Properties

Label 65.2.f.b.18.1
Level $65$
Weight $2$
Character 65.18
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [65,2,Mod(18,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.18");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.619810816.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 18.1
Root \(0.561103 - 0.561103i\) of defining polynomial
Character \(\chi\) \(=\) 65.18
Dual form 65.2.f.b.47.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.03032i q^{2} +(-1.33000 - 1.33000i) q^{3} -2.12221 q^{4} +(1.70032 + 1.45220i) q^{5} +(-2.70032 + 2.70032i) q^{6} -1.61845 q^{7} +0.248119i q^{8} +0.537789i q^{9} +O(q^{10})\) \(q-2.03032i q^{2} +(-1.33000 - 1.33000i) q^{3} -2.12221 q^{4} +(1.70032 + 1.45220i) q^{5} +(-2.70032 + 2.70032i) q^{6} -1.61845 q^{7} +0.248119i q^{8} +0.537789i q^{9} +(2.94844 - 3.45220i) q^{10} +(2.70032 + 2.70032i) q^{11} +(2.82253 + 2.82253i) q^{12} +(3.45220 - 1.04033i) q^{13} +3.28596i q^{14} +(-0.329998 - 4.19286i) q^{15} -3.74065 q^{16} +(2.24812 + 2.24812i) q^{17} +1.09188 q^{18} +(-2.33000 - 2.33000i) q^{19} +(-3.60844 - 3.08188i) q^{20} +(2.15253 + 2.15253i) q^{21} +(5.48253 - 5.48253i) q^{22} +(-4.82253 + 4.82253i) q^{23} +(0.329998 - 0.329998i) q^{24} +(0.782203 + 4.93844i) q^{25} +(-2.11220 - 7.00909i) q^{26} +(-3.27474 + 3.27474i) q^{27} +3.43468 q^{28} +4.27844i q^{29} +(-8.51285 + 0.670002i) q^{30} +(3.36032 - 3.36032i) q^{31} +8.09097i q^{32} -7.18285i q^{33} +(4.56441 - 4.56441i) q^{34} +(-2.75188 - 2.35031i) q^{35} -1.14130i q^{36} -7.78220 q^{37} +(-4.73065 + 4.73065i) q^{38} +(-5.97506 - 3.20779i) q^{39} +(-0.360320 + 0.421883i) q^{40} +(2.87409 - 2.87409i) q^{41} +(4.37033 - 4.37033i) q^{42} +(3.97876 - 3.97876i) q^{43} +(-5.73065 - 5.73065i) q^{44} +(-0.780980 + 0.914416i) q^{45} +(9.79129 + 9.79129i) q^{46} +5.36662 q^{47} +(4.97506 + 4.97506i) q^{48} -4.38064 q^{49} +(10.0266 - 1.58812i) q^{50} -5.97999i q^{51} +(-7.32629 + 2.20779i) q^{52} +(-4.61845 - 4.61845i) q^{53} +(6.64877 + 6.64877i) q^{54} +(0.670002 + 8.51285i) q^{55} -0.401567i q^{56} +6.19779i q^{57} +8.68661 q^{58} +(4.47130 - 4.47130i) q^{59} +(0.700324 + 8.89811i) q^{60} -12.1479 q^{61} +(-6.82253 - 6.82253i) q^{62} -0.870382i q^{63} +8.94596 q^{64} +(7.38064 + 3.24441i) q^{65} -14.5835 q^{66} -5.84285i q^{67} +(-4.77097 - 4.77097i) q^{68} +12.8279 q^{69} +(-4.77189 + 5.58720i) q^{70} +(-1.37155 + 1.37155i) q^{71} -0.133436 q^{72} +4.02662i q^{73} +15.8004i q^{74} +(5.52778 - 7.60844i) q^{75} +(4.94474 + 4.94474i) q^{76} +(-4.37033 - 4.37033i) q^{77} +(-6.51285 + 12.1313i) q^{78} +8.63754i q^{79} +(-6.36032 - 5.43219i) q^{80} +10.3242 q^{81} +(-5.83532 - 5.83532i) q^{82} -7.48791 q^{83} +(-4.56811 - 4.56811i) q^{84} +(0.557801 + 7.08726i) q^{85} +(-8.07817 - 8.07817i) q^{86} +(5.69032 - 5.69032i) q^{87} +(-0.670002 + 0.670002i) q^{88} +(8.59843 - 8.59843i) q^{89} +(1.85656 + 1.58564i) q^{90} +(-5.58720 + 1.68371i) q^{91} +(10.2344 - 10.2344i) q^{92} -8.93844 q^{93} -10.8960i q^{94} +(-0.578117 - 7.34539i) q^{95} +(10.7610 - 10.7610i) q^{96} -8.63754i q^{97} +8.89410i q^{98} +(-1.45220 + 1.45220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.03032i 1.43565i −0.696221 0.717827i \(-0.745137\pi\)
