695 1.34430i
\(372\) 188.326 + 281.594i 0.506252 + 0.756973i
\(373\) −66.5552 21.6251i −0.178432 0.0579761i 0.218438 0.975851i \(-0.429904\pi\)
−0.396870 + 0.917875i \(0.629904\pi\)
\(374\) 78.3686i 0.209542i
\(375\) −373.165 37.0500i −0.995107 0.0987999i
\(376\) −133.001 −0.353725
\(377\) −68.8031 + 211.754i −0.182501 + 0.561682i
\(378\) 407.478 + 47.7092i 1.07798 + 0.126215i
\(379\) 37.0251 + 26.9003i 0.0976915 + 0.0709770i 0.635559 0.772053i \(-0.280770\pi\)
−0.537867 + 0.843030i \(0.680770\pi\)
\(380\) −50.2539 + 215.136i −0.132247 + 0.566148i
\(381\) 36.4945 + 129.193i 0.0957861 + 0.339088i
\(382\) 341.104i 0.892943i
\(383\) 243.336 176.794i 0.635341 0.461602i −0.222906 0.974840i \(-0.571554\pi\)
0.858246 + 0.513238i \(0.171554\pi\)
\(384\) 1.31832 33.9155i 0.00343313 0.0883216i
\(385\) −261.023 157.758i −0.677982 0.409760i
\(386\) 70.0443 + 22.7588i 0.181462 + 0.0589606i
\(387\) 35.5686 + 14.6981i 0.0919084 + 0.0379796i
\(388\) −99.0833 + 32.1941i −0.255369 + 0.0829745i
\(389\) −543.991 176.753i −1.39843 0.454379i −0.489750 0.871863i \(-0.662912\pi\)
−0.908684 + 0.417484i \(0.862912\pi\)
\(390\) −136.784 363.406i −0.350727 0.931812i
\(391\) −87.0795 268.003i −0.222710 0.685430i
\(392\) 152.036 110.460i 0.387846 0.281786i
\(393\) 71.8096 194.900i 0.182722 0.495928i
\(394\) −116.969 + 84.9831i −0.296876 + 0.215693i
\(395\) 378.828 327.596i 0.959058 0.829356i
\(396\) 99.3468 23.9391i 0.250876 0.0604522i
\(397\) 271.005 373.006i 0.682632 0.939562i −0.317330 0.948315i \(-0.602786\pi\)
0.999962 + 0.00875294i \(0.00278618\pi\)
\(398\) −100.539 + 309.428i −0.252611 + 0.777457i
\(399\) 246.197 668.208i 0.617035 1.67471i
\(400\) 14.4288 98.9536i 0.0360720 0.247384i
\(401\) 739.000i 1.84289i −0.388505 0.921446i \(-0.627008\pi\)
0.388505 0.921446i \(-0.372992\pi\)
\(402\) 297.570 + 234.384i 0.740225 + 0.583044i
\(403\) −607.467 + 836.107i −1.50736 + 2.07471i
\(404\) −55.5440 + 76.4498i −0.137485 + 0.189232i
\(405\) −343.654 + 214.305i −0.848529 + 0.529149i
\(406\) 149.528 108.639i 0.368296 0.267583i
\(407\) 182.390 0.448132
\(408\) 79.7050 22.5152i 0.195355 0.0551842i
\(409\) 55.0616 + 169.462i 0.134625 + 0.414333i 0.995531 0.0944303i \(-0.0301029\pi\)
−0.860907 + 0.508763i \(0.830103\pi\)
\(410\) −113.710 26.5616i −0.277341 0.0647844i
\(411\) −135.661 + 172.234i −0.330076 + 0.419060i
\(412\) −45.8332 + 14.8921i −0.111246 + 0.0361459i
\(413\) 377.193 + 1160.88i 0.913300 + 2.81085i
\(414\) −313.144 + 192.256i −0.756386 + 0.464386i
\(415\) 60.8658 + 144.427i 0.146665 + 0.348017i
\(416\) 98.4778 31.9974i 0.236725 0.0769168i
\(417\) 295.247 83.4016i 0.708025 0.200004i
\(418\) 177.379i 0.424352i
\(419\) −63.3107 87.1397i −0.151100 0.207971i 0.726757 0.686895i \(-0.241027\pi\)
−0.877856 + 0.478924i \(0.841027\pi\)
\(420\) −85.4563 + 310.797i −0.203467 + 0.739994i
\(421\) 397.404 + 288.731i 0.943952 + 0.685821i 0.949369 0.314164i \(-0.101724\pi\)
−0.00541690 + 0.999985i \(0.501724\pi\)
\(422\) 417.090 + 303.034i 0.988366 + 0.718090i
\(423\) −360.657 + 221.426i −0.852616 + 0.523466i
\(424\) −162.285 −0.382747
\(425\) 240.531 41.1318i 0.565955 0.0967808i
\(426\) −38.4235 + 104.286i −0.0901959 + 0.244802i
\(427\) −437.862 142.270i −1.02544 0.333185i
\(428\) −292.117 212.236i −0.682517 0.495878i
\(429\) 173.311 + 259.144i 0.403989 + 0.604064i
\(430\) −15.6403 + 25.8781i −0.0363727 + 0.0601816i
\(431\) 193.058 + 265.722i 0.447931 + 0.616525i 0.971952 0.235181i \(-0.0755684\pi\)
−0.524020 + 0.851706i \(0.675568\pi\)
\(432\) −52.8894 94.1632i −0.122429 0.217970i
\(433\) −145.933 200.860i −0.337029 0.463880i 0.606542 0.795051i \(-0.292556\pi\)
−0.943571 + 0.331171i \(0.892556\pi\)
\(434\) 815.925 265.110i 1.88001 0.610853i
\(435\) −48.3727 + 175.928i −0.111202 + 0.404431i
\(436\) 18.4808 56.8780i 0.0423871 0.130454i
\(437\) 197.095 + 606.597i 0.451019 + 1.38809i
\(438\) −135.488 5.26651i −0.309333 0.0120240i
\(439\) 49.6041 152.666i 0.112993 0.347758i −0.878530 0.477687i \(-0.841475\pi\)
0.991523 + 0.129930i \(0.0414752\pi\)
\(440\) 6.79093 + 80.0006i 0.0154339 + 0.181820i
\(441\) 228.373 552.651i 0.517854 1.25318i
\(442\) 148.519 + 204.418i 0.336015 + 0.462485i
\(443\) 54.0408 0.121988 0.0609941 0.998138i \(-0.480573\pi\)
0.0609941 + 0.998138i \(0.480573\pi\)
\(444\) −52.4002 185.500i −0.118019 0.417792i
\(445\) −79.8622 + 132.139i −0.179466 + 0.296941i
\(446\) 174.496 240.173i 0.391247 0.538505i
\(447\) 606.043 405.312i 1.35580 0.906738i
\(448\) −81.7482 26.5616i −0.182474 0.0592893i
