Properties

Label 125.2.h.a.104.12
Level $125$
Weight $2$
Character 125.104
Analytic conductor $0.998$
Analytic rank $0$
Dimension $240$
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] = [125,2,Mod(4,125)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(125, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("125.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.h (of order \(50\), degree \(20\), 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: \(0.998130025266\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{50})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label 104.12
Character \(\chi\) \(=\) 125.104
Dual form 125.2.h.a.119.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.650201 + 2.53237i) q^{2} +(-2.78727 + 0.531700i) q^{3} +(-4.23750 + 2.32959i) q^{4} +(2.10703 - 0.748604i) q^{5} +(-3.15874 - 6.71267i) q^{6} +(-1.24444 + 1.71282i) q^{7} +(-5.07509 - 5.40442i) q^{8} +(4.69683 - 1.85961i) q^{9} +O(q^{10})\) \(q+(0.650201 + 2.53237i) q^{2} +(-2.78727 + 0.531700i) q^{3} +(-4.23750 + 2.32959i) q^{4} +(2.10703 - 0.748604i) q^{5} +(-3.15874 - 6.71267i) q^{6} +(-1.24444 + 1.71282i) q^{7} +(-5.07509 - 5.40442i) q^{8} +(4.69683 - 1.85961i) q^{9} +(3.26573 + 4.84904i) q^{10} +(-1.46742 + 0.376769i) q^{11} +(10.5724 - 8.74627i) q^{12} +(1.00106 + 2.52838i) q^{13} +(-5.14662 - 2.03769i) q^{14} +(-5.47484 + 3.20687i) q^{15} +(5.20402 - 8.20022i) q^{16} +(-3.01517 + 5.48457i) q^{17} +(7.76309 + 10.6850i) q^{18} +(-0.109986 + 0.576568i) q^{19} +(-7.18463 + 8.08073i) q^{20} +(2.55787 - 5.43575i) q^{21} +(-1.90823 - 3.47106i) q^{22} +(4.83466 + 0.304171i) q^{23} +(17.0192 + 12.3652i) q^{24} +(3.87918 - 3.15467i) q^{25} +(-5.75191 + 4.17901i) q^{26} +(-4.91517 + 3.11926i) q^{27} +(1.28314 - 10.1571i) q^{28} +(6.59877 + 0.833618i) q^{29} +(-11.6807 - 11.7792i) q^{30} +(-1.61572 - 0.888251i) q^{31} +(10.0477 + 3.26471i) q^{32} +(3.88976 - 1.83038i) q^{33} +(-15.8494 - 4.06944i) q^{34} +(-1.33985 + 4.54056i) q^{35} +(-15.5707 + 18.8218i) q^{36} +(-0.227558 - 0.144412i) q^{37} +(-1.53159 + 0.0963597i) q^{38} +(-4.13456 - 6.51503i) q^{39} +(-14.7392 - 7.58807i) q^{40} +(0.0810824 + 1.28877i) q^{41} +(15.4284 + 2.94313i) q^{42} +(8.95252 - 2.90885i) q^{43} +(5.34047 - 5.01504i) q^{44} +(8.50428 - 7.43432i) q^{45} +(2.37323 + 12.4409i) q^{46} +(0.639643 - 0.681150i) q^{47} +(-10.1449 + 25.6232i) q^{48} +(0.777991 + 2.39441i) q^{49} +(10.5110 + 7.77235i) q^{50} +(5.48794 - 16.8901i) q^{51} +(-10.1321 - 8.38199i) q^{52} +(-8.33686 - 3.92303i) q^{53} +(-11.0950 - 10.4189i) q^{54} +(-2.80985 + 1.89238i) q^{55} +(15.5724 - 1.96725i) q^{56} -1.66553i q^{57} +(2.17950 + 17.2525i) q^{58} +(4.11638 + 4.97585i) q^{59} +(15.7290 - 26.3432i) q^{60} +(0.758535 - 12.0566i) q^{61} +(1.19883 - 4.66914i) q^{62} +(-2.65974 + 10.3590i) q^{63} +(-0.514728 + 8.18137i) q^{64} +(4.00202 + 4.57800i) q^{65} +(7.16432 + 8.66018i) q^{66} +(-0.491373 - 3.88962i) q^{67} -30.2650i q^{68} +(-13.6372 + 1.72278i) q^{69} +(-12.3695 - 0.440704i) q^{70} +(10.2506 + 9.62593i) q^{71} +(-33.8870 - 15.9460i) q^{72} +(-4.89900 - 4.05280i) q^{73} +(0.217747 - 0.670156i) q^{74} +(-9.13499 + 10.8555i) q^{75} +(-0.877098 - 2.69943i) q^{76} +(1.18077 - 2.98228i) q^{77} +(13.8101 - 14.7063i) q^{78} +(-0.0302324 - 0.158484i) q^{79} +(4.82633 - 21.1739i) q^{80} +(0.994067 - 0.933491i) q^{81} +(-3.21091 + 1.04329i) q^{82} +(-3.16982 - 0.604675i) q^{83} +(1.82407 + 28.9928i) q^{84} +(-2.24729 + 13.8134i) q^{85} +(13.1872 + 20.7797i) q^{86} +(-18.8358 + 1.18505i) q^{87} +(9.48350 + 6.01841i) q^{88} +(-8.15633 + 9.85930i) q^{89} +(24.3559 + 16.7021i) q^{90} +(-5.57642 - 1.43178i) q^{91} +(-21.1955 + 9.97383i) q^{92} +(4.97574 + 1.61671i) q^{93} +(2.14082 + 1.17692i) q^{94} +(0.199876 + 1.29718i) q^{95} +(-29.7416 - 3.75724i) q^{96} +(0.605212 - 4.79075i) q^{97} +(-5.55767 + 3.52701i) q^{98} +(-6.19157 + 4.49844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{21}{50}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.650201 + 2.53237i 0.459762 + 1.79065i 0.599399 + 0.800451i \(0.295406\pi\)
−0.139637 + 0.990203i \(0.544594\pi\)
\(3\) −2.78727 + 0.531700i −1.60923 + 0.306977i −0.912100 0.409967i \(-0.865540\pi\)
−0.697130 + 0.716945i \(0.745540\pi\)
\(4\) −4.23750 + 2.32959i −2.11875 + 1.16479i
\(5\) 2.10703 0.748604i 0.942294 0.334786i
\(6\) −3.15874 6.71267i −1.28955 2.74044i
\(7\) −1.24444 + 1.71282i −0.470352 + 0.647385i −0.976615 0.214995i \(-0.931027\pi\)
0.506263 + 0.862379i \(0.331027\pi\)
\(8\) −5.07509 5.40442i −1.79432 1.91075i
\(9\) 4.69683 1.85961i 1.56561 0.619869i
\(10\) 3.26573 + 4.84904i 1.03272 + 1.53340i
\(11\) −1.46742 + 0.376769i −0.442443 + 0.113600i −0.463338 0.886182i \(-0.653348\pi\)
0.0208951 + 0.999782i \(0.493348\pi\)
\(12\) 10.5724 8.74627i 3.05199 2.52483i
\(13\) 1.00106 + 2.52838i 0.277644 + 0.701248i 0.999953 + 0.00967789i \(0.00308062\pi\)
−0.722310 + 0.691570i \(0.756919\pi\)
\(14\) −5.14662 2.03769i −1.37549 0.544596i
\(15\) −5.47484 + 3.20687i −1.41360 + 0.828010i
\(16\) 5.20402 8.20022i 1.30100 2.05006i
\(17\) −3.01517 + 5.48457i −0.731286 + 1.33020i 0.204929 + 0.978777i \(0.434304\pi\)
−0.936215 + 0.351428i \(0.885696\pi\)
\(18\) 7.76309 + 10.6850i 1.82978 + 2.51847i
\(19\) −0.109986 + 0.576568i −0.0252326 + 0.132274i −0.992675 0.120819i \(-0.961448\pi\)
0.967442 + 0.253093i \(0.0814478\pi\)
\(20\) −7.18463 + 8.08073i −1.60653 + 1.80691i
\(21\) 2.55787 5.43575i 0.558173 1.18618i
\(22\) −1.90823 3.47106i −0.406837 0.740033i
\(23\) 4.83466 + 0.304171i 1.00810 + 0.0634240i 0.558242 0.829678i \(-0.311476\pi\)
0.449854 + 0.893102i \(0.351476\pi\)
\(24\) 17.0192 + 12.3652i 3.47403 + 2.52403i
\(25\) 3.87918 3.15467i 0.775837 0.630934i
\(26\) −5.75191 + 4.17901i −1.12804 + 0.819570i
\(27\) −4.91517 + 3.11926i −0.945924 + 0.600302i
\(28\) 1.28314 10.1571i 0.242491 1.91951i
\(29\) 6.59877 + 0.833618i 1.22536 + 0.154799i 0.711259 0.702930i \(-0.248125\pi\)
0.514102 + 0.857729i \(0.328125\pi\)
\(30\) −11.6807 11.7792i −2.13260 2.15057i
\(31\) −1.61572 0.888251i −0.290192 0.159535i 0.330008 0.943978i \(-0.392949\pi\)
−0.620200 + 0.784444i \(0.712949\pi\)
\(32\) 10.0477 + 3.26471i 1.77621 + 0.577125i
\(33\) 3.88976 1.83038i 0.677120 0.318629i
\(34\) −15.8494 4.06944i −2.71815 0.697903i
\(35\) −1.33985 + 4.54056i −0.226475 + 0.767494i
\(36\) −15.5707 + 18.8218i −2.59512 + 3.13696i
\(37\) −0.227558 0.144412i −0.0374102 0.0237412i 0.516990 0.855991i \(-0.327052\pi\)
−0.554400 + 0.832250i \(0.687052\pi\)
\(38\) −1.53159 + 0.0963597i −0.248457 + 0.0156316i
\(39\) −4.13456 6.51503i −0.662060 1.04324i
\(40\) −14.7392 7.58807i −2.33047 1.19978i
\(41\) 0.0810824 + 1.28877i 0.0126629 + 0.201272i 0.999271 + 0.0381654i \(0.0121514\pi\)
−0.986608 + 0.163106i \(0.947849\pi\)
\(42\) 15.4284 + 2.94313i 2.38066 + 0.454135i
\(43\) 8.95252 2.90885i 1.36525 0.443595i 0.467455 0.884017i \(-0.345171\pi\)
0.897791 + 0.440421i \(0.145171\pi\)
\(44\) 5.34047 5.01504i 0.805106 0.756045i
\(45\) 8.50428 7.43432i 1.26774 1.10824i
\(46\) 2.37323 + 12.4409i 0.349913 + 1.83431i
\(47\) 0.639643 0.681150i 0.0933015 0.0993560i −0.680623 0.732634i \(-0.738291\pi\)
0.773925 + 0.633278i \(0.218291\pi\)
\(48\) −10.1449 + 25.6232i −1.46430 + 3.69839i
\(49\) 0.777991 + 2.39441i 0.111142 + 0.342059i
\(50\) 10.5110 + 7.77235i 1.48648 + 1.09918i
\(51\) 5.48794 16.8901i 0.768465 2.36509i
\(52\) −10.1321 8.38199i −1.40507 1.16237i
\(53\) −8.33686 3.92303i −1.14516 0.538869i −0.242892 0.970053i \(-0.578096\pi\)
−0.902264 + 0.431184i \(0.858096\pi\)
\(54\) −11.0950 10.4189i −1.50983 1.41783i
\(55\) −2.80985 + 1.89238i −0.378880 + 0.255168i
\(56\) 15.5724 1.96725i 2.08095 0.262885i
\(57\) 1.66553i 0.220605i
\(58\) 2.17950 + 17.2525i 0.286182 + 2.26537i
\(59\) 4.11638 + 4.97585i 0.535907 + 0.647800i 0.967081 0.254468i \(-0.0819005\pi\)
−0.431174 + 0.902269i \(0.641900\pi\)
\(60\) 15.7290 26.3432i 2.03060 3.40090i
\(61\) 0.758535 12.0566i 0.0971205 1.54369i −0.584145 0.811649i \(-0.698570\pi\)