0.696221 0.717827i \(-0.254863\pi\)
\(3\) −1.33000 1.33000i −0.767875 0.767875i 0.209857 0.977732i \(-0.432700\pi\)
−0.977732 + 0.209857i \(0.932700\pi\)
\(4\) −2.12221 −1.06110
\(5\) 1.70032 + 1.45220i 0.760408 + 0.649446i
\(6\) −2.70032 + 2.70032i −1.10240 + 1.10240i
\(7\) −1.61845 −0.611715 −0.305857 0.952077i \(-0.598943\pi\)
−0.305857 + 0.952077i \(0.598943\pi\)
\(8\) 0.248119i 0.0877234i
\(9\) 0.537789i 0.179263i
\(10\) 2.94844 3.45220i 0.932380 1.09168i
\(11\) 2.70032 + 2.70032i 0.814178 + 0.814178i 0.985257 0.171079i \(-0.0547253\pi\)
−0.171079 + 0.985257i \(0.554725\pi\)
\(12\) 2.82253 + 2.82253i 0.814794 + 0.814794i
\(13\) 3.45220 1.04033i 0.957469 0.288535i
\(14\) 3.28596i 0.878211i
\(15\) −0.329998 4.19286i −0.0852051 1.08259i
\(16\) −3.74065 −0.935163
\(17\) 2.24812 + 2.24812i 0.545249 + 0.545249i 0.925063 0.379814i \(-0.124012\pi\)
−0.379814 + 0.925063i \(0.624012\pi\)
\(18\) 1.09188 0.257360
\(19\) −2.33000 2.33000i −0.534538 0.534538i 0.387381 0.921920i \(-0.373380\pi\)
−0.921920 + 0.387381i \(0.873380\pi\)
\(20\) −3.60844 3.08188i −0.806871 0.689129i
\(21\) 2.15253 + 2.15253i 0.469720 + 0.469720i
\(22\) 5.48253 5.48253i 1.16888 1.16888i
\(23\) −4.82253 + 4.82253i −1.00557 + 1.00557i −0.00558275 + 0.999984i \(0.501777\pi\)
−0.999984 + 0.00558275i \(0.998223\pi\)
\(24\) 0.329998 0.329998i 0.0673605 0.0673605i
\(25\) 0.782203 + 4.93844i 0.156441 + 0.987687i
\(26\) −2.11220 7.00909i −0.414237 1.37460i
\(27\) −3.27474 + 3.27474i −0.630223 + 0.630223i
\(28\) 3.43468 0.649093
\(29\) 4.27844i 0.794487i 0.917713 + 0.397243i \(0.130033\pi\)
−0.917713 + 0.397243i \(0.869967\pi\)
\(30\) −8.51285 + 0.670002i −1.55423 + 0.122325i
\(31\) 3.36032 3.36032i 0.603531 0.603531i −0.337717 0.941248i \(-0.609655\pi\)
0.941248 + 0.337717i \(0.109655\pi\)
\(32\) 8.09097i 1.43029i
\(33\) 7.18285i 1.25037i
\(34\) 4.56441 4.56441i 0.782789 0.782789i
\(35\) −2.75188 2.35031i −0.465153 0.397276i
\(36\) 1.14130i 0.190217i
\(37\) −7.78220 −1.27939 −0.639693 0.768630i \(-0.720939\pi\)
−0.639693 + 0.768630i \(0.720939\pi\)
\(38\) −4.73065 + 4.73065i −0.767412 + 0.767412i
\(39\) −5.97506 3.20779i −0.956775 0.513658i
\(40\) −0.360320 + 0.421883i −0.0569716 + 0.0667055i
\(41\) 2.87409 2.87409i 0.448857 0.448857i −0.446117 0.894974i \(-0.647194\pi\)
0.894974 + 0.446117i \(0.147194\pi\)
\(42\) 4.37033 4.37033i 0.674356 0.674356i