\(449\) 327.606i 0.729634i 0.931079 + 0.364817i \(0.118868\pi\)
−0.931079 + 0.364817i \(0.881132\pi\)
\(450\) −125.617 292.353i −0.279148 0.649674i
\(451\) 93.7534 0.207879
\(452\) −60.4923 + 186.176i −0.133832 + 0.411894i
\(453\) −343.827 514.107i −0.759000 1.13489i
\(454\) 127.693 + 92.7744i 0.281262 + 0.204349i
\(455\) −979.828 + 83.1737i −2.15347 + 0.182799i
\(456\) −180.404 + 50.9607i −0.395622 + 0.111756i
\(457\) 461.110i 1.00899i −0.863414 0.504497i \(-0.831678\pi\)
0.863414 0.504497i \(-0.168322\pi\)
\(458\) 15.5946 11.3302i 0.0340494 0.0247384i
\(459\) 178.651 193.751i 0.389218 0.422116i
\(460\) −112.116 266.038i −0.243731 0.578344i
\(461\) −183.777 59.7127i −0.398648 0.129529i 0.102830 0.994699i \(-0.467210\pi\)
−0.501478 + 0.865170i \(0.667210\pi\)
\(462\) 10.0519 258.599i 0.0217575 0.559739i
\(463\) −57.8338 + 18.7914i −0.124911 + 0.0405861i −0.370806 0.928711i \(-0.620918\pi\)
0.245894 + 0.969297i \(0.420918\pi\)
\(464\) −46.2737 15.0353i −0.0997279 0.0324036i
\(465\) −465.888 + 707.254i −1.00191 + 1.52098i
\(466\) 1.12328 + 3.45710i 0.00241047 + 0.00741868i
\(467\) 127.368 92.5379i 0.272736 0.198154i −0.443007 0.896518i \(-0.646088\pi\)
0.715743 + 0.698364i \(0.246088\pi\)
\(468\) 213.770 250.718i 0.456774 0.535722i
\(469\) 776.077 563.853i 1.65475 1.20225i
\(470\) −129.128 306.404i −0.274739 0.651923i
\(471\) −133.459 + 89.2551i −0.283352 + 0.189501i
\(472\) 188.870 259.957i 0.400148 0.550757i
\(473\) 7.50201 23.0888i 0.0158605 0.0488136i
\(474\) 398.762 + 146.921i 0.841270 + 0.309961i
\(475\) −544.416 + 93.0975i −1.14614 + 0.195995i
\(476\) 209.750i 0.440651i
\(477\) −440.066 + 270.180i −0.922569 + 0.566415i
\(478\) 128.774 177.242i 0.269401 0.370799i
\(479\) 25.8292 35.5508i 0.0539231 0.0742188i −0.781204 0.624276i \(-0.785394\pi\)
0.835127 + 0.550057i \(0.185394\pi\)
\(480\) 79.4137 29.8908i 0.165445 0.0622724i
\(481\) 475.749 345.652i 0.989083 0.718611i
\(482\) −264.670 −0.549108
\(483\) 252.968 + 895.522i 0.523743 + 1.85408i
\(484\) 54.8622 + 168.849i 0.113352 + 0.348861i
\(485\) −170.366 197.009i −0.351270 0.406205i
\(486\) −300.188 167.288i −0.617670 0.344215i
\(487\) 835.528 271.479i 1.71566 0.557452i 0.724403 0.689377i \(-0.242116\pi\)
0.991260 + 0.131925i \(0.0421157\pi\)
\(488\) 37.4521 + 115.266i 0.0767462 + 0.236200i
\(489\) −595.209 468.821i −1.21720 0.958734i
\(490\) 402.084 + 243.013i 0.820580 + 0.495944i
\(491\) 456.837 148.435i 0.930421 0.302312i 0.195686 0.980667i \(-0.437307\pi\)
0.734735 + 0.678355i \(0.237307\pi\)
\(492\) −26.9352 95.3521i −0.0547463 0.193805i
\(493\) 118.729i 0.240830i
\(494\) −336.156 462.679i −0.680478 0.936597i
\(495\) 151.604 + 205.631i 0.306271 + 0.415416i
\(496\) −182.711 132.747i −0.368369 0.267636i
\(497\) 227.704 + 165.436i 0.458156 + 0.332870i
\(498\) −82.2887 + 104.473i −0.165238 + 0.209784i
\(499\) −234.536 −0.470012 −0.235006 0.971994i \(-0.575511\pi\)
−0.235006 + 0.971994i \(0.575511\pi\)
\(500\) 241.976 62.8313i 0.483951 0.125663i
\(501\) 343.316 + 126.493i 0.685261 + 0.252480i
\(502\) −168.788 54.8424i −0.336230 0.109248i
\(503\) 51.1143 + 37.1367i 0.101619 + 0.0738304i 0.637434 0.770505i \(-0.279996\pi\)
−0.535815 + 0.844335i \(0.679996\pi\)
\(504\) −265.897 + 64.0718i −0.527573 + 0.127127i
\(505\) −230.050 53.7376i −0.455544 0.106411i
\(506\) 136.243 + 187.523i 0.269255 + 0.370598i
\(507\) 467.442 + 172.226i 0.921976 + 0.339696i
\(508\) −52.6061 72.4061i −0.103555 0.142532i
\(509\) −473.533 + 153.860i −0.930320 + 0.302279i −0.734693 0.678399i \(-0.762674\pi\)
−0.195626 + 0.980679i \(0.562674\pi\)
\(510\) 129.254 + 161.763i 0.253439 + 0.317182i
\(511\) −106.110 + 326.573i −0.207652 + 0.639086i
\(512\) 6.99226 + 21.5200i 0.0136568 + 0.0420312i
\(513\) −404.357 + 438.535i −0.788221 + 0.854844i
\(514\) −59.3073 + 182.529i −0.115384 + 0.355115i
\(515\) −78.8067 91.1312i −0.153023 0.176954i
\(516\) −25.6378 0.996561i −0.0496857 0.00193132i
\(517\) 156.915 + 215.975i 0.303511 + 0.417747i
\(518\) −488.157 −0.942389
\(519\) −56.5681 + 15.9794i −0.108994 + 0.0307889i
\(520\) 169.325 + 195.805i 0.325625 + 0.376549i
\(521\) 443.746 610.764i 0.851720 1.17229i −0.131761 0.991281i \(-0.542063\pi\)
0.983481 0.181010i \(-0.0579367\pi\)
\(522\) −150.512 + 36.2680i −0.288336 + 0.0694789i
\(523\) 525.939 + 170.888i 1.00562 + 0.326746i 0.765109 0.643901i \(-0.222685\pi\)
0.240511 + 0.970646i \(0.422685\pi\)
\(524\) 138.472i 0.264259i
\(525\) −798.976 + 104.874i −1.52186 + 0.199761i
\(526\) −609.142 −1.15806
\(527\) 170.302 524.135i 0.323153 0.994564i