0.681265 0.732037i \(-0.261430\pi\)
\(62\) 1.19883 4.66914i 0.152252 0.592982i
\(63\) −2.65974 + 10.3590i −0.335095 + 1.30511i
\(64\) −0.514728 + 8.18137i −0.0643410 + 1.02267i
\(65\) 4.00202 + 4.57800i 0.496390 + 0.567831i
\(66\) 7.16432 + 8.66018i 0.881867 + 1.06599i
\(67\) −0.491373 3.88962i −0.0600308 0.475193i −0.993260 0.115910i \(-0.963022\pi\)
0.933229 0.359282i \(-0.116978\pi\)
\(68\) 30.2650i 3.67017i
\(69\) −13.6372 + 1.72278i −1.64173 + 0.207398i
\(70\) −12.3695 0.440704i −1.47844 0.0526742i
\(71\) 10.2506 + 9.62593i 1.21652 + 1.14239i 0.985542 + 0.169429i \(0.0541924\pi\)
0.230978 + 0.972959i \(0.425808\pi\)
\(72\) −33.8870 15.9460i −3.99362 1.87925i
\(73\) −4.89900 4.05280i −0.573384 0.474345i 0.304965 0.952363i \(-0.401355\pi\)
−0.878350 + 0.478019i \(0.841355\pi\)
\(74\) 0.217747 0.670156i 0.0253126 0.0779041i
\(75\) −9.13499 + 10.8555i −1.05482 + 1.25348i
\(76\) −0.877098 2.69943i −0.100610 0.309646i
\(77\) 1.18077 2.98228i 0.134561 0.339863i
\(78\) 13.8101 14.7063i 1.56369 1.66516i
\(79\) −0.0302324 0.158484i −0.00340141 0.0178308i 0.980546 0.196289i \(-0.0628891\pi\)
−0.983947 + 0.178458i \(0.942889\pi\)
\(80\) 4.82633 21.1739i 0.539600 2.36731i
\(81\) 0.994067 0.933491i 0.110452 0.103721i
\(82\) −3.21091 + 1.04329i −0.354586 + 0.115212i
\(83\) −3.16982 0.604675i −0.347932 0.0663717i 0.0104530 0.999945i \(-0.496673\pi\)
−0.358385 + 0.933574i \(0.616673\pi\)
\(84\) 1.82407 + 28.9928i 0.199023 + 3.16337i
\(85\) −2.24729 + 13.8134i −0.243753 + 1.49827i
\(86\) 13.1872 + 20.7797i 1.42201 + 2.24073i
\(87\) −18.8358 + 1.18505i −2.01941 + 0.127050i
\(88\) 9.48350 + 6.01841i 1.01094 + 0.641565i
\(89\) −8.15633 + 9.85930i −0.864569 + 1.04508i 0.133967 + 0.990986i \(0.457228\pi\)
−0.998536 + 0.0540983i \(0.982772\pi\)
\(90\) 24.3559 + 16.7021i 2.56734 + 1.76056i
\(91\) −5.57642 1.43178i −0.584567 0.150091i
\(92\) −21.1955 + 9.97383i −2.20978 + 1.03984i
\(93\) 4.97574 + 1.61671i 0.515960 + 0.167645i
\(94\) 2.14082 + 1.17692i 0.220808 + 0.121390i
\(95\) 0.199876 + 1.29718i 0.0205069 + 0.133088i
\(96\) −29.7416 3.75724i −3.03549 0.383472i
\(97\) 0.605212 4.79075i 0.0614500 0.486427i −0.931116 0.364722i \(-0.881164\pi\)
0.992566 0.121704i \(-0.0388360\pi\)
\(98\) −5.55767 + 3.52701i −0.561410 + 0.356281i
\(99\) −6.19157 + 4.49844i −0.622276 + 0.452110i
\(100\) −9.08898 + 22.4048i −0.908898 + 2.24048i
\(101\) −1.28902 0.936530i −0.128263 0.0931882i 0.521804 0.853065i \(-0.325259\pi\)
−0.650067 + 0.759877i \(0.725259\pi\)
\(102\) 46.3403 + 2.91548i 4.58837 + 0.288676i
\(103\) −0.898896 1.63509i −0.0885709 0.161110i 0.828311 0.560269i \(-0.189302\pi\)
−0.916882 + 0.399159i \(0.869302\pi\)
\(104\) 8.58400 18.2419i 0.841731 1.78877i
\(105\) 1.32030 13.3681i 0.128848 1.30460i
\(106\) 4.51391 23.6627i 0.438430 2.29833i
\(107\) −3.30818 4.55332i −0.319814 0.440187i 0.618596 0.785709i \(-0.287702\pi\)
−0.938410 + 0.345523i \(0.887702\pi\)
\(108\) 13.5614 24.6682i 1.30495 2.37370i
\(109\) 9.67930 15.2521i 0.927109 1.46089i 0.0400690 0.999197i \(-0.487242\pi\)
0.887040 0.461693i \(-0.152758\pi\)
\(110\) −6.61916 5.88514i −0.631112 0.561126i
\(111\) 0.711048 + 0.281524i 0.0674897 + 0.0267211i
\(112\) 7.56943 + 19.1182i 0.715244 + 1.80650i
\(113\) −3.70909 + 3.06842i −0.348921 + 0.288653i −0.795330 0.606176i \(-0.792703\pi\)
0.446409 + 0.894829i \(0.352703\pi\)
\(114\) 4.21773 1.08293i 0.395026 0.101426i
\(115\) 10.4145 2.97834i 0.971156 0.277732i
\(116\) −29.9043 + 11.8399i −2.77654 + 1.09931i
\(117\) 9.40361 + 10.0138i 0.869364 + 0.925778i
\(118\) −9.92420 + 13.6595i −0.913596 + 1.25746i
\(119\) −5.64190 11.9896i −0.517192 1.09909i
\(120\) 45.1166 + 13.3132i 4.11856 + 1.21532i
\(121\) −7.62801 + 4.19354i −0.693456 + 0.381231i
\(122\) 31.0249 5.91831i 2.80886 0.535818i
\(123\) −0.911236 3.54903i −0.0821634 0.320005i
\(124\) 8.91589 0.800670
\(125\) 5.81198 9.55096i 0.519839 0.854264i
\(126\) −27.9621 −2.49106
\(127\) −0.884699 3.44568i −0.0785043 0.305754i 0.917190 0.398450i \(-0.130452\pi\)
−0.995695 + 0.0926955i \(0.970452\pi\)
\(128\) −0.297499 + 0.0567509i −0.0262954 + 0.00501612i
\(129\) −23.4064 + 12.8678i −2.06082 + 1.13295i
\(130\) −8.99104 + 13.1112i −0.788567 + 1.14993i
\(131\) 4.90195 + 10.4172i 0.428285 + 0.910153i 0.996202 + 0.0870671i \(0.0277495\pi\)
−0.567917 + 0.823086i \(0.692251\pi\)
\(132\) −12.2188 + 16.8178i −1.06351 + 1.46380i
\(133\) −0.850685 0.905888i −0.0737638 0.0785504i
\(134\) 9.53045 3.77337i 0.823305 0.325970i
\(135\) −8.02133 + 10.2519i −0.690366 + 0.882343i
\(136\) 44.9432 11.5395i 3.85385 0.989501i
\(137\) −9.14149 + 7.56250i −0.781010 + 0.646108i −0.940001 0.341172i \(-0.889176\pi\)
0.158991 + 0.987280i \(0.449176\pi\)
\(138\) −13.2296 33.4143i −1.12618 2.84441i
\(139\) 5.72767 + 2.26774i 0.485814 + 0.192347i 0.598247 0.801312i \(-0.295864\pi\)
−0.112433 + 0.993659i \(0.535864\pi\)
\(140\) −4.90002 22.3619i −0.414128 1.88993i
\(141\) −1.42069 + 2.23865i −0.119644 + 0.188528i
\(142\) −17.7115 + 32.2170i −1.48631 + 2.70359i
\(143\) −2.42159 3.33303i −0.202503 0.278722i
\(144\) 9.19321 48.1925i 0.766101 4.01604i
\(145\) 14.5279 3.18340i 1.20647 0.264367i
\(146\) 7.07785 15.0412i 0.585767 1.24482i
\(147\) −3.44158 6.26021i −0.283857 0.516333i
\(148\) 1.30070 + 0.0818329i 0.106917 + 0.00672662i
\(149\) 8.39207 + 6.09719i 0.687505 + 0.499502i 0.875839 0.482604i \(-0.160309\pi\)
−0.188334 + 0.982105i \(0.560309\pi\)
\(150\) −33.4296 16.0749i −2.72952 1.31251i
\(151\) 6.96498 5.06036i 0.566802 0.411806i −0.267140 0.963658i \(-0.586079\pi\)
0.833942 + 0.551852i \(0.186079\pi\)
\(152\) 3.67421 2.33172i 0.298017 0.189128i
\(153\) −3.96259 + 31.3672i −0.320357 + 2.53588i
\(154\) 8.31997 + 1.05106i 0.670443 + 0.0846966i
\(155\) −4.06933 0.662039i −0.326856 0.0531762i
\(156\) 32.6975 + 17.9756i 2.61790 + 1.43920i
\(157\) 15.0172 + 4.87938i 1.19850 + 0.389417i 0.839209 0.543809i \(-0.183018\pi\)
0.359292 + 0.933225i \(0.383018\pi\)
\(158\) 0.381682 0.179606i 0.0303650 0.0142887i
\(159\) 25.3229 + 6.50183i 2.00824 + 0.515628i
\(160\) 23.6149 0.642926i 1.86692 0.0508278i
\(161\) −6.53741 + 7.90237i −0.515220 + 0.622794i
\(162\) 3.01029 + 1.91039i 0.236510 + 0.150094i
\(163\) 15.3504 0.965766i 1.20234 0.0756446i 0.551047 0.834474i \(-0.314228\pi\)
0.651289 + 0.758829i \(0.274228\pi\)
\(164\) −3.34588 5.27227i −0.261270 0.411695i
\(165\) 6.82562 6.76856i 0.531374 0.526932i
\(166\) −0.529760 8.42029i −0.0411174 0.653542i
\(167\) −5.01307 0.956294i −0.387923 0.0740003i −0.0102696 0.999947i \(-0.503269\pi\)
−0.377654 + 0.925947i \(0.623269\pi\)
\(168\) −42.3585 + 13.7631i −3.26803 + 1.06185i
\(169\) 4.08598 3.83699i 0.314306 0.295153i
\(170\) −36.4417 + 3.29049i −2.79495 + 0.252369i
\(171\) 0.555603 + 2.91257i 0.0424880 + 0.222730i
\(172\) −31.1599 + 33.1819i −2.37592 + 2.53010i
\(173\) 6.87214 17.3570i 0.522479 1.31963i −0.393839 0.919180i \(-0.628853\pi\)
0.916318 0.400452i \(-0.131147\pi\)
\(174\) −15.2480 46.9286i −1.15595 3.55765i
\(175\) 0.575979 + 10.5701i 0.0435399 + 0.799026i
\(176\) −4.54688 + 13.9939i −0.342734 + 1.05483i
\(177\) −14.1191 11.6803i −1.06126 0.877949i
\(178\) −30.2706 14.2443i −2.26888 1.06765i
\(179\) 1.47298 + 1.38322i 0.110096 + 0.103387i 0.737641 0.675194i \(-0.235940\pi\)
−0.627544 + 0.778581i \(0.715940\pi\)
\(180\) −18.7180 + 51.3144i −1.39516 + 3.82475i
\(181\) −15.8272 + 1.99944i −1.17643 + 0.148617i −0.689142 0.724626i \(-0.742013\pi\)
−0.487285 + 0.873243i \(0.662013\pi\)
\(182\) 15.0525i 1.11576i
\(183\) 4.29624 + 34.0082i 0.317587 + 2.51396i
\(184\) −22.8925 27.6722i −1.68765 2.04002i
\(185\) −0.587579 0.133931i −0.0431997 0.00984683i
\(186\) −0.858884 + 13.6516i −0.0629764 + 1.00098i
\(187\) 2.35810 9.18418i 0.172441 0.671614i
\(188\) −1.12369 + 4.37648i −0.0819534 + 0.319188i
\(189\) 0.773882 12.3005i 0.0562917 0.894730i
\(190\) −3.15498 + 1.34959i −0.228887 + 0.0979095i
\(191\) −11.8637 14.3408i −0.858427 1.03766i −0.998868 0.0475712i \(-0.984852\pi\)
0.140441 0.990089i \(-0.455148\pi\)