\(43\) 3.97876 3.97876i 0.606756 0.606756i −0.335341 0.942097i \(-0.608851\pi\)
0.942097 + 0.335341i \(0.108851\pi\)
\(44\) −5.73065 5.73065i −0.863927 0.863927i
\(45\) −0.780980 + 0.914416i −0.116422 + 0.136313i
\(46\) 9.79129 + 9.79129i 1.44365 + 1.44365i
\(47\) 5.36662 0.782802 0.391401 0.920220i \(-0.371991\pi\)
0.391401 + 0.920220i \(0.371991\pi\)
\(48\) 4.97506 + 4.97506i 0.718088 + 0.718088i
\(49\) −4.38064 −0.625805
\(50\) 10.0266 1.58812i 1.41798 0.224595i
\(51\) 5.97999i 0.837366i
\(52\) −7.32629 + 2.20779i −1.01597 + 0.306166i
\(53\) −4.61845 4.61845i −0.634392 0.634392i 0.314774 0.949167i \(-0.398071\pi\)
−0.949167 + 0.314774i \(0.898071\pi\)
\(54\) 6.64877 + 6.64877i 0.904783 + 0.904783i
\(55\) 0.670002 + 8.51285i 0.0903431 + 1.14787i
\(56\) 0.401567i 0.0536617i
\(57\) 6.19779i 0.820917i
\(58\) 8.68661 1.14061
\(59\) 4.47130 4.47130i 0.582113 0.582113i −0.353370 0.935484i \(-0.614964\pi\)
0.935484 + 0.353370i \(0.114964\pi\)
\(60\) 0.700324 + 8.89811i 0.0904114 + 1.14874i
\(61\) −12.1479 −1.55538 −0.777690 0.628648i \(-0.783609\pi\)
−0.777690 + 0.628648i \(0.783609\pi\)
\(62\) −6.82253 6.82253i −0.866462 0.866462i
\(63\) 0.870382i 0.109658i
\(64\) 8.94596 1.11825
\(65\) 7.38064 + 3.24441i 0.915455 + 0.402420i
\(66\) −14.5835 −1.79510
\(67\) 5.84285i 0.713817i −0.934139 0.356909i \(-0.883831\pi\)
0.934139 0.356909i \(-0.116169\pi\)
\(68\) −4.77097 4.77097i −0.578566 0.578566i
\(69\) 12.8279 1.54430
\(70\) −4.77189 + 5.58720i −0.570350 + 0.667799i
\(71\) −1.37155 + 1.37155i −0.162773 + 0.162773i −0.783794 0.621021i \(-0.786718\pi\)
0.621021 + 0.783794i \(0.286718\pi\)
\(72\) −0.133436 −0.0157256
\(73\) 4.02662i 0.471280i 0.971840 + 0.235640i \(0.0757186\pi\)
−0.971840 + 0.235640i \(0.924281\pi\)
\(74\) 15.8004i 1.83676i
\(75\) 5.52778 7.60844i 0.638293 0.878547i
\(76\) 4.94474 + 4.94474i 0.567200 + 0.567200i
\(77\) −4.37033 4.37033i −0.498045 0.498045i
\(78\) −6.51285 + 12.1313i −0.737435 + 1.37360i
\(79\) 8.63754i 0.971799i 0.874015 + 0.485899i \(0.161508\pi\)
−0.874015 + 0.485899i \(0.838492\pi\)
\(80\) −6.36032 5.43219i −0.711105 0.607338i
\(81\) 10.3242 1.14713
\(82\) −5.83532 5.83532i −0.644404 0.644404i
\(83\) −7.48791 −0.821905 −0.410952 0.911657i \(-0.634804\pi\)
−0.410952 + 0.911657i \(0.634804\pi\)
\(84\) −4.56811 4.56811i −0.498422 0.498422i
\(85\) 0.557801 + 7.08726i 0.0605021 + 0.768721i
\(86\) −8.07817 8.07817i −0.871092 0.871092i
\(87\) 5.69032 5.69032i 0.610066 0.610066i
\(88\) −0.670002 + 0.670002i −0.0714225 + 0.0714225i
\(89\) 8.59843 8.59843i 0.911432 0.911432i −0.0849529 0.996385i \(-0.527074\pi\)
0.996385 + 0.0849529i \(0.0270740\pi\)
\(90\) 1.85656 + 1.58564i 0.195698 + 0.167141i
\(91\) −5.58720 + 1.68371i −0.585698 + 0.176501i
\(92\) 10.2344 10.2344i 1.06701 1.06701i
\(93\) −8.93844 −0.926873
\(94\) 10.8960i 1.12383i