\(528\) −56.6296 + 37.8730i −0.107253 + 0.0717291i
\(529\) −246.318 178.960i −0.465629 0.338299i
\(530\) −157.559 373.868i −0.297281 0.705411i
\(531\) 79.3668 1019.36i 0.149467 1.91971i
\(532\) 474.747i 0.892381i
\(533\) 244.548 177.675i 0.458815 0.333348i
\(534\) −130.912 5.08863i −0.245153 0.00952927i
\(535\) 205.333 879.029i 0.383800 1.64305i
\(536\) −240.169 78.0356i −0.448076 0.145589i
\(537\) −109.562 4.25875i −0.204026 0.00793063i
\(538\) 481.632 156.492i 0.895227 0.290877i
\(539\) −358.745 116.563i −0.665576 0.216259i
\(540\) 165.582 213.267i 0.306633 0.394938i
\(541\) 155.137 + 477.462i 0.286759 + 0.882555i 0.985866 + 0.167537i \(0.0535814\pi\)
−0.699106 + 0.715018i \(0.746419\pi\)
\(542\) 109.046 79.2265i 0.201192 0.146174i
\(543\) 896.256 + 330.220i 1.65056 + 0.608140i
\(544\) −44.6707 + 32.4552i −0.0821152 + 0.0596602i
\(545\) 148.977 12.6461i 0.273352 0.0232038i
\(546\) −463.859 693.585i −0.849559 1.27030i
\(547\) −196.590 + 270.583i −0.359397 + 0.494667i −0.949981 0.312309i \(-0.898898\pi\)
0.590584 + 0.806976i \(0.298898\pi\)
\(548\) 45.1670 139.010i 0.0824215 0.253667i
\(549\) 293.459 + 250.213i 0.534534 + 0.455761i
\(550\) −177.710 + 93.3157i −0.323110 + 0.169665i
\(551\) 268.731i 0.487716i
\(552\) 151.578 192.441i 0.274598 0.348626i
\(553\) 632.586 870.680i 1.14392 1.57447i
\(554\) −53.4384 + 73.5516i −0.0964591 + 0.132765i
\(555\) 376.476 300.816i 0.678335 0.542012i
\(556\) −165.471 + 120.222i −0.297610 + 0.216226i
\(557\) 645.778 1.15939 0.579693 0.814835i \(-0.303172\pi\)
0.579693 + 0.814835i \(0.303172\pi\)
\(558\) −716.460 55.7829i −1.28398 0.0999694i
\(559\) −24.1879 74.4426i −0.0432699 0.133171i
\(560\) −18.1756 214.118i −0.0324565 0.382353i
\(561\) −130.598 102.867i −0.232795 0.183363i
\(562\) −189.137 + 61.4543i −0.336543 + 0.109349i
\(563\) 126.556 + 389.500i 0.224789 + 0.691829i 0.998313 + 0.0580620i \(0.0184921\pi\)
−0.773524 + 0.633767i \(0.781508\pi\)
\(564\) 174.576 221.640i 0.309533 0.392979i
\(565\) −487.639 + 41.3937i −0.863078 + 0.0732633i
\(566\) −252.576 + 82.0668i −0.446246 + 0.144994i
\(567\) −614.360 + 616.422i −1.08353 + 1.08716i
\(568\) 74.0927i 0.130445i
\(569\) 335.206 + 461.371i 0.589114 + 0.810845i 0.994657 0.103230i \(-0.0329179\pi\)
−0.405544 + 0.914076i \(0.632918\pi\)
\(570\) −292.552 366.133i −0.513250 0.642339i
\(571\) −397.542 288.831i −0.696221 0.505834i 0.182479 0.983210i \(-0.441588\pi\)
−0.878699 + 0.477376i \(0.841588\pi\)
\(572\) −168.144 122.164i −0.293958 0.213573i
\(573\) −568.436 447.733i −0.992035 0.781384i
\(574\) −250.927 −0.437154
\(575\) 504.042 516.582i 0.876595 0.898404i
\(576\) 54.7884 + 46.7144i 0.0951187 + 0.0811014i
\(577\) −585.703 190.306i −1.01508 0.329821i −0.246207 0.969217i \(-0.579184\pi\)
−0.768877 + 0.639397i \(0.779184\pi\)
\(578\) 221.645 + 161.034i 0.383469 + 0.278606i
\(579\) −129.867 + 86.8528i −0.224295 + 0.150005i
\(580\) −10.2883 121.202i −0.0177385 0.208969i
\(581\) 197.961 + 272.469i 0.340724 + 0.468966i
\(582\) 76.4064 207.376i 0.131283 0.356316i
\(583\) 191.464 + 263.528i 0.328412 + 0.452021i
\(584\) 85.9693 27.9331i 0.147208 0.0478307i
\(585\) 785.144 + 249.063i 1.34213 + 0.425748i
\(586\) −218.028 + 671.021i −0.372061 + 1.14509i
\(587\) 19.9835 + 61.5030i 0.0340435 + 0.104775i 0.966634 0.256160i \(-0.0824575\pi\)
−0.932591 + 0.360935i \(0.882457\pi\)
\(588\) −15.4842 + 398.351i −0.0263337 + 0.677468i
\(589\) −385.460 + 1186.32i −0.654431 + 2.01413i
\(590\) 782.254 + 182.727i 1.32585 + 0.309708i
\(591\) 11.9128 306.473i 0.0201571 0.518567i
\(592\) 75.5339 + 103.963i 0.127591 + 0.175614i
\(593\) 146.438 0.246945 0.123472 0.992348i \(-0.460597\pi\)
0.123472 + 0.992348i \(0.460597\pi\)
\(594\) −90.5090 + 196.980i −0.152372 + 0.331616i
\(595\) 483.217 203.642i 0.812130 0.342255i
\(596\) −285.697 + 393.228i −0.479357 + 0.659779i
\(597\) −383.681 573.699i −0.642682 0.960970i
\(598\) 710.759 + 230.939i 1.18856 + 0.386186i
\(599\) 54.5992i 0.0911506i −0.998961 0.0455753i \(-0.985488\pi\)
0.998961 0.0455753i \(-0.0145121\pi\)
\(600\) 145.963 + 153.931i 0.243271 + 0.256552i
\(601\) 800.099 1.33128 0.665640 0.746273i \(-0.268159\pi\)
0.665640 + 0.746273i \(0.268159\pi\)
\(602\) −20.0788 + 61.7961i −0.0333534 + 0.102651i
\(603\) −781.181 + 188.237i −1.29549 + 0.312168i
\(604\) 333.576 + 242.357i 0.552279 + 0.401254i
\(605\) −335.725 + 290.322i −0.554917 + 0.479871i
\(606\) −54.4934 192.910i −0.0899231 0.318333i
\(607\) 825.813i 1.36048i −0.732988 0.680241i \(-0.761875\pi\)
0.732988 0.680241i \(-0.238125\pi\)