\(192\) −2.91535 23.0773i −0.210397 1.66546i
\(193\) 7.81977i 0.562879i 0.959579 + 0.281440i \(0.0908119\pi\)
−0.959579 + 0.281440i \(0.909188\pi\)
\(194\) 12.5254 1.58233i 0.899274 0.113605i
\(195\) −13.5888 10.6322i −0.973117 0.761390i
\(196\) −8.87473 8.33392i −0.633909 0.595280i
\(197\) 19.0754 + 8.97621i 1.35907 + 0.639529i 0.960672 0.277685i \(-0.0895672\pi\)
0.398395 + 0.917214i \(0.369567\pi\)
\(198\) −15.4175 12.7544i −1.09567 0.906418i
\(199\) −0.0212525 + 0.0654085i −0.00150655 + 0.00463669i −0.951807 0.306698i \(-0.900776\pi\)
0.950300 + 0.311334i \(0.100776\pi\)
\(200\) −36.7364 4.95453i −2.59765 0.350338i
\(201\) 3.43770 + 10.5801i 0.242477 + 0.746266i
\(202\) 1.53351 3.87321i 0.107898 0.272518i
\(203\) −9.63958 + 10.2651i −0.676566 + 0.720470i
\(204\) 16.0919 + 84.3567i 1.12666 + 5.90615i
\(205\) 1.13562 + 2.65478i 0.0793151 + 0.185418i
\(206\) 3.55617 3.33947i 0.247770 0.232672i
\(207\) 23.2732 7.56192i 1.61760 0.525590i
\(208\) 25.9428 + 4.94886i 1.79881 + 0.343142i
\(209\) −0.0558371 0.887505i −0.00386233 0.0613900i
\(210\) 34.7115 5.34851i 2.39532 0.369082i
\(211\) −13.8860 21.8808i −0.955950 1.50634i −0.859587 0.510989i \(-0.829279\pi\)
−0.0963624 0.995346i \(-0.530721\pi\)
\(212\) 44.4665 2.79760i 3.05397 0.192140i
\(213\) −33.6892 21.3798i −2.30835 1.46492i
\(214\) 9.37970 11.3381i 0.641183 0.775057i
\(215\) 16.6857 12.8309i 1.13795 0.875063i
\(216\) 41.8027 + 10.7331i 2.84432 + 0.730296i
\(217\) 3.53208 1.66207i 0.239773 0.112829i
\(218\) 44.9175 + 14.5946i 3.04220 + 0.988469i
\(219\) 15.8097 + 8.69145i 1.06832 + 0.587314i
\(220\) 7.49828 14.5647i 0.505534 0.981955i
\(221\) −16.8855 2.13313i −1.13584 0.143490i
\(222\) −0.250597 + 1.98368i −0.0168190 + 0.133136i
\(223\) −17.2022 + 10.9168i −1.15194 + 0.731046i −0.967767 0.251848i \(-0.918962\pi\)
−0.184177 + 0.982893i \(0.558962\pi\)
\(224\) −18.0956 + 13.1472i −1.20907 + 0.878438i
\(225\) 12.3534 22.0307i 0.823562 1.46871i
\(226\) −10.1820 7.39767i −0.677298 0.492086i
\(227\) −20.6969 1.30214i −1.37370 0.0864259i −0.641295 0.767295i \(-0.721602\pi\)
−0.732406 + 0.680869i \(0.761602\pi\)
\(228\) 3.87999 + 7.05768i 0.256959 + 0.467406i
\(229\) 1.16145 2.46820i 0.0767505 0.163103i −0.862769 0.505598i \(-0.831272\pi\)
0.939520 + 0.342495i \(0.111272\pi\)
\(230\) 14.3138 + 24.4368i 0.943822 + 1.61131i
\(231\) −1.70544 + 8.94024i −0.112210 + 0.588225i
\(232\) −28.9841 39.8932i −1.90290 2.61912i
\(233\) 12.3562 22.4758i 0.809482 1.47244i −0.0705404 0.997509i \(-0.522472\pi\)
0.880022 0.474933i \(-0.157528\pi\)
\(234\) −19.2444 + 30.3244i −1.25805 + 1.98237i
\(235\) 0.837837 1.91405i 0.0546545 0.124859i
\(236\) −29.0348 11.4957i −1.89001 0.748307i
\(237\) 0.168532 + 0.425662i 0.0109473 + 0.0276497i
\(238\) 26.6938 22.0830i 1.73030 1.43143i
\(239\) 7.31314 1.87769i 0.473047 0.121458i −0.00463731 0.999989i \(-0.501476\pi\)
0.477685 + 0.878531i \(0.341476\pi\)
\(240\) −2.19411 + 61.5835i −0.141629 + 3.97520i
\(241\) 6.65527 2.63501i 0.428704 0.169736i −0.143856 0.989599i \(-0.545950\pi\)
0.572560 + 0.819863i \(0.305950\pi\)
\(242\) −15.5793 16.5903i −1.00148 1.06646i
\(243\) 7.99079 10.9984i 0.512610 0.705547i
\(244\) 24.8725 + 52.8568i 1.59230 + 3.38381i
\(245\) 3.43172 + 4.46270i 0.219244 + 0.285111i
\(246\) 8.39496 4.61517i 0.535243 0.294252i
\(247\) −1.56789 + 0.299091i −0.0997623 + 0.0190307i
\(248\) 3.39946 + 13.2400i 0.215866 + 0.840741i
\(249\) 9.15663 0.580278
\(250\) 27.9655 + 8.50801i 1.76869 + 0.538094i
\(251\) −7.84911 −0.495431 −0.247716 0.968833i \(-0.579680\pi\)
−0.247716 + 0.968833i \(0.579680\pi\)
\(252\) −12.8615 50.0923i −0.810200 3.15552i
\(253\) −7.20906 + 1.37520i −0.453230 + 0.0864582i
\(254\) 8.15048 4.48076i 0.511407 0.281148i
\(255\) −1.08075 39.6964i −0.0676792 2.48589i
\(256\) 6.64354 + 14.1182i 0.415221 + 0.882390i
\(257\) −10.3180 + 14.2015i −0.643617 + 0.885862i −0.998802 0.0489337i \(-0.984418\pi\)
0.355186 + 0.934796i \(0.384418\pi\)
\(258\) −47.8049 50.9070i −2.97620 3.16933i
\(259\) 0.530533 0.210053i 0.0329657 0.0130520i
\(260\) −27.6234 10.0762i −1.71313 0.624900i
\(261\) 32.5435 8.35576i 2.01439 0.517208i
\(262\) −23.1929 + 19.1868i −1.43286 + 1.18536i
\(263\) 8.76267 + 22.1320i 0.540329 + 1.36472i 0.901728 + 0.432305i \(0.142299\pi\)
−0.361398 + 0.932412i \(0.617701\pi\)
\(264\) −29.6330 11.7326i −1.82379 0.722089i
\(265\) −20.5028 2.02495i −1.25948 0.124392i
\(266\) 1.74092 2.74326i 0.106743 0.168200i
\(267\) 17.4917 31.8172i 1.07047 1.94718i
\(268\) 11.1434 + 15.3376i 0.680692 + 0.936892i
\(269\) −4.81473 + 25.2397i −0.293559 + 1.53889i 0.463828 + 0.885926i \(0.346476\pi\)
−0.757387 + 0.652966i \(0.773524\pi\)
\(270\) −31.1770 13.6472i −1.89737 0.830539i
\(271\) −6.21921 + 13.2165i −0.377790 + 0.802844i 0.622013 + 0.783007i \(0.286315\pi\)
−0.999803 + 0.0198377i \(0.993685\pi\)
\(272\) 29.2837 + 53.2669i 1.77559 + 3.22978i
\(273\) 16.3043 + 1.02578i 0.986778 + 0.0620828i
\(274\) −25.0948 18.2324i −1.51603 1.10146i
\(275\) −4.50380 + 6.09077i −0.271589 + 0.367287i
\(276\) 53.7744 39.0694i 3.23684 2.35170i
\(277\) 2.04010 1.29469i 0.122578 0.0777902i −0.473124 0.880996i \(-0.656874\pi\)
0.595702 + 0.803205i \(0.296874\pi\)
\(278\) −2.01862 + 15.9790i −0.121069 + 0.958359i
\(279\) −9.24058 1.16736i −0.553219 0.0698878i
\(280\) 31.3389 15.8027i 1.87286 0.944389i
\(281\) 13.5815 + 7.46650i 0.810205 + 0.445414i 0.832289 0.554342i \(-0.187030\pi\)
−0.0220840 + 0.999756i \(0.507030\pi\)
\(282\) −6.59281 2.14213i −0.392596 0.127562i
\(283\) 26.5684 12.5021i 1.57932 0.743174i 0.581789 0.813339i \(-0.302353\pi\)
0.997535 + 0.0701657i \(0.0223528\pi\)
\(284\) −65.8613 16.9103i −3.90815 1.00344i
\(285\) −1.24682 3.50933i −0.0738553 0.207874i
\(286\) 6.86593 8.29948i 0.405991 0.490759i
\(287\) −2.30833 1.46491i −0.136256 0.0864709i
\(288\) 53.2637 3.35107i 3.13859 0.197463i
\(289\) −11.8802 18.7203i −0.698838 1.10119i
\(290\) 17.5076 + 34.7201i 1.02808 + 2.03883i
\(291\) 0.860351 + 13.6749i 0.0504347 + 0.801636i
\(292\) 30.2009 + 5.76112i 1.76737 + 0.337144i
\(293\) −14.0675 + 4.57081i −0.821832 + 0.267030i −0.689601 0.724189i \(-0.742214\pi\)
−0.132231 + 0.991219i \(0.542214\pi\)
\(294\) 13.6154 12.7857i 0.794067 0.745679i
\(295\) 12.3983 + 7.40274i 0.721857 + 0.431004i
\(296\) 0.374410 + 1.96272i 0.0217621 + 0.114081i
\(297\) 6.03736 6.42914i 0.350323 0.373056i
\(298\) −9.98379 + 25.2162i −0.578346 + 1.46073i
\(299\) 4.07071 + 12.5284i 0.235415 + 0.724534i
\(300\) 13.4208 67.2808i 0.774850 3.88446i
\(301\) −6.15850 + 18.9539i −0.354970 + 1.09249i
\(302\) 17.3433 + 14.3476i 0.997995 + 0.825614i
\(303\) 4.09081 + 1.92499i 0.235011 + 0.110588i
\(304\) 4.15561 + 3.90238i 0.238341 + 0.223817i
\(305\) −7.42734 25.9715i −0.425288 1.48712i
\(306\) −82.0096 + 10.3602i −4.68818 + 0.592255i
\(307\) 17.9259i 1.02309i −0.859257 0.511544i \(-0.829074\pi\)
0.859257 0.511544i \(-0.170926\pi\)
\(308\) 1.94397 + 15.3881i 0.110768 + 0.876821i
\(309\) 3.37484 + 4.07948i 0.191988 + 0.232074i
\(310\) −0.969358 10.7355i −0.0550559 0.609735i
\(311\) 0.615247 9.77907i 0.0348875 0.554520i −0.941297 0.337579i \(-0.890392\pi\)
0.976185 0.216941i \(-0.0696080\pi\)
\(312\) −14.2267 + 55.4093i −0.805427 + 3.13693i
\(313\) −1.80493 + 7.02973i −0.102021 + 0.397344i −0.998999 0.0447301i \(-0.985757\pi\)
0.896979 + 0.442074i \(0.145757\pi\)
\(314\) −2.59218 + 41.2016i −0.146285 + 2.32514i
\(315\) 2.15062 + 23.8178i 0.121174 + 1.34198i
\(316\) 0.497311 + 0.601146i 0.0279760 + 0.0338171i
\(317\) 0.790970 + 6.26117i 0.0444253 + 0.351663i 0.998622 + 0.0524821i \(0.0167132\pi\)
−0.954197 + 0.299180i \(0.903287\pi\)
\(318\) 68.3544i 3.83313i
\(319\) −9.99723 + 1.26294i −0.559737 + 0.0707113i
\(320\) 5.04005 + 17.6237i 0.281748 + 0.985197i
\(321\) 11.6418 + 10.9324i 0.649782 + 0.610186i
\(322\) −24.2623 11.4170i −1.35209 0.636243i
\(323\) −2.83060 2.34168i −0.157499 0.130294i
\(324\) −2.03771 + 6.27144i −0.113206 + 0.348413i
\(325\) 11.8595 + 6.65006i 0.657847 + 0.368879i