\(95\) −0.578117 7.34539i −0.0593136 0.753621i
\(96\) 10.7610 10.7610i 1.09829 1.09829i
\(97\) 8.63754i 0.877009i −0.898729 0.438505i \(-0.855508\pi\)
0.898729 0.438505i \(-0.144492\pi\)
\(98\) 8.89410i 0.898440i
\(99\) −1.45220 + 1.45220i −0.145952 + 0.145952i
\(100\) −1.66000 10.4804i −0.166000 1.04804i
\(101\) 0.823754i 0.0819665i −0.999160 0.0409833i \(-0.986951\pi\)
0.999160 0.0409833i \(-0.0130490\pi\)
\(102\) −12.1413 −1.20217
\(103\) −0.867787 + 0.867787i −0.0855056 + 0.0855056i −0.748566 0.663060i \(-0.769257\pi\)
0.663060 + 0.748566i \(0.269257\pi\)
\(104\) 0.258125 + 0.856558i 0.0253113 + 0.0839924i
\(105\) 0.534084 + 6.78591i 0.0521212 + 0.662237i
\(106\) −9.37693 + 9.37693i −0.910768 + 0.910768i
\(107\) −3.28474 + 3.28474i −0.317548 + 0.317548i −0.847825 0.530277i \(-0.822088\pi\)
0.530277 + 0.847825i \(0.322088\pi\)
\(108\) 6.94967 6.94967i 0.668732 0.668732i
\(109\) −5.07187 5.07187i −0.485797 0.485797i 0.421180 0.906977i \(-0.361616\pi\)
−0.906977 + 0.421180i \(0.861616\pi\)
\(110\) 17.2838 1.36032i 1.64795 0.129701i
\(111\) 10.3503 + 10.3503i 0.982408 + 0.982408i
\(112\) 6.05404 0.572053
\(113\) 9.24720 + 9.24720i 0.869903 + 0.869903i 0.992461 0.122558i \(-0.0391097\pi\)
−0.122558 + 0.992461i \(0.539110\pi\)
\(114\) 12.5835 1.17855
\(115\) −15.2032 + 1.19656i −1.41770 + 0.111580i
\(116\) 9.07974i 0.843032i
\(117\) 0.559477 + 1.85656i 0.0517237 + 0.171639i
\(118\) −9.07817 9.07817i −0.835714 0.835714i
\(119\) −3.63846 3.63846i −0.333537 0.333537i
\(120\) 1.04033 0.0818788i 0.0949685 0.00747448i
\(121\) 3.58350i 0.325773i
\(122\) 24.6642i 2.23299i
\(123\) −7.64506 −0.689332
\(124\) −7.13129 + 7.13129i −0.640409 + 0.640409i
\(125\) −5.84162 + 9.53286i −0.522491 + 0.852645i
\(126\) −1.76716 −0.157431
\(127\) 11.4779 + 11.4779i 1.01850 + 1.01850i 0.999826 + 0.0186734i \(0.00594429\pi\)
0.0186734 + 0.999826i \(0.494056\pi\)
\(128\) 1.98125i 0.175119i
\(129\) −10.5835 −0.931825
\(130\) 6.58720 14.9851i 0.577736 1.31428i
\(131\) 1.80882 0.158037 0.0790186 0.996873i \(-0.474821\pi\)
0.0790186 + 0.996873i \(0.474821\pi\)
\(132\) 15.2435i 1.32678i
\(133\) 3.77097 + 3.77097i 0.326985 + 0.326985i
\(134\) −11.8629 −1.02479
\(135\) −10.3237 + 0.812525i −0.888522 + 0.0699310i
\(136\) −0.557801 + 0.557801i −0.0478311 + 0.0478311i
\(137\) −8.96505 −0.765936 −0.382968 0.923762i \(-0.625098\pi\)
−0.382968 + 0.923762i \(0.625098\pi\)
\(138\) 26.0448i 2.21708i
\(139\) 5.37819i 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732468\pi\)
\(140\) 5.84006 + 4.98785i 0.493575 + 0.421550i
\(141\) −7.13759 7.13759i −0.601094 0.601094i
\(142\) 2.78469 + 2.78469i 0.233686 + 0.233686i
\(143\) 12.1313 + 6.51285i 1.01447 + 0.544632i
\(144\) 2.01168i 0.167640i
\(145\) −6.21317 + 7.27474i −0.515976 + 0.604134i
\(146\) 8.17533 0.676595
\(147\) 5.82624 + 5.82624i 0.480540 + 0.480540i