\(608\) 101.107 73.4588i 0.166295 0.120820i
\(609\) −15.2288 + 391.781i −0.0250063 + 0.643319i
\(610\) −229.185 + 198.191i −0.375714 + 0.324903i
\(611\) 818.600 + 265.979i 1.33977 + 0.435318i
\(612\) −67.1001 + 162.378i −0.109641 + 0.265324i
\(613\) 1155.81 375.544i 1.88549 0.612633i 0.901980 0.431778i \(-0.142114\pi\)
0.983510 0.180855i \(-0.0578864\pi\)
\(614\) 378.493 + 122.980i 0.616438 + 0.200293i
\(615\) 193.519 154.628i 0.314665 0.251428i
\(616\) 53.3146 + 164.086i 0.0865498 + 0.266373i
\(617\) 569.666 413.887i 0.923284 0.670805i −0.0210556 0.999778i \(-0.506703\pi\)
0.944339 + 0.328974i \(0.106703\pi\)
\(618\) 35.3436 95.9266i 0.0571902 0.155221i
\(619\) −237.496 + 172.551i −0.383678 + 0.278758i −0.762860 0.646564i \(-0.776205\pi\)
0.379182 + 0.925322i \(0.376205\pi\)
\(620\) 128.430 549.807i 0.207145 0.886786i
\(621\) 90.6461 774.196i 0.145968 1.24669i
\(622\) −150.360 + 206.952i −0.241736 + 0.332721i
\(623\) −102.526 + 315.543i −0.164568 + 0.506489i
\(624\) −75.9395 + 206.109i −0.121698 + 0.330303i
\(625\) 379.679 + 496.457i 0.607486 + 0.794331i
\(626\) 322.516i 0.515201i
\(627\) 295.595 + 232.828i 0.471443 + 0.371336i
\(628\) 62.9143 86.5941i 0.100182 0.137889i
\(629\) −184.320 + 253.694i −0.293036 + 0.403330i
\(630\) −405.761 550.362i −0.644065 0.873590i
\(631\) 4.12853 2.99955i 0.00654284 0.00475365i −0.584509 0.811387i \(-0.698713\pi\)
0.591052 + 0.806634i \(0.298713\pi\)
\(632\) −283.312 −0.448278
\(633\) −1052.47 + 297.302i −1.66266 + 0.469671i
\(634\) −56.2867 173.233i −0.0887803 0.273238i
\(635\) 115.733 191.490i 0.182257 0.301560i
\(636\) 213.015 270.440i 0.334928 0.425221i
\(637\) −1156.66 + 375.822i −1.81579 + 0.589987i
\(638\) 30.1789 + 92.8810i 0.0473023 + 0.145582i
\(639\) −123.353 200.917i −0.193041 0.314423i
\(640\) −42.7886 + 37.0019i −0.0668571 + 0.0578154i
\(641\) −704.333 + 228.852i −1.09880 + 0.357023i −0.801642 0.597804i \(-0.796040\pi\)
−0.297162 + 0.954827i \(0.596040\pi\)
\(642\) 737.115 208.221i 1.14815 0.324332i
\(643\) 994.252i 1.54627i 0.634241 + 0.773135i \(0.281313\pi\)
−0.634241 + 0.773135i \(0.718687\pi\)
\(644\) −364.648 501.895i −0.566224 0.779341i
\(645\) −22.5954 60.0314i −0.0350316 0.0930720i
\(646\) 246.725 + 179.256i 0.381927 + 0.277486i
\(647\) 824.393 + 598.957i 1.27418 + 0.925744i 0.999361 0.0357523i \(-0.0113827\pi\)
0.274817 + 0.961497i \(0.411383\pi\)
\(648\) 226.342 + 35.4605i 0.349293 + 0.0547230i
\(649\) −644.966 −0.993784
\(650\) −286.698 + 580.190i −0.441074 + 0.892601i
\(651\) −629.187 + 1707.69i −0.966493 + 2.62318i
\(652\) 480.393 + 156.089i 0.736799 + 0.239400i
\(653\) −53.3390 38.7530i −0.0816829 0.0593461i 0.546194 0.837659i \(-0.316076\pi\)
−0.627877 + 0.778312i \(0.716076\pi\)
\(654\) 70.5270 + 105.455i 0.107839 + 0.161247i
\(655\) −319.008 + 134.439i −0.487035 + 0.205251i
\(656\) 38.8265 + 53.4401i 0.0591868 + 0.0814636i
\(657\) 186.618 218.872i 0.284045 0.333139i
\(658\) −419.976 578.047i −0.638261 0.878491i
\(659\) −712.635 + 231.549i −1.08139 + 0.351364i −0.794913 0.606723i \(-0.792484\pi\)
−0.286475 + 0.958088i \(0.592484\pi\)
\(660\) −142.231 93.6919i −0.215502 0.141957i
\(661\) −187.036 + 575.636i −0.282959 + 0.870857i 0.704045 + 0.710156i \(0.251375\pi\)
−0.987003 + 0.160701i \(0.948625\pi\)
\(662\) 127.103 + 391.181i 0.191998 + 0.590908i
\(663\) −535.600 20.8192i −0.807843 0.0314014i
\(664\) 27.3972 84.3198i 0.0412608 0.126988i
\(665\) −1093.71 + 460.922i −1.64468 + 0.693115i
\(666\) 377.908 + 156.164i 0.567430 + 0.234481i
\(667\) −206.410 284.099i −0.309460 0.425936i
\(668\) −243.918 −0.365147
\(669\) 171.195 + 606.041i 0.255897 + 0.905891i
\(670\) −53.3983 629.059i −0.0796990 0.938894i
\(671\) 142.990 196.809i 0.213100 0.293306i
\(672\) 151.566 101.365i 0.225545 0.150841i
\(673\) −460.927 149.764i −0.684885 0.222533i −0.0541520 0.998533i \(-0.517246\pi\)
−0.630733 + 0.776000i \(0.717246\pi\)
\(674\) 804.476i 1.19358i
\(675\) 652.079 + 174.408i 0.966043 + 0.258382i
\(676\) −332.107 −0.491282
\(677\) 116.715 359.212i 0.172400 0.530594i −0.827105 0.562048i \(-0.810014\pi\)
0.999505 + 0.0314538i \(0.0100137\pi\)
\(678\) −230.853 345.182i −0.340491 0.509118i
\(679\) −452.797 328.976i −0.666858 0.484501i
\(680\) −118.139 71.4013i −0.173734 0.105002i
\(681\) −322.214 + 91.0195i −0.473149 + 0.133656i
\(682\) 453.314i 0.664684i
\(683\) −152.279 + 110.637i −0.222955 + 0.161987i −0.693656 0.720306i \(-0.744001\pi\)
0.470701 + 0.882293i \(0.344001\pi\)
\(684\) 151.874 367.526i 0.222038 0.537319i
\(685\) 364.099 30.9069i 0.531532 0.0451196i