\(326\) 12.4265 + 38.2449i 0.688242 + 2.11819i
\(327\) −18.8693 + 47.6583i −1.04347 + 2.63551i
\(328\) 6.55355 6.97882i 0.361859 0.385341i
\(329\) 0.370693 + 1.94324i 0.0204370 + 0.107134i
\(330\) 21.5785 + 12.8840i 1.18786 + 0.709243i
\(331\) −20.9419 + 19.6657i −1.15107 + 1.08093i −0.155410 + 0.987850i \(0.549670\pi\)
−0.995659 + 0.0930752i \(0.970330\pi\)
\(332\) 14.8407 4.82205i 0.814492 0.264644i
\(333\) −1.33735 0.255113i −0.0732863 0.0139801i
\(334\) −0.837817 13.3167i −0.0458433 0.728658i
\(335\) −3.94712 7.82772i −0.215654 0.427674i
\(336\) −31.2632 49.2629i −1.70555 2.68751i
\(337\) 11.0925 0.697882i 0.604248 0.0380161i 0.242280 0.970206i \(-0.422105\pi\)
0.361968 + 0.932190i \(0.382105\pi\)
\(338\) 12.3734 + 7.85238i 0.673023 + 0.427113i
\(339\) 8.70674 10.5246i 0.472885 0.571620i
\(340\) −22.6565 63.7694i −1.22872 3.45838i
\(341\) 2.70560 + 0.694681i 0.146517 + 0.0376191i
\(342\) −7.01445 + 3.30075i −0.379298 + 0.178484i
\(343\) −19.1641 6.22680i −1.03477 0.336216i
\(344\) −61.1555 33.6205i −3.29728 1.81270i
\(345\) −27.4444 + 13.8388i −1.47756 + 0.745057i
\(346\) 48.4227 + 6.11720i 2.60322 + 0.328863i
\(347\) 2.18132 17.2669i 0.117099 0.926937i −0.818655 0.574285i \(-0.805280\pi\)
0.935755 0.352652i \(-0.114720\pi\)
\(348\) 77.0560 48.9012i 4.13064 2.62138i
\(349\) 6.80186 4.94184i 0.364095 0.264531i −0.390663 0.920534i \(-0.627754\pi\)
0.754758 + 0.656003i \(0.227754\pi\)
\(350\) −26.3929 + 8.33129i −1.41076 + 0.445326i
\(351\) −12.8071 9.30487i −0.683590 0.496657i
\(352\) −15.9743 1.00502i −0.851432 0.0535676i
\(353\) −4.26094 7.75062i −0.226787 0.412524i 0.738293 0.674480i \(-0.235632\pi\)
−0.965080 + 0.261957i \(0.915632\pi\)
\(354\) 20.3987 43.3493i 1.08418 2.30399i
\(355\) 28.8043 + 12.6085i 1.52878 + 0.669192i
\(356\) 11.5943 60.7797i 0.614499 3.22132i
\(357\) 22.1004 + 30.4186i 1.16968 + 1.60992i
\(358\) −2.54509 + 4.62951i −0.134512 + 0.244677i
\(359\) −13.8884 + 21.8846i −0.733002 + 1.15503i 0.249427 + 0.968393i \(0.419758\pi\)
−0.982430 + 0.186633i \(0.940242\pi\)
\(360\) −83.3382 8.23084i −4.39231 0.433803i
\(361\) 17.3454 + 6.86754i 0.912917 + 0.361449i
\(362\) −15.3542 38.7802i −0.806998 2.03824i
\(363\) 19.0316 15.7443i 0.998901 0.826363i
\(364\) 26.9655 6.92358i 1.41338 0.362894i
\(365\) −13.3563 4.87198i −0.699101 0.255011i
\(366\) −83.3279 + 32.9918i −4.35562 + 1.72451i
\(367\) −0.116994 0.124586i −0.00610704 0.00650334i 0.725908 0.687792i \(-0.241420\pi\)
−0.732015 + 0.681289i \(0.761420\pi\)
\(368\) 27.6539 38.0623i 1.44156 1.98414i
\(369\) 2.77743 + 5.90235i 0.144587 + 0.307264i
\(370\) −0.0428813 1.57505i −0.00222929 0.0818828i
\(371\) 17.0941 9.39757i 0.887483 0.487898i
\(372\) −24.8510 + 4.74058i −1.28846 + 0.245787i
\(373\) −6.66270 25.9495i −0.344981 1.34361i −0.870222 0.492660i \(-0.836025\pi\)
0.525240 0.850954i \(-0.323975\pi\)
\(374\) 24.7909 1.28191
\(375\) −11.1213 + 29.7113i −0.574301 + 1.53429i
\(376\) −6.92747 −0.357257
\(377\) 4.49805 + 17.5187i 0.231661 + 0.902261i
\(378\) 31.6526 6.03805i 1.62803 0.310564i
\(379\) −12.1914 + 6.70225i −0.626228 + 0.344272i −0.763065 0.646322i \(-0.776306\pi\)
0.136837 + 0.990594i \(0.456306\pi\)
\(380\) −3.86888 5.03119i −0.198469 0.258095i
\(381\) 4.29796 + 9.13363i 0.220191 + 0.467930i
\(382\) 28.6022 39.3676i 1.46342 2.01422i
\(383\) −11.4184 12.1594i −0.583453 0.621314i 0.367733 0.929931i \(-0.380134\pi\)
−0.951186 + 0.308617i \(0.900134\pi\)
\(384\) 0.799035 0.316360i 0.0407756 0.0161442i
\(385\) 0.255373 7.16770i 0.0130150 0.365300i
\(386\) −19.8025 + 5.08442i −1.00792 + 0.258790i
\(387\) 36.6392 30.3106i 1.86247 1.54077i
\(388\) 8.59587 + 21.7107i 0.436389 + 1.10219i
\(389\) −14.0216 5.55155i −0.710924 0.281475i −0.0153020 0.999883i \(-0.504871\pi\)
−0.695622 + 0.718408i \(0.744871\pi\)
\(390\) 18.0892 41.3250i 0.915984 2.09257i
\(391\) −16.2456 + 25.5989i −0.821573 + 1.29459i
\(392\) 8.99203 16.3564i 0.454166 0.826125i
\(393\) −19.2019 26.4291i −0.968606 1.33317i
\(394\) −10.3282 + 54.1423i −0.520327 + 2.72765i
\(395\) −0.182342 0.311299i −0.00917463 0.0156631i
\(396\) 15.7573 33.4860i 0.791834 1.68273i
\(397\) 3.48872 + 6.34595i 0.175094 + 0.318494i 0.949262 0.314485i \(-0.101832\pi\)
−0.774169 + 0.632979i \(0.781832\pi\)
\(398\) −0.179457 0.0112905i −0.00899535 0.000565940i
\(399\) 2.85275 + 2.07264i 0.142816 + 0.103762i
\(400\) −5.68163 48.2271i −0.284081 2.41136i
\(401\) −3.99026 + 2.89909i −0.199264 + 0.144774i −0.682943 0.730472i \(-0.739300\pi\)
0.483679 + 0.875245i \(0.339300\pi\)
\(402\) −24.5576 + 15.5847i −1.22482 + 0.777296i
\(403\) 0.628408 4.97436i 0.0313032 0.247790i
\(404\) 7.64397 + 0.965658i 0.380302 + 0.0480433i
\(405\) 1.39572 2.71106i 0.0693538 0.134714i
\(406\) −32.2627 17.7366i −1.60117 0.880251i
\(407\) 0.388332 + 0.126177i 0.0192489 + 0.00625435i
\(408\) −119.133 + 56.0599i −5.89798 + 2.77538i
\(409\) 8.34584 + 2.14285i 0.412675 + 0.105957i 0.449319 0.893371i \(-0.351667\pi\)
−0.0366437 + 0.999328i \(0.511667\pi\)
\(410\) −5.98449 + 4.60195i −0.295553 + 0.227274i
\(411\) 21.4588 25.9392i 1.05848 1.27949i
\(412\) 7.61815 + 4.83463i 0.375319 + 0.238185i
\(413\) −13.6453 + 0.858489i −0.671441 + 0.0422435i
\(414\) 34.2818 + 54.0195i 1.68486 + 2.65491i
\(415\) −7.13157 + 1.09887i −0.350075 + 0.0539412i
\(416\) 1.80394 + 28.6727i 0.0884452 + 1.40580i
\(417\) −17.1703 3.27541i −0.840833 0.160398i
\(418\) 2.21118 0.718456i 0.108152 0.0351409i
\(419\) 15.2436 14.3147i 0.744697 0.699317i −0.216161 0.976358i \(-0.569354\pi\)
0.960858 + 0.277040i \(0.0893536\pi\)
\(420\) 25.5475 + 59.7233i 1.24659 + 2.91420i
\(421\) −3.38424 17.7408i −0.164938 0.864634i −0.964506 0.264059i \(-0.914938\pi\)
0.799569 0.600575i \(-0.205062\pi\)
\(422\) 46.3815 49.3913i 2.25782 2.40433i
\(423\) 1.73762 4.38873i 0.0844861 0.213387i
\(424\) 21.1086 + 64.9657i 1.02513 + 3.15501i
\(425\) 5.60561 + 30.7875i 0.271912 + 1.49341i
\(426\) 32.2368 99.2147i 1.56188 4.80697i
\(427\) 19.7068 + 16.3029i 0.953678 + 0.788951i
\(428\) 24.6258 + 11.5880i 1.19033 + 0.560128i
\(429\) 8.52178 + 8.00249i 0.411436 + 0.386364i
\(430\) 43.3417 + 33.9116i 2.09012 + 1.63536i
\(431\) 27.8749 3.52142i 1.34269 0.169621i 0.579063 0.815283i \(-0.303419\pi\)
0.763623 + 0.645662i \(0.223419\pi\)
\(432\) 56.5381i 2.72019i
\(433\) 0.658486 + 5.21246i 0.0316448 + 0.250495i 1.00000 0.000916837i \(0.000291838\pi\)
−0.968355 + 0.249578i \(0.919708\pi\)
\(434\) 6.50553 + 7.86383i 0.312275 + 0.377476i
\(435\) −38.8005 + 16.5975i −1.86034 + 0.795788i
\(436\) −5.48489 + 87.1798i −0.262678 + 4.17515i
\(437\) −0.707120 + 2.75405i −0.0338261 + 0.131744i
\(438\) −11.7305 + 45.6871i −0.560503 + 2.18302i
\(439\) −0.489441 + 7.77944i −0.0233597 + 0.371292i 0.968929 + 0.247341i \(0.0795568\pi\)
−0.992288 + 0.123952i \(0.960443\pi\)
\(440\) 24.4875 + 5.58161i 1.16739 + 0.266093i
\(441\) 8.10676 + 9.79939i 0.386036 + 0.466637i
\(442\) −5.57708 44.1472i −0.265275 2.09987i
\(443\) 1.17325i 0.0557427i 0.999612 + 0.0278713i \(0.00887287\pi\)
−0.999612 + 0.0278713i \(0.991127\pi\)
\(444\) −3.66890 + 0.463490i −0.174118 + 0.0219963i
\(445\) −9.80494 + 26.8797i −0.464799 + 1.27422i
\(446\) −38.8303 36.4641i −1.83867 1.72662i
\(447\) −26.6328 12.5325i −1.25969 0.592765i
\(448\) −13.3727 11.0628i −0.631798 0.522669i
\(449\) 10.4879 32.2784i 0.494954 1.52331i −0.322075 0.946714i \(-0.604380\pi\)
0.817029 0.576597i \(-0.195620\pi\)
\(450\) 63.8220 + 16.9590i 3.00860 + 0.799456i
\(451\) −0.604549 1.86061i −0.0284671 0.0876128i
\(452\) 8.56910 21.6431i 0.403057 1.01801i
\(453\) −16.7227 + 17.8079i −0.785700 + 0.836686i
\(454\) −10.1596 53.2587i −0.476816 2.49956i
\(455\) −12.8215 + 1.15772i −0.601083 + 0.0542746i
\(456\) −9.00122 + 8.45271i −0.421521 + 0.395834i
\(457\) 19.9999 6.49835i 0.935554 0.303980i 0.198722 0.980056i \(-0.436321\pi\)
0.736832 + 0.676076i \(0.236321\pi\)
\(458\) 7.00555 + 1.33638i 0.327348 + 0.0624450i
\(459\) −2.28775 36.3627i −0.106783 1.69727i
\(460\) −37.1931 + 36.8822i −1.73414 + 1.71964i