\(148\) 16.5154 1.35756
\(149\) 7.78591 + 7.78591i 0.637846 + 0.637846i 0.950024 0.312177i \(-0.101058\pi\)
−0.312177 + 0.950024i \(0.601058\pi\)
\(150\) −15.4476 11.2232i −1.26129 0.916369i
\(151\) 1.86038 + 1.86038i 0.151395 + 0.151395i 0.778741 0.627346i \(-0.215859\pi\)
−0.627346 + 0.778741i \(0.715859\pi\)
\(152\) 0.578117 0.578117i 0.0468915 0.0468915i
\(153\) −1.20901 + 1.20901i −0.0977430 + 0.0977430i
\(154\) −8.87317 + 8.87317i −0.715020 + 0.715020i
\(155\) 10.5935 0.833760i 0.850891 0.0669692i
\(156\) 12.6803 + 6.80760i 1.01524 + 0.545044i
\(157\) 9.89318 9.89318i 0.789562 0.789562i −0.191860 0.981422i \(-0.561452\pi\)
0.981422 + 0.191860i \(0.0614521\pi\)
\(158\) 17.5370 1.39517
\(159\) 12.2850i 0.974267i
\(160\) −11.7497 + 13.7573i −0.928898 + 1.08761i
\(161\) 7.80500 7.80500i 0.615120 0.615120i
\(162\) 20.9613i 1.64688i
\(163\) 7.53779i 0.590405i −0.955435 0.295203i \(-0.904613\pi\)
0.955435 0.295203i \(-0.0953871\pi\)
\(164\) −6.09941 + 6.09941i −0.476284 + 0.476284i
\(165\) 10.4310 12.2132i 0.812050 0.950794i
\(166\) 15.2029i 1.17997i
\(167\) 18.9086 1.46319 0.731594 0.681740i \(-0.238776\pi\)
0.731594 + 0.681740i \(0.238776\pi\)
\(168\) −0.534084 + 0.534084i −0.0412054 + 0.0412054i
\(169\) 10.8354 7.18285i 0.833495 0.552527i
\(170\) 14.3894 1.13252i 1.10362 0.0868600i
\(171\) 1.25305 1.25305i 0.0958229 0.0958229i
\(172\) −8.44376 + 8.44376i −0.643831 + 0.643831i
\(173\) 2.80882 2.80882i 0.213551 0.213551i −0.592223 0.805774i \(-0.701750\pi\)
0.805774 + 0.592223i \(0.201750\pi\)
\(174\) −11.5532 11.5532i −0.875844 0.875844i
\(175\) −1.26595 7.99259i −0.0956970 0.604183i
\(176\) −10.1010 10.1010i −0.761389 0.761389i
\(177\) −11.8936 −0.893980
\(178\) −17.4576 17.4576i −1.30850 1.30850i
\(179\) −21.6632 −1.61919 −0.809593 0.586991i \(-0.800312\pi\)
−0.809593 + 0.586991i \(0.800312\pi\)
\(180\) 1.65740 1.94058i 0.123535 0.144642i
\(181\) 6.82791i 0.507515i −0.967268 0.253757i \(-0.918334\pi\)
0.967268 0.253757i \(-0.0816665\pi\)
\(182\) 3.41848 + 11.3438i 0.253395 + 0.840860i
\(183\) 16.1567 + 16.1567i 1.19434 + 1.19434i
\(184\) −1.19656 1.19656i −0.0882117 0.0882117i
\(185\) −13.2323 11.3014i −0.972855 0.830892i
\(186\) 18.1479i 1.33067i
\(187\) 12.1413i 0.887860i
\(188\) −11.3891 −0.830634
\(189\) 5.29998 5.29998i 0.385517 0.385517i
\(190\) −14.9135 + 1.17376i −1.08194 + 0.0851538i
\(191\) −18.9450 −1.37082 −0.685408 0.728160i \(-0.740376\pi\)
−0.685408 + 0.728160i \(0.740376\pi\)
\(192\) −11.8981 11.8981i −0.858672 0.858672i
\(193\) 7.18885i 0.517465i 0.965949 + 0.258732i \(0.0833047\pi\)
−0.965949 + 0.258732i \(0.916695\pi\)
\(194\) −17.5370 −1.25908
\(195\) −5.50117 14.1313i −0.393947 1.01196i
\(196\) 9.29661 0.664044
\(197\) 4.41558i 0.314597i −0.987551 0.157299i \(-0.949721\pi\)