\(686\) 252.057 + 81.8983i 0.367430 + 0.119385i
\(687\) −1.58825 + 40.8598i −0.00231186 + 0.0594757i
\(688\) 16.2676 5.28567i 0.0236448 0.00768267i
\(689\) 998.839 + 324.542i 1.44969 + 0.471034i
\(690\) 590.506 + 162.364i 0.855806 + 0.235311i
\(691\) −12.9839 39.9602i −0.0187900 0.0578296i 0.941222 0.337789i \(-0.109679\pi\)
−0.960012 + 0.279959i \(0.909679\pi\)
\(692\) 31.7036 23.0340i 0.0458145 0.0332862i
\(693\) 417.751 + 356.189i 0.602815 + 0.513981i
\(694\) −751.246 + 545.812i −1.08249 + 0.786473i
\(695\) −437.617 264.488i −0.629664 0.380558i
\(696\) 85.7945 57.3780i 0.123268 0.0824397i
\(697\) −94.7455 + 130.406i −0.135933 + 0.187096i
\(698\) 253.767 781.014i 0.363563 1.11893i
\(699\) −7.23554 2.66589i −0.0103513 0.00381386i
\(700\) 475.634 249.755i 0.679477 0.356793i
\(701\) 805.755i 1.14944i −0.818351 0.574718i \(-0.805112\pi\)
0.818351 0.574718i \(-0.194888\pi\)
\(702\) 137.216 + 685.332i 0.195465 + 0.976256i
\(703\) 417.188 574.210i 0.593439 0.816799i
\(704\) 26.6960 36.7439i 0.0379204 0.0521930i
\(705\) 680.102 + 187.000i 0.964684 + 0.265248i
\(706\) 537.247 390.333i 0.760973 0.552879i
\(707\) −507.657 −0.718044
\(708\) 185.298 + 655.964i 0.261720 + 0.926503i
\(709\) 76.7737 + 236.285i 0.108284 + 0.333265i 0.990487 0.137604i \(-0.0439402\pi\)
−0.882203 + 0.470870i \(0.843940\pi\)
\(710\) 170.693 71.9351i 0.240413 0.101317i
\(711\) −768.253 + 471.672i −1.08052 + 0.663392i
\(712\) 83.0656 26.9897i 0.116665 0.0379068i
\(713\) −503.701 1550.23i −0.706454 2.17424i
\(714\) 349.540 + 275.318i 0.489551 + 0.385599i
\(715\) 118.191 505.973i 0.165302 0.707655i
\(716\) 69.5188 22.5880i 0.0970932 0.0315475i
\(717\) 126.338 + 447.244i 0.176204 + 0.623771i
\(718\) 826.549i 1.15118i
\(719\) −202.462 278.665i −0.281589 0.387573i 0.644671 0.764460i \(-0.276994\pi\)
−0.926259 + 0.376887i \(0.876994\pi\)
\(720\) −54.4267 + 171.574i −0.0755926 + 0.238298i
\(721\) −209.452 152.176i −0.290502 0.211062i
\(722\) −145.407 105.644i −0.201395 0.146322i
\(723\) 347.405 441.061i 0.480505 0.610043i
\(724\) −636.770 −0.879516
\(725\) 269.233 141.374i 0.371356 0.194999i
\(726\) −353.391 130.205i −0.486765 0.179345i
\(727\) −350.810 113.985i −0.482545 0.156788i 0.0576354 0.998338i \(-0.481644\pi\)
−0.540180 + 0.841549i \(0.681644\pi\)
\(728\) 450.030 + 326.966i 0.618173 + 0.449129i
\(729\) 672.805 280.667i 0.922915 0.385003i
\(730\) 147.818 + 170.934i 0.202490 + 0.234157i
\(731\) 24.5339 + 33.7680i 0.0335621 + 0.0461943i
\(732\) −241.245 88.8853i −0.329570 0.121428i
\(733\) 52.4471 + 72.1873i 0.0715513 + 0.0984819i 0.843293 0.537455i \(-0.180614\pi\)
−0.771741 + 0.635936i \(0.780614\pi\)
\(734\) −183.665 + 59.6764i −0.250225 + 0.0813030i
\(735\) −932.746 + 351.079i −1.26904 + 0.477658i
\(736\) −50.4663 + 155.319i −0.0685683 + 0.211031i
\(737\) 156.634 + 482.069i 0.212529 + 0.654096i
\(738\) 194.255 + 80.2727i 0.263219 + 0.108771i
\(739\) 98.6633 303.655i 0.133509 0.410899i −0.861846 0.507170i \(-0.830692\pi\)
0.995355 + 0.0962710i \(0.0306915\pi\)
\(740\) −166.174 + 274.949i −0.224560 + 0.371553i
\(741\) 1212.27 + 47.1219i 1.63600 + 0.0635924i
\(742\) −512.446 705.321i −0.690627 0.950567i
\(743\) −271.347 −0.365205 −0.182603 0.983187i \(-0.558452\pi\)
−0.182603 + 0.983187i \(0.558452\pi\)
\(744\) 461.044 130.236i 0.619683 0.175049i
\(745\) −1183.29 276.405i −1.58831 0.371014i
\(746\) −58.1714 + 80.0661i −0.0779777 + 0.107327i
\(747\) −66.0873 274.261i −0.0884703 0.367151i
\(748\) 105.406 + 34.2484i 0.140917 + 0.0457866i
\(749\) 1939.78i 2.58982i
\(750\) −212.911 + 485.715i −0.283882 + 0.647620i
\(751\) 335.603 0.446874 0.223437 0.974718i \(-0.428272\pi\)
0.223437 + 0.974718i \(0.428272\pi\)
\(752\) −58.1234 + 178.885i −0.0772917 + 0.237880i
\(753\) 312.943 209.292i 0.415595 0.277944i
\(754\) 254.741 + 185.080i 0.337852 + 0.245464i
\(755\) −234.475 + 1003.79i −0.310563 + 1.32952i
\(756\) 242.243 527.207i 0.320427 0.697364i
\(757\) 299.536i 0.395688i −0.980234 0.197844i \(-0.936606\pi\)
0.980234 0.197844i \(-0.0633939\pi\)
\(758\) 52.3614 38.0428i 0.0690783 0.0501883i
\(759\) −491.331 19.0984i −0.647340 0.0251626i
\(760\) 267.396 + 161.609i 0.351837 + 0.212644i
\(761\) −928.556 301.706i −1.22018 0.396460i −0.373032 0.927819i \(-0.621682\pi\)
−0.847147 + 0.531359i \(0.821682\pi\)
\(762\) 189.713 + 7.37426i 0.248967 + 0.00967751i
\(763\) 305.560 99.2824i 0.400471 0.130121i
\(764\) 458.784 + 149.068i 0.600503 + 0.195115i
\(765\) −439.230 + 3.06618i −0.574157 + 0.00400808i