\(461\) −5.23092 8.24260i −0.243628 0.383896i 0.700406 0.713745i \(-0.253002\pi\)
−0.944034 + 0.329848i \(0.893002\pi\)
\(462\) −23.7489 + 1.49415i −1.10490 + 0.0695142i
\(463\) −15.5248 9.85233i −0.721498 0.457877i 0.123707 0.992319i \(-0.460522\pi\)
−0.845205 + 0.534442i \(0.820522\pi\)
\(464\) 41.1760 49.7732i 1.91155 2.31066i
\(465\) 11.6943 0.318383i 0.542311 0.0147646i
\(466\) 64.9511 + 16.6766i 3.00880 + 0.772529i
\(467\) 14.5223 6.83369i 0.672013 0.316225i −0.0593266 0.998239i \(-0.518895\pi\)
0.731340 + 0.682013i \(0.238895\pi\)
\(468\) −63.1759 20.5271i −2.92031 0.948865i
\(469\) 7.27369 + 3.99875i 0.335868 + 0.184645i
\(470\) 5.39183 + 0.877195i 0.248706 + 0.0404620i
\(471\) −44.4513 5.61550i −2.04821 0.258749i
\(472\) 6.00059 47.4996i 0.276200 2.18634i
\(473\) −12.0411 + 7.64153i −0.553651 + 0.351358i
\(474\) −0.968353 + 0.703550i −0.0444779 + 0.0323151i
\(475\) 1.39222 + 2.58358i 0.0638796 + 0.118543i
\(476\) 51.8385 + 37.6628i 2.37601 + 1.72627i
\(477\) −46.4521 2.92252i −2.12690 0.133813i
\(478\) 9.51002 + 17.2987i 0.434978 + 0.791222i
\(479\) 6.56458 13.9504i 0.299943 0.637412i −0.696869 0.717199i \(-0.745424\pi\)
0.996812 + 0.0797870i \(0.0254240\pi\)
\(480\) −65.4793 + 14.3481i −2.98871 + 0.654896i
\(481\) 0.137332 0.719918i 0.00626179 0.0328254i
\(482\) 11.0001 + 15.1403i 0.501040 + 0.689622i
\(483\) 14.0198 25.5020i 0.637924 1.16038i
\(484\) 22.5545 35.5402i 1.02521 1.61547i
\(485\) −2.31117 10.5473i −0.104945 0.478930i
\(486\) 33.0476 + 13.0845i 1.49907 + 0.593523i
\(487\) 5.50598 + 13.9065i 0.249500 + 0.630164i 0.999511 0.0312606i \(-0.00995217\pi\)
−0.750012 + 0.661425i \(0.769952\pi\)
\(488\) −69.0085 + 57.0888i −3.12387 + 2.58429i
\(489\) −42.2722 + 10.8537i −1.91162 + 0.490819i
\(490\) −9.06987 + 11.5920i −0.409735 + 0.523674i
\(491\) 8.86528 3.51001i 0.400084 0.158405i −0.159461 0.987204i \(-0.550976\pi\)
0.559546 + 0.828800i \(0.310976\pi\)
\(492\) 12.1291 + 12.9162i 0.546824 + 0.582308i
\(493\) −24.4685 + 33.6779i −1.10200 + 1.51678i
\(494\) −1.77685 3.77600i −0.0799442 0.169890i
\(495\) −9.67830 + 14.1134i −0.435007 + 0.634350i
\(496\) −15.6921 + 8.62681i −0.704596 + 0.387355i
\(497\) −29.2437 + 5.57853i −1.31176 + 0.250231i
\(498\) 5.95365 + 23.1880i 0.266790 + 1.03908i
\(499\) 6.23772 0.279239 0.139619 0.990205i \(-0.455412\pi\)
0.139619 + 0.990205i \(0.455412\pi\)
\(500\) −2.37847 + 54.0117i −0.106368 + 2.41548i
\(501\) 14.4812 0.646974
\(502\) −5.10350 19.8768i −0.227780 0.887146i
\(503\) 36.8604 7.03150i 1.64352 0.313519i 0.719107 0.694900i \(-0.244551\pi\)
0.924418 + 0.381381i \(0.124551\pi\)
\(504\) 69.4828 38.1985i 3.09501 1.70149i
\(505\) −3.41711 1.00833i −0.152059 0.0448702i
\(506\) −8.16985 17.3618i −0.363194 0.771827i
\(507\) −9.34860 + 12.8672i −0.415186 + 0.571454i
\(508\) 11.7759 + 12.5401i 0.522472 + 0.556376i
\(509\) −19.3757 + 7.67139i −0.858814 + 0.340028i −0.755920 0.654664i \(-0.772810\pi\)
−0.102894 + 0.994692i \(0.532810\pi\)
\(510\) 99.8231 28.5475i 4.42024 1.26410i
\(511\) 13.0382 3.34764i 0.576776 0.148091i
\(512\) −31.8996 + 26.3897i −1.40978 + 1.16627i
\(513\) −1.25786 3.17700i −0.0555360 0.140268i
\(514\) −42.6720 16.8950i −1.88218 0.745209i
\(515\) −3.11804 2.77227i −0.137397 0.122161i
\(516\) 69.2082 109.055i 3.04672 4.80086i
\(517\) −0.681987 + 1.24053i −0.0299937 + 0.0545584i
\(518\) 0.876884 + 1.20693i 0.0385281 + 0.0530293i
\(519\) −9.92576 + 52.0327i −0.435692 + 2.28398i
\(520\) 4.43080 44.8624i 0.194303 1.96735i
\(521\) −2.08919 + 4.43976i −0.0915292 + 0.194509i −0.945350 0.326058i \(-0.894280\pi\)
0.853821 + 0.520567i \(0.174280\pi\)
\(522\) 42.3197 + 76.9792i 1.85228 + 3.36929i
\(523\) −26.8011 1.68618i −1.17193 0.0737317i −0.535137 0.844765i \(-0.679740\pi\)
−0.636794 + 0.771034i \(0.719740\pi\)
\(524\) −45.0398 32.7233i −1.96757 1.42952i
\(525\) −7.22554 29.1555i −0.315348 1.27245i
\(526\) −50.3488 + 36.5805i −2.19531 + 1.59499i
\(527\) 9.74335 6.18332i 0.424427 0.269350i
\(528\) 5.23284 41.4222i 0.227730 1.80267i
\(529\) 0.462733 + 0.0584568i 0.0201188 + 0.00254160i
\(530\) −8.20306 53.2373i −0.356318 2.31248i
\(531\) 28.5871 + 15.7159i 1.24057 + 0.682011i
\(532\) 5.71513 + 1.85696i 0.247782 + 0.0805093i
\(533\) −3.17733 + 1.49514i −0.137626 + 0.0647617i
\(534\) 91.9460 + 23.6077i 3.97889 + 1.02161i
\(535\) −10.3791 7.11749i −0.448727 0.307716i
\(536\) −18.5274 + 22.3958i −0.800261 + 0.967350i
\(537\) −4.84106 3.07223i −0.208907 0.132577i
\(538\) −67.0467 + 4.21822i −2.89059 + 0.181860i
\(539\) −2.04378 3.22048i −0.0880317 0.138716i
\(540\) 10.1077 62.1288i 0.434968 2.67360i
\(541\) −2.34914 37.3385i −0.100997 1.60531i −0.643631 0.765336i \(-0.722573\pi\)
0.542633 0.839970i \(-0.317427\pi\)
\(542\) −37.5127 7.15593i −1.61131 0.307374i
\(543\) 43.0516 13.9883i 1.84752 0.600296i
\(544\) −48.2012 + 45.2640i −2.06661 + 1.94068i
\(545\) 8.97681 39.3827i 0.384524 1.68697i
\(546\) 8.00340 + 41.9553i 0.342514 + 1.79552i
\(547\) −3.88401 + 4.13606i −0.166068 + 0.176845i −0.806620 0.591070i \(-0.798706\pi\)
0.640552 + 0.767915i \(0.278706\pi\)
\(548\) 21.1196 53.3420i 0.902184 2.27866i
\(549\) −18.8578 58.0383i −0.804831 2.47701i
\(550\) −18.3524 7.44505i −0.782550 0.317458i
\(551\) −1.20641 + 3.71295i −0.0513948 + 0.158177i
\(552\) 78.5207 + 64.9580i 3.34206 + 2.76480i
\(553\) 0.309076 + 0.145440i 0.0131433 + 0.00618475i
\(554\) 4.60510 + 4.32447i 0.195652 + 0.183729i
\(555\) 1.70895 + 0.0608869i 0.0725410 + 0.00258451i
\(556\) −29.5539 + 3.73353i −1.25336 + 0.158337i
\(557\) 35.5369i 1.50575i 0.658166 + 0.752873i \(0.271332\pi\)
−0.658166 + 0.752873i \(0.728668\pi\)
\(558\) −3.05206 24.1595i −0.129204 1.02275i
\(559\) 16.3167 + 19.7235i 0.690122 + 0.834215i
\(560\) 30.2610 + 34.6162i 1.27876 + 1.46280i
\(561\) −1.68942 + 26.8526i −0.0713274 + 1.13372i
\(562\) −10.0772 + 39.2481i −0.425081 + 1.65558i
\(563\) 10.7608 41.9107i 0.453515 1.76632i −0.170959 0.985278i \(-0.554687\pi\)
0.624474 0.781046i \(-0.285313\pi\)
\(564\) 0.805049 12.7959i 0.0338987 0.538804i
\(565\) −5.51814 + 9.24191i −0.232150 + 0.388810i
\(566\) 48.9347 + 59.1519i 2.05688 + 2.48634i
\(567\) 0.361849 + 2.86433i 0.0151962 + 0.120290i
\(568\) 104.251i 4.37427i
\(569\) −33.1894 + 4.19279i −1.39137 + 0.175771i −0.785042 0.619443i \(-0.787359\pi\)
−0.606329 + 0.795214i \(0.707359\pi\)
\(570\) 8.07621 5.43917i 0.338275 0.227822i
\(571\) 8.79856 + 8.26240i 0.368208 + 0.345771i 0.846460 0.532452i \(-0.178729\pi\)
−0.478252 + 0.878223i \(0.658729\pi\)
\(572\) 18.0261 + 8.48242i 0.753708 + 0.354668i
\(573\) 40.6923 + 33.6636i 1.69995 + 1.40632i
\(574\) 2.20881 6.79802i 0.0921939 0.283744i
\(575\) 19.7141 14.0718i 0.822134 0.586834i
\(576\) 12.7965 + 39.3837i 0.533189 + 1.64099i
\(577\) 8.41059 21.2427i 0.350138 0.884346i −0.642835 0.766004i \(-0.722242\pi\)
0.992973 0.118342i \(-0.0377579\pi\)
\(578\) 39.6820 42.2571i 1.65055 1.75766i
\(579\) −4.15777 21.7958i −0.172791 0.905802i
\(580\) −54.1459 + 47.3336i −2.24829 + 1.96542i
\(581\) 4.98033 4.67684i 0.206619 0.194028i
\(582\) −34.0704 + 11.0702i −1.41226 + 0.458873i
\(583\) 13.7117 + 2.61565i 0.567882 + 0.108329i
\(584\) 2.95980 + 47.0446i 0.122477 + 1.94672i
\(585\) 27.3101 + 14.0599i 1.12913 + 0.581305i
\(586\) −20.7217 32.6521i −0.856004 1.34885i
\(587\) 24.2725 1.52709i 1.00183 0.0630299i 0.446607 0.894730i \(-0.352632\pi\)
0.555225 + 0.831700i \(0.312632\pi\)
\(588\) 29.1674 + 18.5102i 1.20284 + 0.763347i
\(589\) 0.689844 0.833878i 0.0284245 0.0343593i
\(590\) −10.6851 + 36.2103i −0.439898 + 1.49075i
\(591\) −57.9410 14.8767i −2.38337 0.611946i
\(592\) −2.36843 + 1.11450i −0.0973418 + 0.0458056i
\(593\) 37.0688 + 12.0444i 1.52223 + 0.494604i 0.946409 0.322969i \(-0.104681\pi\)
0.575825 + 0.817573i \(0.304681\pi\)
\(594\) 20.2064 + 11.1086i 0.829080 + 0.455790i
\(595\) −20.8632 21.0390i −0.855306 0.862516i
\(596\) −49.7653 6.28683i −2.03847 0.257518i
\(597\) 0.0244588 0.193611i 0.00100103 0.00792397i
\(598\) −29.0796 + 18.4545i −1.18915 + 0.754660i