0.987551 0.157299i \(-0.0502785\pi\)
\(198\) 2.94844 + 2.94844i 0.209537 + 0.209537i
\(199\) 0.312468 0.0221503 0.0110751 0.999939i \(-0.496475\pi\)
0.0110751 + 0.999939i \(0.496475\pi\)
\(200\) −1.22532 + 0.194079i −0.0866433 + 0.0137235i
\(201\) −7.77097 + 7.77097i −0.548122 + 0.548122i
\(202\) −1.67248 −0.117676
\(203\) 6.92442i 0.485999i
\(204\) 12.6908i 0.888532i
\(205\) 9.06064 0.713116i 0.632823 0.0498062i
\(206\) 1.76189 + 1.76189i 0.122756 + 0.122756i
\(207\) −2.59350 2.59350i −0.180261 0.180261i
\(208\) −12.9135 + 3.89150i −0.895390 + 0.269827i
\(209\) 12.5835i 0.870419i
\(210\) 13.7776 1.08436i 0.950743 0.0748281i
\(211\) −10.7182 −0.737871 −0.368935 0.929455i \(-0.620278\pi\)
−0.368935 + 0.929455i \(0.620278\pi\)
\(212\) 9.80130 + 9.80130i 0.673156 + 0.673156i
\(213\) 3.64831 0.249978
\(214\) 6.66908 + 6.66908i 0.455889 + 0.455889i
\(215\) 12.5432 0.987208i 0.855437 0.0673270i
\(216\) −0.812525 0.812525i −0.0552853 0.0552853i
\(217\) −5.43849 + 5.43849i −0.369189 + 0.369189i
\(218\) −10.2975 + 10.2975i −0.697437 + 0.697437i
\(219\) 5.35539 5.35539i 0.361884 0.361884i
\(220\) −1.42188 18.0660i −0.0958633 1.21801i
\(221\) 10.0997 + 5.42219i 0.679383 + 0.364736i
\(222\) 21.0145 21.0145i 1.41040 1.41040i
\(223\) 6.81715 0.456510 0.228255 0.973601i \(-0.426698\pi\)
0.228255 + 0.973601i \(0.426698\pi\)
\(224\) 13.0948i 0.874932i
\(225\) −2.65584 + 0.420660i −0.177056 + 0.0280440i
\(226\) 18.7748 18.7748i 1.24888 1.24888i
\(227\) 4.56288i 0.302849i 0.988469 + 0.151424i \(0.0483860\pi\)
−0.988469 + 0.151424i \(0.951614\pi\)
\(228\) 13.1530i 0.871077i
\(229\) −13.5635 + 13.5635i −0.896300 + 0.896300i −0.995107 0.0988063i \(-0.968498\pi\)
0.0988063 + 0.995107i \(0.468498\pi\)
\(230\) 2.42941 + 30.8673i 0.160190 + 2.03533i
\(231\) 11.6250i 0.764872i
\(232\) −1.06156 −0.0696950
\(233\) −0.665074 + 0.665074i −0.0435704 + 0.0435704i −0.728556 0.684986i \(-0.759808\pi\)
0.684986 + 0.728556i \(0.259808\pi\)
\(234\) 3.76941 1.13592i 0.246414 0.0742573i
\(235\) 9.12499 + 7.79343i 0.595249 + 0.508387i
\(236\) −9.48902 + 9.48902i −0.617682 + 0.617682i
\(237\) 11.4879 11.4879i 0.746220 0.746220i
\(238\) −7.38724 + 7.38724i −0.478844 + 0.478844i
\(239\) 9.47004 + 9.47004i 0.612566 + 0.612566i 0.943614 0.331048i \(-0.107402\pi\)
−0.331048 + 0.943614i \(0.607402\pi\)
\(240\) 1.23441 + 15.6840i 0.0796807 + 1.01240i
\(241\) −11.9072 11.9072i −0.767010 0.767010i 0.210569 0.977579i \(-0.432468\pi\)
−0.977579 + 0.210569i \(0.932468\pi\)
\(242\) 7.27565 0.467697
\(243\) −3.90689 3.90689i −0.250627 0.250627i
\(244\) 25.7804 1.65042
\(245\) −7.44850 6.36158i −0.475867 0.406426i
\(246\) 15.5219i 0.989642i
\(247\) −10.4676 5.61967i −0.666037 0.357571i
\(248\) 0.833760 + 0.833760i 0.0529438 + 0.0529438i
\(249\) 9.95890 + 9.95890i 0.631120 + 0.631120i
\(250\) 19.3548 + 11.8604i 1.22410 + 0.750116i