\(766\) −131.445 404.547i −0.171600 0.528129i
\(767\) −1682.34 + 1222.29i −2.19340 + 1.59360i
\(768\) −45.0401 16.5948i −0.0586460 0.0216078i
\(769\) −158.573 + 115.210i −0.206207 + 0.149818i −0.686096 0.727511i \(-0.740677\pi\)
0.479889 + 0.877329i \(0.340677\pi\)
\(770\) −326.255 + 282.132i −0.423707 + 0.366406i
\(771\) −226.330 338.420i −0.293554 0.438937i
\(772\) 61.2210 84.2635i 0.0793018 0.109150i
\(773\) −20.6629 + 63.5937i −0.0267307 + 0.0822687i −0.963532 0.267593i \(-0.913772\pi\)
0.936801 + 0.349862i \(0.113772\pi\)
\(774\) 35.3129 41.4163i 0.0456239 0.0535094i
\(775\) 1391.32 237.922i 1.79526 0.306997i
\(776\) 147.336i 0.189866i
\(777\) 640.755 813.494i 0.824652 1.04697i
\(778\) −475.465 + 654.422i −0.611138 + 0.841159i
\(779\) 214.446 295.160i 0.275284 0.378896i
\(780\) −548.557 + 25.1590i −0.703279 + 0.0322552i
\(781\) −120.317 + 87.4151i −0.154055 + 0.111927i
\(782\) −398.519 −0.509615
\(783\) 137.122 298.427i 0.175124 0.381132i
\(784\) −82.1268 252.760i −0.104754 0.322398i
\(785\) 260.576 + 60.8682i 0.331944 + 0.0775391i
\(786\) −230.757 181.758i −0.293585 0.231244i
\(787\) 171.036 55.5731i 0.217327 0.0706138i −0.198330 0.980135i \(-0.563552\pi\)
0.415657 + 0.909522i \(0.363552\pi\)
\(788\) 63.1846 + 194.462i 0.0801835 + 0.246779i
\(789\) 799.559 1015.11i 1.01338 1.28658i
\(790\) −275.061 652.687i −0.348179 0.826186i
\(791\) −1000.17 + 324.976i −1.26444 + 0.410842i
\(792\) 11.2182 144.083i 0.0141643 0.181923i
\(793\) 784.343i 0.989083i
\(794\) −383.259 527.510i −0.482694 0.664371i
\(795\) 829.846 + 228.173i 1.04383 + 0.287010i
\(796\) 372.242 + 270.450i 0.467641 + 0.339761i
\(797\) −933.552 678.265i −1.17133 0.851023i −0.180165 0.983636i \(-0.557663\pi\)
−0.991168 + 0.132614i \(0.957663\pi\)
\(798\) −791.146 623.152i −0.991411 0.780892i
\(799\) −458.985 −0.574449
\(800\) −126.787 62.6510i −0.158483 0.0783137i
\(801\) 180.315 211.480i 0.225112 0.264019i
\(802\) −993.953 322.955i −1.23934 0.402687i
\(803\) −146.787 106.647i −0.182798 0.132811i
\(804\) 445.288 297.802i 0.553841 0.370400i
\(805\) 802.226 1327.35i 0.996554 1.64888i
\(806\) 859.088 + 1182.43i 1.06587 + 1.46704i
\(807\) −371.403 + 1008.03i −0.460227 + 1.24911i
\(808\) 78.5511 + 108.116i 0.0972167 + 0.133807i
\(809\) −40.9097 + 13.2924i −0.0505683 + 0.0164306i −0.334192 0.942505i \(-0.608463\pi\)
0.283624 + 0.958936i \(0.408463\pi\)
\(810\) 138.057 + 555.869i 0.170441 + 0.686258i
\(811\) 136.537 420.218i 0.168357 0.518149i −0.830911 0.556405i \(-0.812180\pi\)
0.999268 + 0.0382564i \(0.0121803\pi\)
\(812\) −80.7723 248.592i −0.0994733 0.306147i
\(813\) −11.1059 + 285.713i −0.0136604 + 0.351431i
\(814\) 79.7072 245.314i 0.0979204 0.301368i
\(815\) 106.809 + 1258.26i 0.131054 + 1.54388i
\(816\) 4.54952 117.042i 0.00557540 0.143434i
\(817\) −55.5299 76.4303i −0.0679680 0.0935500i
\(818\) 251.989 0.308055
\(819\) 1764.69 + 137.397i 2.15469 + 0.167762i
\(820\) −85.4183 + 141.332i −0.104169 + 0.172356i
\(821\) −801.953 + 1103.79i −0.976801 + 1.34445i −0.0382655 + 0.999268i \(0.512183\pi\)
−0.938535 + 0.345183i \(0.887817\pi\)
\(822\) 172.368 + 257.733i 0.209693 + 0.313544i
\(823\) −367.027 119.254i −0.445963 0.144902i 0.0774224 0.996998i \(-0.475331\pi\)
−0.523385 + 0.852096i \(0.675331\pi\)
\(824\) 68.1537i 0.0827108i
\(825\) 77.7557 418.633i 0.0942494 0.507434i
\(826\) 1726.22 2.08986
\(827\) 313.007 963.336i 0.378485 1.16486i −0.562613 0.826720i \(-0.690204\pi\)
0.941098 0.338135i \(-0.109796\pi\)
\(828\) 121.735 + 505.196i 0.147022 + 0.610141i
\(829\) 931.210 + 676.564i 1.12329 + 0.816120i 0.984705 0.174230i \(-0.0557436\pi\)
0.138588 + 0.990350i \(0.455744\pi\)
\(830\) 220.853 18.7474i 0.266088 0.0225872i
\(831\) −52.4276 185.597i −0.0630897 0.223341i
\(832\) 146.436i 0.176004i
\(833\) 524.675 381.199i 0.629862 0.457621i
\(834\) 16.8525 433.554i 0.0202069 0.519848i
\(835\) −236.815 561.933i −0.283611 0.672974i
\(836\) −238.574 77.5175i −0.285376 0.0927243i
\(837\) 1033.39 1120.73i 1.23463 1.33899i
\(838\) −144.870 + 47.0713i −0.172876 + 0.0561710i
\(839\) 245.827 + 79.8739i 0.293000 + 0.0952014i 0.451829 0.892105i \(-0.350772\pi\)
−0.158829 + 0.987306i \(0.550772\pi\)
\(840\) 380.676 + 250.762i 0.453185 + 0.298526i
\(841\) 214.162 + 659.123i 0.254652 + 0.783737i
\(842\) 562.014 408.327i 0.667475 0.484949i
\(843\) 145.850 395.854i 0.173013 0.469577i
\(844\) 589.855 428.555i 0.698880 0.507766i
\(845\) −322.436 765.100i −0.381581 0.905444i
\(846\) 140.205 + 581.849i 0.165727 + 0.687765i
\(847\) −560.611 + 771.615i −0.661878 + 0.910997i