\(599\) 1.89604 1.37756i 0.0774703 0.0562855i −0.548376 0.836232i \(-0.684754\pi\)
0.625846 + 0.779946i \(0.284754\pi\)
\(600\) 105.028 5.72313i 4.28777 0.233646i
\(601\) −10.9984 7.99079i −0.448633 0.325951i 0.340423 0.940272i \(-0.389430\pi\)
−0.789056 + 0.614321i \(0.789430\pi\)
\(602\) −52.0025 3.27172i −2.11946 0.133345i
\(603\) −9.54106 17.3551i −0.388542 0.706755i
\(604\) −17.7256 + 37.6688i −0.721244 + 1.53272i
\(605\) −12.9332 + 14.5463i −0.525809 + 0.591391i
\(606\) −2.21493 + 11.6110i −0.0899752 + 0.471667i
\(607\) 19.6071 + 26.9868i 0.795827 + 1.09536i 0.993358 + 0.115065i \(0.0367077\pi\)
−0.197531 + 0.980297i \(0.563292\pi\)
\(608\) −2.98744 + 5.43413i −0.121157 + 0.220383i
\(609\) 21.4101 33.7370i 0.867583 1.36709i
\(610\) 60.9400 35.6954i 2.46739 1.44526i
\(611\) 2.36253 + 0.935392i 0.0955777 + 0.0378419i
\(612\) −56.2810 142.150i −2.27503 5.74606i
\(613\) −0.218964 + 0.181143i −0.00884388 + 0.00731630i −0.641835 0.766842i \(-0.721827\pi\)
0.632992 + 0.774159i \(0.281827\pi\)
\(614\) 45.3950 11.6555i 1.83199 0.470376i
\(615\) −4.57682 6.79577i −0.184555 0.274032i
\(616\) −22.1100 + 8.75399i −0.890839 + 0.352708i
\(617\) −23.5949 25.1260i −0.949895 1.01154i −0.999918 0.0127870i \(-0.995930\pi\)
0.0500236 0.998748i \(-0.484070\pi\)
\(618\) −8.13642 + 11.1988i −0.327295 + 0.450483i
\(619\) −11.2284 23.8616i −0.451308 0.959079i −0.992957 0.118474i \(-0.962200\pi\)
0.541649 0.840605i \(-0.317800\pi\)
\(620\) 18.7861 6.67447i 0.754467 0.268053i
\(621\) −24.7119 + 13.5855i −0.991655 + 0.545167i
\(622\) 25.1642 4.80033i 1.00899 0.192476i
\(623\) −6.73718 26.2396i −0.269919 1.05127i
\(624\) −74.9410 −3.00004
\(625\) 5.09614 24.4751i 0.203846 0.979003i
\(626\) −18.9754 −0.758411
\(627\) 0.627519 + 2.44403i 0.0250607 + 0.0976050i
\(628\) −75.0022 + 14.3074i −2.99292 + 0.570929i
\(629\) 1.47816 0.812628i 0.0589383 0.0324016i
\(630\) −58.9171 + 20.9325i −2.34731 + 0.833972i
\(631\) −14.4360 30.6781i −0.574689 1.22128i −0.955052 0.296440i \(-0.904201\pi\)
0.380362 0.924838i \(-0.375799\pi\)
\(632\) −0.703081 + 0.967708i −0.0279671 + 0.0384934i
\(633\) 50.3379 + 53.6045i 2.00075 + 2.13059i
\(634\) −15.3413 + 6.07405i −0.609281 + 0.241231i
\(635\) −4.44354 6.59787i −0.176336 0.261828i
\(636\) −122.453 + 31.4405i −4.85556 + 1.24670i
\(637\) −5.27518 + 4.36400i −0.209010 + 0.172908i
\(638\) −9.69845 24.4955i −0.383965 0.969785i
\(639\) 66.0457 + 26.1493i 2.61273 + 1.03445i
\(640\) −0.584356 + 0.342285i −0.0230987 + 0.0135300i
\(641\) 22.4086 35.3103i 0.885087 1.39467i −0.0334938 0.999439i \(-0.510663\pi\)
0.918580 0.395234i \(-0.129337\pi\)
\(642\) −20.1153 + 36.5895i −0.793887 + 1.44407i
\(643\) 19.2326 + 26.4714i 0.758460 + 1.04393i 0.997341 + 0.0728815i \(0.0232195\pi\)
−0.238881 + 0.971049i \(0.576781\pi\)
\(644\) 9.29303 48.7158i 0.366197 1.91967i
\(645\) −39.6853 + 44.6350i −1.56261 + 1.75750i
\(646\) 4.08952 8.69068i 0.160900 0.341930i
\(647\) −4.13612 7.52358i −0.162608 0.295782i 0.782433 0.622735i \(-0.213978\pi\)
−0.945041 + 0.326952i \(0.893978\pi\)
\(648\) −10.0900 0.634807i −0.396371 0.0249376i
\(649\) −7.91519 5.75072i −0.310698 0.225736i
\(650\) −9.12934 + 34.3565i −0.358082 + 1.34757i
\(651\) −8.96112 + 6.51064i −0.351214 + 0.255172i
\(652\) −62.7976 + 39.8525i −2.45934 + 1.56075i
\(653\) −6.01723 + 47.6313i −0.235472 + 1.86396i 0.222423 + 0.974950i \(0.428603\pi\)
−0.457896 + 0.889006i \(0.651397\pi\)
\(654\) −132.957 16.7964i −5.19903 0.656790i
\(655\) 18.1269 + 18.2797i 0.708277 + 0.714248i
\(656\) 10.9901 + 6.04188i 0.429093 + 0.235896i
\(657\) −30.5464 9.92512i −1.19173 0.387216i
\(658\) −4.67997 + 2.20223i −0.182444 + 0.0858517i
\(659\) −30.1718 7.74680i −1.17533 0.301773i −0.389977 0.920825i \(-0.627517\pi\)
−0.785350 + 0.619052i \(0.787517\pi\)
\(660\) −13.1556 + 44.5827i −0.512083 + 1.73538i
\(661\) −6.88953 + 8.32801i −0.267972 + 0.323922i −0.887285 0.461222i \(-0.847411\pi\)
0.619313 + 0.785144i \(0.287411\pi\)
\(662\) −63.4172 40.2458i −2.46478 1.56420i
\(663\) 48.1985 3.03240i 1.87188 0.117768i
\(664\) 12.8192 + 20.1998i 0.497481 + 0.783905i
\(665\) −2.47057 1.27191i −0.0958047 0.0493226i
\(666\) −0.223507 3.55253i −0.00866070 0.137658i
\(667\) 31.6492 + 6.03741i 1.22546 + 0.233769i
\(668\) 23.4707 7.62609i 0.908108 0.295062i
\(669\) 42.1426 39.5746i 1.62933 1.53004i
\(670\) 17.2562 15.0852i 0.666666 0.582790i
\(671\) 3.42945 + 17.9778i 0.132393 + 0.694026i
\(672\) 43.4470 46.2664i 1.67600 1.78476i
\(673\) 2.37890 6.00841i 0.0916997 0.231607i −0.876687 0.481062i \(-0.840251\pi\)
0.968386 + 0.249455i \(0.0802513\pi\)
\(674\) 8.97966 + 27.6365i 0.345884 + 1.06452i
\(675\) −9.22661 + 27.6059i −0.355132 + 1.06255i
\(676\) −8.37575 + 25.7779i −0.322144 + 0.991458i
\(677\) 3.21881 + 2.66283i 0.123709 + 0.102341i 0.697221 0.716856i \(-0.254419\pi\)
−0.573512 + 0.819197i \(0.694419\pi\)
\(678\) 32.3134 + 15.2055i 1.24099 + 0.583964i
\(679\) 7.45253 + 6.99839i 0.286002 + 0.268574i
\(680\) 86.0584 57.9587i 3.30019 2.22262i
\(681\) 58.3801 7.37512i 2.23713 0.282615i
\(682\) 7.30326i 0.279656i
\(683\) −1.27779 10.1148i −0.0488933 0.387030i −0.997505 0.0705892i \(-0.977512\pi\)
0.948612 0.316441i \(-0.102488\pi\)
\(684\) −9.13946 11.0477i −0.349456 0.422420i
\(685\) −13.6001 + 22.7778i −0.519633 + 0.870295i
\(686\) 3.30801 52.5793i 0.126300 2.00749i
\(687\) −1.92492 + 7.49707i −0.0734403 + 0.286031i
\(688\) 22.7359 88.5504i 0.866797 3.37595i
\(689\) 1.57324 25.0060i 0.0599358 0.952652i
\(690\) −52.8893 60.5012i −2.01346 2.30324i
\(691\) −22.0360 26.6370i −0.838290 1.01332i −0.999651 0.0264230i \(-0.991588\pi\)
0.161361 0.986895i \(-0.448412\pi\)
\(692\) 11.3140 + 89.5598i 0.430095 + 3.40455i
\(693\) 16.2031i 0.615503i
\(694\) 45.1445 5.70307i 1.71366 0.216486i
\(695\) 13.7660 + 0.490459i 0.522175 + 0.0186042i
\(696\) 101.998 + 95.7823i 3.86622 + 3.63062i
\(697\) −7.31282 3.44115i −0.276993 0.130343i
\(698\) 16.9371 + 14.0116i 0.641079 + 0.530347i
\(699\) −22.4896 + 69.2160i −0.850637 + 2.61799i
\(700\) −27.0647 43.4491i −1.02295 1.64222i
\(701\) 7.25228 + 22.3202i 0.273915 + 0.843024i 0.989504 + 0.144503i \(0.0461582\pi\)
−0.715589 + 0.698521i \(0.753842\pi\)
\(702\) 15.2362 38.4822i 0.575053 1.45242i
\(703\) 0.108292 0.115319i 0.00408430 0.00434934i
\(704\) −2.32716 12.1994i −0.0877082 0.459783i
\(705\) −1.31758 + 5.78044i −0.0496229 + 0.217704i
\(706\) 16.8569 15.8297i 0.634419 0.595759i
\(707\) 3.20821 1.04241i 0.120657 0.0392039i
\(708\) 87.0402 + 16.6038i 3.27117 + 0.624009i
\(709\) 1.30770 + 20.7853i 0.0491117 + 0.780608i 0.943098 + 0.332514i \(0.107897\pi\)
−0.893986 + 0.448094i \(0.852103\pi\)
\(710\) −13.2009 + 81.1412i −0.495419 + 3.04518i
\(711\) −0.436714 0.688151i −0.0163781 0.0258077i
\(712\) 94.6780 5.95663i 3.54821 0.223234i
\(713\) −7.54128 4.78584i −0.282423 0.179231i
\(714\) −62.6612 + 75.7444i −2.34504 + 2.83466i
\(715\) −7.59748 5.20999i −0.284130 0.194843i
\(716\) −9.46412 2.42997i −0.353691 0.0908123i
\(717\) −19.3853 + 9.12203i −0.723958 + 0.340669i
\(718\) −64.4502 20.9411i −2.40526 0.781516i
\(719\) −42.3226 23.2671i −1.57837 0.867715i −0.998598 0.0529355i \(-0.983142\pi\)
−0.579770 0.814780i \(-0.696858\pi\)
\(720\) −16.7067 108.425i −0.622622 4.04077i
\(721\) 3.91923 + 0.495113i 0.145960 + 0.0184390i
\(722\) −6.11311 + 48.3902i −0.227506 + 1.80090i
\(723\) −17.1490 + 10.8831i −0.637778 + 0.404746i
\(724\) 62.4100 45.3435i 2.31945 1.68518i
\(725\) 28.2276 17.5832i 1.04835 0.653022i
\(726\) 52.2448 + 37.9581i 1.93899 + 1.40876i
\(727\) 28.3628 + 1.78443i 1.05192 + 0.0661810i 0.579322 0.815099i \(-0.303317\pi\)
0.472595 + 0.881280i \(0.343317\pi\)
\(728\) 20.5629 + 37.4037i 0.762111 + 1.38628i
\(729\) −18.1665 + 38.6058i −0.672834 + 1.42984i
\(730\) 3.65337 36.9908i 0.135217 1.36909i
\(731\) −11.0396 + 57.8714i −0.408313 + 2.14045i
\(732\) −97.4304 134.102i −3.60113 4.95653i
\(733\) −4.24959 + 7.72997i −0.156962 + 0.285513i −0.943081 0.332562i \(-0.892087\pi\)
0.786119 + 0.618075i \(0.212087\pi\)