\(251\) 14.5519i 0.918509i −0.888305 0.459254i \(-0.848117\pi\)
0.888305 0.459254i \(-0.151883\pi\)
\(252\) 1.84713i 0.116358i
\(253\) −26.0448 −1.63742
\(254\) 23.3038 23.3038i 1.46221 1.46221i
\(255\) 8.68417 10.1679i 0.543824 0.636740i
\(256\) 13.8694 0.866834
\(257\) −13.0266 13.0266i −0.812578 0.812578i 0.172442 0.985020i \(-0.444834\pi\)
−0.985020 + 0.172442i \(0.944834\pi\)
\(258\) 21.4879i 1.33778i
\(259\) 12.5951 0.782619
\(260\) −15.6632 6.88532i −0.971393 0.427009i
\(261\) −2.30090 −0.142422
\(262\) 3.67248i 0.226887i
\(263\) −11.0431 11.0431i −0.680948 0.680948i 0.279266 0.960214i \(-0.409909\pi\)
−0.960214 + 0.279266i \(0.909909\pi\)
\(264\) 1.78220 0.109687
\(265\) −1.14592 14.5598i −0.0703936 0.894400i
\(266\) 7.65629 7.65629i 0.469437 0.469437i
\(267\) −22.8718 −1.39973
\(268\) 12.3997i 0.757434i
\(269\) 1.76574i 0.107659i 0.998550 + 0.0538296i \(0.0171428\pi\)
−0.998550 + 0.0538296i \(0.982857\pi\)
\(270\) 1.64969 + 20.9604i 0.100397 + 1.27561i
\(271\) 12.4047 + 12.4047i 0.753529 + 0.753529i 0.975136 0.221607i \(-0.0711302\pi\)
−0.221607 + 0.975136i \(0.571130\pi\)
\(272\) −8.40943 8.40943i −0.509897 0.509897i
\(273\) 9.67031 + 5.19163i 0.585274 + 0.314212i
\(274\) 18.2019i 1.09962i
\(275\) −11.2232 + 15.4476i −0.676783 + 0.931524i
\(276\) −27.2235 −1.63866
\(277\) 11.7206 + 11.7206i 0.704225 + 0.704225i 0.965315 0.261090i \(-0.0840818\pi\)
−0.261090 + 0.965315i \(0.584082\pi\)
\(278\) −10.9195 −0.654905
\(279\) 1.80714 + 1.80714i 0.108191 + 0.108191i
\(280\) 0.583158 0.682794i 0.0348503 0.0408048i
\(281\) −12.5191 12.5191i −0.746830 0.746830i 0.227053 0.973882i \(-0.427091\pi\)
−0.973882 + 0.227053i \(0.927091\pi\)
\(282\) −14.4916 + 14.4916i −0.862963 + 0.862963i
\(283\) 12.8558 12.8558i 0.764195 0.764195i −0.212883 0.977078i \(-0.568285\pi\)
0.977078 + 0.212883i \(0.0682852\pi\)
\(284\) 2.91071 2.91071i 0.172719 0.172719i
\(285\) −9.00045 + 10.5382i −0.533141 + 0.624232i
\(286\) 13.2232 24.6304i 0.781903 1.45643i
\(287\) −4.65155 + 4.65155i −0.274572 + 0.274572i
\(288\) −4.35123 −0.256399
\(289\) 6.89192i 0.405407i
\(290\) 14.7701 + 12.6147i 0.867327 + 0.740763i
\(291\) −11.4879 + 11.4879i −0.673433 + 0.673433i
\(292\) 8.54531i 0.500077i
\(293\) 18.2991i 1.06904i 0.845155 + 0.534521i \(0.179508\pi\)
−0.845155 + 0.534521i \(0.820492\pi\)
\(294\) 11.8291 11.8291i 0.689889 0.689889i
\(295\) 14.0959 1.10941i 0.820695 0.0645926i
\(296\) 1.93091i 0.112232i
\(297\) −17.6857 −1.02623
\(298\) 15.8079 15.8079i 0.915727 0.915727i
\(299\) −11.6313 + 21.6654i −0.672658 + 1.25294i
\(300\) −11.7311 + 16.1467i −0.677295 + 0.932229i
\(301\) −6.43941 + 6.43941i −0.371162 + 0.371162i
\(302\) 3.77716 3.77716i 0.217351 0.217351i
\(303\) −1.09559 + 1.09559i −0.0629400 + 0.0629400i
\(304\) 8.71571 + 8.71571i 0.499880 + 0.499880i