\(848\) −70.9209 + 218.272i −0.0836332 + 0.257397i
\(849\) 194.769 528.627i 0.229410 0.622647i
\(850\) 49.7937 341.489i 0.0585809 0.401752i
\(851\) 927.485i 1.08988i
\(852\) 123.472 + 97.2540i 0.144921 + 0.114148i
\(853\) −631.627 + 869.360i −0.740477 + 1.01918i 0.258114 + 0.966114i \(0.416899\pi\)
−0.998591 + 0.0530648i \(0.983101\pi\)
\(854\) −382.705 + 526.749i −0.448133 + 0.616802i
\(855\) 994.150 6.93997i 1.16275 0.00811693i
\(856\) −413.116 + 300.147i −0.482613 + 0.350639i
\(857\) 687.853 0.802629 0.401315 0.915940i \(-0.368553\pi\)
0.401315 + 0.915940i \(0.368553\pi\)
\(858\) 424.287 119.853i 0.494507 0.139689i
\(859\) 158.818 + 488.791i 0.184887 + 0.569023i 0.999946 0.0103539i \(-0.00329582\pi\)
−0.815060 + 0.579377i \(0.803296\pi\)
\(860\) 27.9709 + 32.3453i 0.0325243 + 0.0376108i
\(861\) 329.366 418.159i 0.382539 0.485666i
\(862\) 441.765 143.538i 0.512488 0.166518i
\(863\) −183.034 563.322i −0.212091 0.652748i −0.999347 0.0361226i \(-0.988499\pi\)
0.787257 0.616625i \(-0.211501\pi\)
\(864\) −149.763 + 29.9853i −0.173337 + 0.0347052i
\(865\) 83.8457 + 50.6748i 0.0969314 + 0.0585836i
\(866\) −333.931 + 108.501i −0.385602 + 0.125290i
\(867\) −559.288 + 157.988i −0.645084 + 0.182224i
\(868\) 1213.27i 1.39778i
\(869\) 334.253 + 460.060i 0.384641 + 0.529413i
\(870\) 215.482 + 141.944i 0.247681 + 0.163154i
\(871\) 1322.15 + 960.596i 1.51797 + 1.10287i
\(872\) −68.4243 49.7132i −0.0784683 0.0570105i
\(873\) 245.293 + 399.530i 0.280977 + 0.457652i
\(874\) 902.005 1.03204
\(875\) 1037.16 + 853.272i 1.18533 + 0.975168i
\(876\) −66.2938 + 179.929i −0.0756779 + 0.205399i
\(877\) 1160.13 + 376.948i 1.32283 + 0.429815i 0.883467 0.468492i \(-0.155203\pi\)
0.439367 + 0.898308i \(0.355203\pi\)
\(878\) −183.657 133.435i −0.209177 0.151976i
\(879\) −832.046 1244.12i −0.946582 1.41538i
\(880\) 110.568 + 25.8278i 0.125646 + 0.0293497i
\(881\) 224.081 + 308.421i 0.254348 + 0.350080i 0.917028 0.398822i \(-0.130581\pi\)
−0.662680 + 0.748903i \(0.730581\pi\)
\(882\) −643.511 548.679i −0.729604 0.622085i
\(883\) −260.923 359.129i −0.295496 0.406715i 0.635294 0.772270i \(-0.280879\pi\)
−0.930789 + 0.365556i \(0.880879\pi\)
\(884\) 339.847 110.423i 0.384442 0.124913i
\(885\) −1331.29 + 1063.75i −1.50429 + 1.20197i
\(886\) 23.6167 72.6847i 0.0266554 0.0820369i
\(887\) −79.2617 243.943i −0.0893593 0.275020i 0.896383 0.443280i \(-0.146185\pi\)
−0.985743 + 0.168260i \(0.946185\pi\)
\(888\) −272.396 10.5882i −0.306753 0.0119237i
\(889\) 148.577 457.273i 0.167128 0.514368i
\(890\) 142.825 + 165.161i 0.160477 + 0.185574i
\(891\) −209.456 409.385i −0.235080 0.459467i
\(892\) −246.775 339.656i −0.276653 0.380780i
\(893\) 1038.86 1.16334
\(894\) −280.293 992.253i −0.313527 1.10990i
\(895\) 119.532 + 138.226i 0.133555 + 0.154442i
\(896\) −71.4505 + 98.3432i −0.0797439 + 0.109758i
\(897\) −1317.79 + 881.319i −1.46911 + 0.982518i
\(898\) 440.628 + 143.169i 0.490678 + 0.159431i
\(899\) 686.776i 0.763934i
\(900\) −448.111 + 41.1909i −0.497901 + 0.0457677i
\(901\) −560.044 −0.621580
\(902\) 40.9717 126.098i 0.0454232 0.139798i
\(903\) −76.6253 114.574i −0.0848564 0.126881i
\(904\) 223.970 + 162.724i 0.247755 + 0.180004i
\(905\) −618.227 1466.98i −0.683123 1.62097i
\(906\) −841.731 + 237.773i −0.929063 + 0.262443i
\(907\) 1145.21i 1.26263i −0.775525 0.631317i \(-0.782515\pi\)
0.775525 0.631317i \(-0.217485\pi\)
\(908\) 180.585 131.203i 0.198882 0.144496i
\(909\) 393.004 + 162.402i 0.432348 + 0.178660i
\(910\) −316.332 + 1354.21i −0.347618 + 1.48815i
\(911\) 619.295 + 201.221i 0.679797 + 0.220880i 0.628507 0.777804i \(-0.283667\pi\)
0.0512906 + 0.998684i \(0.483667\pi\)
\(912\) −10.2974 + 264.913i −0.0112910 + 0.290475i
\(913\) −169.247 + 54.9918i −0.185375 + 0.0602320i
\(914\) −620.192 201.512i −0.678547 0.220473i
\(915\) −29.4480 642.072i −0.0321836 0.701719i
\(916\) −8.42394 25.9262i −0.00919644 0.0283037i
\(917\) −601.826 + 437.252i −0.656299 + 0.476829i
\(918\) −182.521 324.957i −0.198825 0.353984i
\(919\) −228.741 + 166.190i −0.248902 + 0.180838i −0.705240 0.708969i \(-0.749161\pi\)
0.456338 + 0.889806i \(0.349161\pi\)
\(920\) −406.818 + 34.5331i −0.442193 + 0.0375360i
\(921\) −701.750 + 469.320i −0.761944 + 0.509576i
\(922\) −160.627 + 221.084i −0.174216 + 0.239787i
\(923\) −148.173 + 456.031i −0.160534 + 0.494074i
\(924\) −343.423 126.532i −0.371670 0.136939i
\(925\) −794.757 115.886i −0.859197 0.125283i
\(926\) 85.9985i 0.0928709i
\(927\) 113.466 + 184.812i 0.122401 + 0.199365i
\(928\) −40.4447 + 55.6674i −0.0435827 + 0.0599864i