\(734\) 0.239428 0.377278i 0.00883744 0.0139256i
\(735\) −11.9379 10.6141i −0.440337 0.391507i
\(736\) 47.5844 + 18.8400i 1.75398 + 0.694451i
\(737\) 2.18654 + 5.52256i 0.0805421 + 0.203426i
\(738\) −13.1410 + 10.8712i −0.483727 + 0.400174i
\(739\) −17.6013 + 4.51926i −0.647476 + 0.166244i −0.558125 0.829757i \(-0.688479\pi\)
−0.0893506 + 0.996000i \(0.528479\pi\)
\(740\) 2.80187 0.801282i 0.102999 0.0294557i
\(741\) 4.21110 1.66729i 0.154699 0.0612495i
\(742\) 34.9127 + 37.1783i 1.28169 + 1.36486i
\(743\) −1.81192 + 2.49389i −0.0664729 + 0.0914921i −0.840959 0.541099i \(-0.818009\pi\)
0.774486 + 0.632591i \(0.218009\pi\)
\(744\) −16.5149 35.0960i −0.605466 1.28668i
\(745\) 22.2468 + 6.56466i 0.815058 + 0.240511i
\(746\) 61.3815 33.7448i 2.24734 1.23548i
\(747\) −16.0126 + 3.05456i −0.585869 + 0.111760i
\(748\) 11.4029 + 44.4114i 0.416932 + 1.62384i
\(749\) 11.9158 0.435395
\(750\) −82.4710 8.84485i −3.01142 0.322968i
\(751\) −9.96758 −0.363722 −0.181861 0.983324i \(-0.558212\pi\)
−0.181861 + 0.983324i \(0.558212\pi\)
\(752\) −2.25687 8.78993i −0.0822996 0.320536i
\(753\) 21.8776 4.17337i 0.797263 0.152086i
\(754\) −41.4392 + 22.7814i −1.50913 + 0.829649i
\(755\) 10.8873 15.8764i 0.396228 0.577800i
\(756\) 25.3758 + 53.9263i 0.922908 + 1.96128i
\(757\) −8.50383 + 11.7045i −0.309077 + 0.425408i −0.935093 0.354402i \(-0.884684\pi\)
0.626016 + 0.779810i \(0.284684\pi\)
\(758\) −24.8994 26.5152i −0.904387 0.963074i
\(759\) 19.3624 7.66611i 0.702810 0.278262i
\(760\) 5.99614 7.66354i 0.217503 0.277986i
\(761\) 14.1030 3.62103i 0.511233 0.131262i 0.0157434 0.999876i \(-0.494989\pi\)
0.495490 + 0.868614i \(0.334989\pi\)
\(762\) −20.3352 + 16.8227i −0.736665 + 0.609422i
\(763\) 14.0789 + 35.5592i 0.509690 + 1.28733i
\(764\) 83.6805 + 33.1315i 3.02745 + 1.19865i
\(765\) 15.1323 + 69.0581i 0.547108 + 2.49680i
\(766\) 23.3677 36.8216i 0.844309 1.33042i
\(767\) −8.46012 + 15.3889i −0.305477 + 0.555661i
\(768\) −26.0240 35.8190i −0.939060 1.29251i
\(769\) 6.62404 34.7244i 0.238869 1.25219i −0.637461 0.770483i \(-0.720015\pi\)
0.876330 0.481712i \(-0.159985\pi\)
\(770\) 18.3173 4.01375i 0.660109 0.144646i
\(771\) 21.2080 45.0693i 0.763788 1.62313i
\(772\) −18.2168 33.1363i −0.655638 1.19260i
\(773\) −52.3982 3.29661i −1.88463 0.118571i −0.921630 0.388069i \(-0.873142\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(774\) 100.580 + 73.0758i 3.61528 + 2.62666i
\(775\) −9.06982 + 1.65138i −0.325798 + 0.0593193i
\(776\) −28.9627 + 21.0427i −1.03970 + 0.755387i
\(777\) −1.36705 + 0.867558i −0.0490427 + 0.0311235i
\(778\) 4.94168 39.1175i 0.177168 1.40243i
\(779\) −0.751980 0.0949971i −0.0269425 0.00340363i
\(780\) 82.3514 + 13.3977i 2.94865 + 0.479716i
\(781\) −18.6686 10.2632i −0.668016 0.367245i
\(782\) −75.3887 24.4953i −2.69589 0.875949i
\(783\) −35.0343 + 16.4859i −1.25202 + 0.589158i
\(784\) 23.6834 + 6.08086i 0.845835 + 0.217173i
\(785\) 35.2944 0.960905i 1.25971 0.0342962i
\(786\) 54.4431 65.8104i 1.94192 2.34738i
\(787\) −4.08834 2.59454i −0.145733 0.0924852i 0.460961 0.887420i \(-0.347505\pi\)
−0.606694 + 0.794935i \(0.707505\pi\)
\(788\) −101.743 + 6.40113i −3.62444 + 0.228031i
\(789\) −36.1915 57.0287i −1.28845 2.03027i
\(790\) 0.669763 0.664164i 0.0238291 0.0236299i
\(791\) −0.639933 10.1714i −0.0227534 0.361655i
\(792\) 55.7343 + 10.6319i 1.98043 + 0.377787i
\(793\) 31.2430 10.1515i 1.10947 0.360489i
\(794\) −13.8019 + 12.9609i −0.489811 + 0.459964i
\(795\) 58.2236 5.25728i 2.06498 0.186457i
\(796\) −0.0623172 0.326678i −0.00220878 0.0115788i
\(797\) 4.71767 5.02381i 0.167108 0.177952i −0.639964 0.768405i \(-0.721051\pi\)
0.807072 + 0.590453i \(0.201051\pi\)
\(798\) −3.39383 + 8.57184i −0.120140 + 0.303440i
\(799\) 1.80719 + 5.56195i 0.0639337 + 0.196768i
\(800\) 49.2762 19.0329i 1.74218 0.672914i
\(801\) −19.9745 + 61.4751i −0.705763 + 2.17211i
\(802\) −9.93603 8.21980i −0.350853 0.290251i
\(803\) 8.71584 + 4.10136i 0.307575 + 0.144734i
\(804\) −39.2146 36.8250i −1.38299 1.29872i
\(805\) −7.85880 + 21.5445i −0.276986 + 0.759343i
\(806\) 13.0055 1.64298i 0.458099 0.0578713i
\(807\) 72.9098i 2.56655i
\(808\) 1.48051 + 11.7194i 0.0520840 + 0.412287i
\(809\) −12.4141 15.0060i −0.436455 0.527584i 0.505723 0.862696i \(-0.331226\pi\)
−0.942178 + 0.335112i \(0.891226\pi\)
\(810\) 7.77290 + 1.77174i 0.273112 + 0.0622524i
\(811\) −1.82467 + 29.0023i −0.0640728 + 1.01841i 0.826316 + 0.563207i \(0.190433\pi\)
−0.890389 + 0.455201i \(0.849567\pi\)
\(812\) 16.9343 65.9547i 0.594277 2.31456i
\(813\) 10.3074 40.1446i 0.361496 1.40793i
\(814\) −0.0670317 + 1.06544i −0.00234946 + 0.0373436i
\(815\) 31.6209 13.5263i 1.10763 0.473805i
\(816\) −109.944 132.899i −3.84880 4.65240i
\(817\) 0.692495 + 5.48167i 0.0242273 + 0.191779i
\(818\) 22.5280i 0.787673i
\(819\) −28.8541 + 3.64511i −1.00824 + 0.127371i
\(820\) −10.9967 8.60411i −0.384023 0.300469i
\(821\) 8.39308 + 7.88163i 0.292921 + 0.275071i 0.817049 0.576569i \(-0.195609\pi\)
−0.524128 + 0.851639i \(0.675609\pi\)
\(822\) 79.6402 + 37.4758i 2.77777 + 1.30712i
\(823\) 26.3825 + 21.8255i 0.919636 + 0.760789i 0.971296 0.237875i \(-0.0764510\pi\)
−0.0516593 + 0.998665i \(0.516451\pi\)
\(824\) −4.27472 + 13.1562i −0.148917 + 0.458319i
\(825\) 9.31485 19.3713i 0.324301 0.674422i
\(826\) −11.0462 33.9967i −0.384346 1.18290i
\(827\) 2.77158 7.00022i 0.0963774 0.243422i −0.873587 0.486668i \(-0.838212\pi\)
0.969965 + 0.243246i \(0.0782123\pi\)
\(828\) −81.0041 + 86.2606i −2.81509 + 2.99776i
\(829\) −3.08217 16.1573i −0.107048 0.561167i −0.994885 0.101009i \(-0.967793\pi\)
0.887837 0.460158i \(-0.152207\pi\)
\(830\) −7.41969 17.3453i −0.257541 0.602063i
\(831\) −4.99792 + 4.69336i −0.173376 + 0.162811i
\(832\) −21.2009 + 6.88860i −0.735010 + 0.238819i
\(833\) −15.4781 2.95260i −0.536284 0.102302i
\(834\) −2.86961 45.6112i −0.0993665 1.57939i
\(835\) −11.2786 + 1.73786i −0.390312 + 0.0601411i
\(836\) 2.30413 + 3.63073i 0.0796900 + 0.125571i
\(837\) 10.7122 0.673956i 0.370269 0.0232953i
\(838\) 46.1614 + 29.2949i 1.59462 + 1.01198i
\(839\) 0.0193183 0.0233519i 0.000666943 0.000806195i −0.770180 0.637827i \(-0.779833\pi\)
0.770847 + 0.637021i \(0.219833\pi\)
\(840\) −78.9478 + 60.7091i −2.72396 + 2.09466i
\(841\) 14.7599 + 3.78971i 0.508963 + 0.130679i
\(842\) 42.7258 20.1052i 1.47243 0.692872i
\(843\) −41.8252 13.5898i −1.44054 0.468059i
\(844\) 109.815 + 60.3713i 3.77999 + 2.07807i
\(845\) 5.73691 11.1434i 0.197356 0.383346i
\(846\) 12.2437 + 1.54674i 0.420946 + 0.0531779i
\(847\) 2.30981 18.2840i 0.0793659 0.628245i
\(848\) −75.5549 + 47.9486i −2.59457 + 1.64656i
\(849\) −67.4058 + 48.9732i −2.31336 + 1.68075i
\(850\) −74.3205 + 34.2135i −2.54917 + 1.17351i
\(851\) −1.05624 0.767400i −0.0362073 0.0263061i
\(852\) 192.564 + 12.1151i 6.59715 + 0.415057i
\(853\) −3.34723 6.08859i −0.114607 0.208469i 0.812782 0.582568i \(-0.197952\pi\)
−0.927389 + 0.374099i \(0.877952\pi\)
\(854\) −28.4715 + 60.5049i −0.974273 + 2.07044i
\(855\) 3.35104 + 5.72096i 0.114603 + 0.195653i
\(856\) −7.81876 + 40.9874i −0.267240 + 1.40092i
\(857\) 9.97123 + 13.7242i 0.340611 + 0.468811i 0.944620 0.328167i \(-0.106431\pi\)
−0.604009 + 0.796978i \(0.706431\pi\)
\(858\) −14.7244 + 26.7835i −0.502681 + 0.914374i
\(859\) −24.2074 + 38.1447i −0.825945 + 1.30148i 0.125011 + 0.992155i \(0.460103\pi\)
−0.950956 + 0.309326i \(0.899897\pi\)
\(860\) −40.8149 + 93.2419i −1.39178 + 3.17952i
\(861\) 7.21282 + 2.85576i 0.245812 + 0.0973240i
\(862\) 27.0418 + 68.2998i 0.921047 + 2.32630i
\(863\) 26.2689 21.7315i 0.894204 0.739749i −0.0720341 0.997402i \(-0.522949\pi\)
0.966238 + 0.257653i \(0.0829490\pi\)
\(864\) −59.5698 + 15.2949i −2.02661 + 0.520344i
\(865\) 1.48628 41.7164i 0.0505351 1.41840i
\(866\) −12.7717 + 5.05667i −0.434000 + 0.171833i
\(867\) 43.0670 + 45.8617i 1.46263 + 1.55754i
\(868\) −11.0952 + 15.2713i −0.376597 + 0.518342i
\(869\) 0.104075 + 0.221171i 0.00353051 + 0.00750272i
\(870\) −67.2590 87.4654i −2.28029 2.96535i
\(871\) 9.34256 5.13612i 0.316561 0.174031i
\(872\) −131.552 + 25.0950i −4.45493 + 0.849822i
\(873\) −6.06633 23.6268i −0.205314 0.799646i
\(874\) −7.43404 −0.251460
\(875\) 9.12644 + 21.8404i 0.308530 + 0.738341i
\(876\) −87.2411 −2.94760
\(877\) −0.00573073 0.0223197i −0.000193513 0.000753684i 0.968486 0.249067i \(-0.0801238\pi\)
−0.968680 + 0.248313i \(0.920124\pi\)
\(878\) −20.0186 + 3.81876i −0.675596 + 0.128877i
\(879\) 36.7796 20.2198i 1.24055 0.681996i
\(880\) 0.895426 + 32.8894i 0.0301848 + 1.10870i
\(881\) −15.0639 32.0125i −0.507516 1.07853i −0.980330 0.197365i \(-0.936762\pi\)
0.472814 0.881162i \(-0.343238\pi\)
\(882\) −19.5446 + 26.9008i −0.658101 + 0.905799i
\(883\) −25.7246 27.3939i −0.865701 0.921878i 0.131889 0.991265i \(-0.457896\pi\)
−0.997590 + 0.0693865i \(0.977896\pi\)
\(884\) 76.5216 30.2970i 2.57370 1.01900i
\(885\) −38.4934 14.0413i −1.29394 0.471992i
\(886\) −2.97109 + 0.762847i −0.0998158 + 0.0256283i
\(887\) −26.6611 + 22.0560i −0.895194 + 0.740569i −0.966441 0.256890i \(-0.917302\pi\)
0.0712469 + 0.997459i \(0.477302\pi\)
\(888\) −2.08716 5.27156i −0.0700405 0.176902i
\(889\) 7.00277 + 2.77259i 0.234865 + 0.0929898i
\(890\) −74.4445 7.35246i −2.49539 0.246455i
\(891\) −1.10700 + 1.74436i −0.0370859 + 0.0584381i
\(892\) 47.4626 86.3341i 1.58916 2.89068i
\(893\) 0.322377 + 0.443714i 0.0107879 + 0.0148483i
\(894\) 14.4201 75.5927i 0.482279 2.52820i
\(895\) 4.13912 + 1.81182i 0.138355 + 0.0605624i
\(896\) 0.273014 0.580184i 0.00912076 0.0193826i
\(897\) −18.0075 32.7555i −0.601253 1.09367i
\(898\) 88.5599 + 5.57172i 2.95528 + 0.185931i
\(899\) −9.92132 7.20826i −0.330894 0.240409i
\(900\) −1.02527 + 122.134i −0.0341758 + 4.07112i
\(901\) 46.6532 33.8955i 1.55424 1.12922i
\(902\) 4.31867 2.74071i 0.143796 0.0912557i
\(903\) 7.08760 56.1041i 0.235861 1.86703i
\(904\) 35.4070 + 4.47295i 1.17762 + 0.148768i
\(905\) −31.8517 + 16.0612i −1.05879 + 0.533892i
\(906\) −55.9691 30.7693i −1.85945 1.02224i
\(907\) −54.8771 17.8306i −1.82216 0.592057i −0.999731 0.0231944i \(-0.992616\pi\)
−0.822433 0.568862i \(-0.807384\pi\)
\(908\) 90.7366 42.6974i 3.01120 1.41696i
\(909\) −7.79590 2.00165i −0.258574 0.0663905i
\(910\) −11.2683 31.7161i −0.373542 1.05138i
\(911\) −26.8642 + 32.4732i −0.890050 + 1.07589i 0.106616 + 0.994300i \(0.465998\pi\)
−0.996666 + 0.0815858i \(0.974002\pi\)
\(912\) −13.6577 8.66744i −0.452252 0.287008i
\(913\) 4.87927 0.306977i 0.161480 0.0101595i
\(914\) 29.4601 + 46.4217i 0.974455 + 1.53549i
\(915\) 34.5110 + 68.4403i 1.14090 + 2.26257i
\(916\) 0.828252 + 13.1647i 0.0273662 + 0.434973i
\(917\) −23.9429 4.56735i −0.790664 0.150827i
\(918\) 90.5961 29.4365i 2.99012 0.971548i
\(919\) −4.60295 + 4.32245i −0.151837 + 0.142585i −0.756743 0.653712i \(-0.773211\pi\)
0.604906 + 0.796297i \(0.293211\pi\)
\(920\) −68.9507 41.1689i −2.27324 1.35730i
\(921\) 9.53122 + 49.9644i 0.314064 + 1.64638i
\(922\) 17.4721 18.6059i 0.575414 0.612754i
\(923\) −14.0766 + 35.5535i −0.463338 + 1.17026i
\(924\) −13.6003 41.8573i −0.447416 1.37700i
\(925\) −1.33831 + 0.157666i −0.0440034 + 0.00518403i
\(926\) 14.8555 45.7205i 0.488181 1.50247i
\(927\) −7.26259 6.00813i −0.238535 0.197333i
\(928\) 63.5813 + 29.9191i 2.08716 + 0.982142i
\(929\) 40.1162 + 37.6716i 1.31617 + 1.23596i 0.952537 + 0.304421i \(0.0984631\pi\)
0.363631 + 0.931543i \(0.381537\pi\)
\(930\) 8.40992 + 29.4073i 0.275772 + 0.964303i
\(931\) −1.46611 + 0.185212i −0.0480497 + 0.00607009i
\(932\) 124.026i 4.06262i
\(933\) 3.48467 + 27.5840i 0.114083 + 0.903060i
\(934\) 26.7478 + 32.3326i 0.875216 + 1.05795i
\(935\) −1.90672 21.1167i −0.0623565 0.690589i
\(936\) 6.39478 101.642i 0.209020 3.32228i
\(937\) 12.4339 48.4269i 0.406198 1.58204i −0.355867 0.934537i \(-0.615814\pi\)
0.762065 0.647500i \(-0.224186\pi\)
\(938\) −5.39693 + 21.0196i −0.176216 + 0.686316i
\(939\) 1.29311 20.5534i 0.0421991 0.670736i
\(940\) 0.908599 + 10.0626i 0.0296352 + 0.328205i
\(941\) 18.2669 + 22.0809i 0.595484 + 0.719817i 0.979033 0.203704i \(-0.0652980\pi\)
−0.383548 + 0.923521i \(0.625298\pi\)
\(942\) −14.6818 116.218i −0.478357 3.78659i
\(943\) 6.25541i 0.203704i
\(944\) 62.2248 7.86082i 2.02524 0.255848i
\(945\) −7.57761 26.4969i −0.246500 0.861945i
\(946\) −27.1803 25.5240i −0.883707 0.829857i
\(947\) −3.79240 1.78457i −0.123236 0.0579907i 0.363173 0.931722i \(-0.381694\pi\)
−0.486409 + 0.873731i \(0.661694\pi\)
\(948\) −1.70577 1.41114i −0.0554008 0.0458316i
\(949\) 5.34286 16.4436i 0.173437 0.533783i
\(950\) −5.63735 + 5.20547i −0.182900 + 0.168888i
\(951\) −5.53371 17.0310i −0.179443 0.552268i
\(952\) −36.1640 + 91.3397i −1.17208 + 2.96034i
\(953\) −11.8514 + 12.6204i −0.383904 + 0.408816i −0.891675 0.452676i \(-0.850469\pi\)
0.507771 + 0.861492i \(0.330469\pi\)
\(954\) −22.8023 119.534i −0.738253 3.87006i
\(955\) −35.7328 21.3352i −1.15629 0.690392i
\(956\) −26.6152 + 24.9933i −0.860797 + 0.808342i
\(957\) 27.1935 8.83569i 0.879040 0.285617i
\(958\) 39.5959 + 7.55332i 1.27929 + 0.244037i
\(959\) −1.57719 25.0688i −0.0509302 0.809512i
\(960\) −23.4185 46.4423i −0.755830 1.49892i
\(961\) −14.7891 23.3038i −0.477067 0.751737i
\(962\) 1.91239 0.120317i 0.0616579 0.00387919i
\(963\) −24.0054 15.2343i −0.773563 0.490918i
\(964\) −22.0633 + 26.6699i −0.710610 + 0.858980i
\(965\) 5.85391 + 16.4765i 0.188444 + 0.530398i
\(966\) 73.6960 + 18.9219i 2.37113 + 0.608803i
\(967\) −1.83221 + 0.862172i −0.0589199 + 0.0277256i −0.455013 0.890485i \(-0.650366\pi\)
0.396094 + 0.918210i \(0.370366\pi\)
\(968\) 61.3765 + 19.9424i 1.97272 + 0.640974i
\(969\) 9.13471 + 5.02185i 0.293449 + 0.161325i
\(970\) 25.2070 12.7106i 0.809347 0.408113i
\(971\) 49.1515 + 6.20928i 1.57735 + 0.199265i 0.864711 0.502270i \(-0.167502\pi\)
0.712635 + 0.701535i \(0.247502\pi\)
\(972\) −8.23932 + 65.2209i −0.264276 + 2.09196i
\(973\) −11.0119 + 6.98839i −0.353027 + 0.224038i
\(974\) −31.6364 + 22.9852i −1.01369 + 0.736492i
\(975\) −36.5915 12.2298i −1.17186 0.391668i
\(976\) −94.9192 68.9628i −3.03829 2.20745i
\(977\) 43.6152 + 2.74404i 1.39537 + 0.0877895i 0.742586 0.669751i \(-0.233599\pi\)
0.652788 + 0.757540i \(0.273599\pi\)
\(978\) −54.9709 99.9917i −1.75778 3.19738i
\(979\) 8.25406 17.5408i 0.263801 0.560605i
\(980\) −24.9382 10.9162i −0.796620 0.348705i
\(981\) 17.0991 89.6364i 0.545931 2.86187i
\(982\) 14.6529 + 20.1679i 0.467591 + 0.643584i
\(983\) −9.93323 + 18.0685i −0.316821 + 0.576295i −0.985988 0.166817i \(-0.946651\pi\)
0.669167 + 0.743112i \(0.266651\pi\)
\(984\) −14.5559 + 22.9364i −0.464024 + 0.731185i
\(985\) 46.9122 + 4.63325i 1.49475 + 0.147628i
\(986\) −101.194 40.0656i −3.22268 1.27595i
\(987\) −2.06644 5.21923i −0.0657755 0.166130i
\(988\) 5.94717 4.91993i 0.189205 0.156524i
\(989\) 44.1671 11.3402i 1.40443 0.360597i
\(990\) −42.0331 15.3325i −1.33590 0.487297i
\(991\) −36.4430 + 14.4288i −1.15765 + 0.458346i −0.866914 0.498458i \(-0.833900\pi\)
−0.290735 + 0.956804i \(0.593900\pi\)
\(992\) −13.3345 14.1998i −0.423370 0.450844i
\(993\) 47.9143 65.9484i 1.52052 2.09281i
\(994\) −33.1411 70.4285i −1.05117 2.23386i
\(995\) 0.00418530 + 0.153728i 0.000132683 + 0.00487350i
\(996\) −38.8013 + 21.3312i −1.22947 + 0.675904i
\(997\) 52.3338 9.98320i 1.65743 0.316171i 0.728112 0.685458i \(-0.240398\pi\)
0.929315 + 0.369287i \(0.120398\pi\)
\(998\) 4.05577 + 15.7962i 0.128383 + 0.500020i
\(999\) 1.56894 0.0496392
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 125.2.h.a.104.12 240
5.2 odd 4 625.2.g.b.351.2 480
5.3 odd 4 625.2.g.b.351.23 480
5.4 even 2 625.2.h.a.274.1 240
125.6 even 25 625.2.h.a.349.1 240
125.33 odd 100 625.2.g.b.276.23 480
125.92 odd 100 625.2.g.b.276.2 480
125.119 even 50 inner 125.2.h.a.119.12 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
125.2.h.a.104.12 240 1.1 even 1 trivial
125.2.h.a.119.12 yes 240 125.119 even 50 inner
625.2.g.b.276.2 480 125.92 odd 100
625.2.g.b.276.23 480 125.33 odd 100
625.2.g.b.351.2 480 5.2 odd 4
625.2.g.b.351.23 480 5.3 odd 4
625.2.h.a.274.1 240 5.4 even 2
625.2.h.a.349.1 240 125.6 even 25