\(929\) 57.7599 79.4996i 0.0621742 0.0855755i −0.776798 0.629750i \(-0.783157\pi\)
0.838972 + 0.544175i \(0.183157\pi\)
\(930\) 747.654 + 935.700i 0.803929 + 1.00613i
\(931\) −1187.55 + 862.802i −1.27556 + 0.926748i
\(932\) 5.14068 0.00551576
\(933\) −147.516 522.214i −0.158109 0.559715i
\(934\) −68.8016 211.750i −0.0736634 0.226713i
\(935\) 23.4355 + 276.082i 0.0250647 + 0.295275i
\(936\) −243.794 397.088i −0.260463 0.424240i
\(937\) −1108.39 + 360.137i −1.18291 + 0.384351i −0.833447 0.552599i \(-0.813636\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(938\) −419.222 1290.23i −0.446932 1.37552i
\(939\) 537.459 + 423.334i 0.572374 + 0.450835i
\(940\) −468.543 + 39.7728i −0.498450 + 0.0423115i
\(941\) −1440.19 + 467.945i −1.53049 + 0.497285i −0.948733 0.316080i \(-0.897633\pi\)
−0.581753 + 0.813365i \(0.697633\pi\)
\(942\) 61.7243 + 218.507i 0.0655247 + 0.231961i
\(943\) 476.753i 0.505571i
\(944\) −267.103 367.635i −0.282948 0.389444i
\(945\) 1449.76 + 46.2201i 1.53413 + 0.0489101i
\(946\) −27.7759 20.1804i −0.0293614 0.0213323i
\(947\) −1088.00 790.476i −1.14889 0.834716i −0.160555 0.987027i \(-0.551329\pi\)
−0.988333 + 0.152311i \(0.951329\pi\)
\(948\) 371.874 472.127i 0.392273 0.498024i
\(949\) −584.991 −0.616429
\(950\) −112.703 + 772.924i −0.118635 + 0.813604i
\(951\) 362.567 + 133.586i 0.381248 + 0.140469i
\(952\) −282.113 91.6641i −0.296337 0.0962858i
\(953\) −557.578 405.104i −0.585076 0.425083i 0.255474 0.966816i \(-0.417768\pi\)
−0.840551 + 0.541733i \(0.817768\pi\)
\(954\) 171.075 + 709.960i 0.179324 + 0.744193i
\(955\) 102.004 + 1201.66i 0.106811 + 1.25829i
\(956\) −182.114 250.658i −0.190495 0.262194i
\(957\) −194.395 71.6237i −0.203130 0.0748419i
\(958\) −36.5280 50.2764i −0.0381294 0.0524806i
\(959\) 746.787 242.646i 0.778715 0.253020i
\(960\) −5.49790 119.874i −0.00572698 0.124869i
\(961\) 688.126 2117.83i 0.716052 2.20378i
\(962\) −256.991 790.936i −0.267142 0.822179i
\(963\) −620.544 + 1501.68i −0.644387 + 1.55938i
\(964\) −115.665 + 355.980i −0.119984 + 0.369274i
\(965\) 253.562 + 59.2299i 0.262759 + 0.0613781i
\(966\) 1315.03 + 51.1160i 1.36131 + 0.0529151i
\(967\) 694.997 + 956.581i 0.718714 + 0.989225i 0.999566 + 0.0294738i \(0.00938317\pi\)
−0.280851 + 0.959751i \(0.590617\pi\)
\(968\) 251.076 0.259377
\(969\) −622.573 + 175.865i −0.642491 + 0.181492i
\(970\) −339.429 + 143.046i −0.349927 + 0.147470i
\(971\) 891.361 1226.85i 0.917983 1.26350i −0.0463832 0.998924i \(-0.514770\pi\)
0.964366 0.264571i \(-0.0852305\pi\)
\(972\) −356.189 + 330.644i −0.366450 + 0.340168i
\(973\) −1045.02 339.546i −1.07401 0.348968i
\(974\) 1242.42i 1.27559i
\(975\) −590.544 1239.33i −0.605686 1.27111i
\(976\) 171.399 0.175614
\(977\) −397.705 + 1224.01i −0.407068 + 1.25283i 0.512089 + 0.858932i \(0.328872\pi\)
−0.919156 + 0.393893i \(0.871128\pi\)
\(978\) −890.679 + 595.672i −0.910715 + 0.609072i
\(979\) −141.829 103.045i −0.144871 0.105255i
\(980\) 502.568 434.602i 0.512825 0.443471i
\(981\) −268.311 20.8904i −0.273507 0.0212950i
\(982\) 679.312i 0.691764i
\(983\) 608.165 441.858i 0.618682 0.449499i −0.233779 0.972290i \(-0.575109\pi\)
0.852461 + 0.522791i \(0.175109\pi\)
\(984\) −140.019 5.44266i −0.142296 0.00553115i
\(985\) −386.653 + 334.363i −0.392541 + 0.339454i
\(986\) −159.691 51.8867i −0.161958 0.0526234i
\(987\) 1514.55 + 58.8717i 1.53450 + 0.0596471i
\(988\) −769.207 + 249.931i −0.778550 + 0.252966i
\(989\) 117.411 + 38.1491i 0.118717 + 0.0385734i
\(990\) 342.827 114.043i 0.346289 0.115195i
\(991\) 282.980 + 870.924i 0.285550 + 0.878834i 0.986233 + 0.165361i \(0.0528788\pi\)
−0.700683 + 0.713473i \(0.747121\pi\)
\(992\) −258.392 + 187.733i −0.260476 + 0.189247i
\(993\) −818.722 301.653i −0.824494 0.303780i
\(994\) 322.022 233.962i 0.323965 0.235375i
\(995\) −261.654 + 1120.14i −0.262969 + 1.12577i
\(996\) 104.554 + 156.334i 0.104974 + 0.156962i
\(997\) −765.781 + 1054.01i −0.768085 + 1.05718i 0.228413 + 0.973564i \(0.426646\pi\)
−0.996498 + 0.0836142i \(0.973354\pi\)
\(998\) −102.496 + 315.450i −0.102701 + 0.316082i
\(999\) −756.283 + 424.788i −0.757040 + 0.425213i
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 150.3.i.a.29.18 yes 80
3.2 odd 2 inner 150.3.i.a.29.2 80
25.19 even 10 inner 150.3.i.a.119.2 yes 80
75.44 odd 10 inner 150.3.i.a.119.18 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.i.a.29.2 80 3.2 odd 2 inner
150.3.i.a.29.18 yes 80 1.1 even 1 trivial
150.3.i.a.119.2 yes 80 25.19 even 10 inner
150.3.i.a.119.18 yes 80 75.44 odd 10 inner