\(305\) −20.6554 17.6412i −1.18272 1.01013i
\(306\) 2.45469 + 2.45469i 0.140325 + 0.140325i
\(307\) 18.9366 1.08077 0.540384 0.841418i \(-0.318279\pi\)
0.540384 + 0.841418i \(0.318279\pi\)
\(308\) 9.27474 + 9.27474i 0.528477 + 0.528477i
\(309\) 2.30831 0.131315
\(310\) −1.69280 21.5082i −0.0961446 1.22159i
\(311\) 17.3532i 0.984010i 0.870592 + 0.492005i \(0.163736\pi\)
−0.870592 + 0.492005i \(0.836264\pi\)
\(312\) 0.795914 1.48253i 0.0450598 0.0839315i
\(313\) −5.54565 5.54565i −0.313459 0.313459i 0.532789 0.846248i \(-0.321144\pi\)
−0.846248 + 0.532789i \(0.821144\pi\)
\(314\) −20.0863 20.0863i −1.13354 1.13354i
\(315\) 1.26397 1.47993i 0.0712168 0.0833847i
\(316\) 18.3306i 1.03118i
\(317\) 33.4987i 1.88147i −0.339139 0.940736i \(-0.610136\pi\)
0.339139 0.940736i \(-0.389864\pi\)
\(318\) 24.9426 1.39871
\(319\) −11.5532 + 11.5532i −0.646854 + 0.646854i
\(320\) 15.2110 + 12.9914i 0.850322 + 0.726239i
\(321\) 8.73740 0.487674
\(322\) −15.8467 15.8467i −0.883100 0.883100i
\(323\) 10.4762i 0.582913i
\(324\) −21.9100 −1.21722
\(325\) 7.83792 + 16.2347i 0.434769 + 0.900542i
\(326\) −15.3041 −0.847618
\(327\) 13.4912i 0.746063i
\(328\) 0.713116 + 0.713116i 0.0393753 + 0.0393753i
\(329\) −8.68558 −0.478852
\(330\) −24.7967 21.1782i −1.36501 1.16582i
\(331\) 18.7185 18.7185i 1.02886 1.02886i 0.0292907 0.999571i \(-0.490675\pi\)
0.999571 0.0292907i \(-0.00932486\pi\)
\(332\) 15.8909 0.872126
\(333\) 4.18518i 0.229347i
\(334\) 38.3905i 2.10063i
\(335\) 8.48501 9.93473i 0.463586 0.542792i
\(336\) −8.05186 8.05186i −0.439265 0.439265i
\(337\) 12.3554 + 12.3554i 0.673041 + 0.673041i 0.958416 0.285375i \(-0.0921181\pi\)
−0.285375 + 0.958416i \(0.592118\pi\)
\(338\) −14.5835 21.9994i −0.793238 1.19661i
\(339\) 24.5975i 1.33595i
\(340\) −1.18377 15.0406i −0.0641989 0.815693i
\(341\) 18.1479 0.982764
\(342\) −2.54409 2.54409i −0.137569 0.137569i
\(343\) 18.4189 0.994529
\(344\) 0.987208 + 0.987208i 0.0532267 + 0.0532267i
\(345\) 21.8116 + 18.6288i 1.17430 + 1.00294i
\(346\) −5.70281 5.70281i −0.306585 0.306585i
\(347\) −0.962458 + 0.962458i −0.0516675 + 0.0516675i −0.732468 0.680801i \(-0.761632\pi\)
0.680801 + 0.732468i \(0.261632\pi\)
\(348\) −12.0760 + 12.0760i −0.647343 + 0.647343i
\(349\) 6.19870 6.19870i 0.331809 0.331809i −0.521464 0.853273i \(-0.674614\pi\)
0.853273 + 0.521464i \(0.174614\pi\)
\(350\) −16.2275 + 2.57029i −0.867398 + 0.137388i
\(351\) −7.89826 + 14.7119i −0.421578 + 0.785261i
\(352\) −21.8482 + 21.8482i −1.16451 + 1.16451i
\(353\) 3.89028 0.207059 0.103529 0.994626i \(-0.466986\pi\)
0.103529 + 0.994626i \(0.466986\pi\)
\(354\) 24.1479i 1.28345i
\(355\) −4.32385 + 0.340308i −0.229486 + 0.0180616i
\(356\) −18.2477 + 18.2477i −0.967124 + 0.967124i
\(357\) 9.67828i 0.512229i
\(358\) 43.9833i 2.32459i
\(359\) −16.1238 + 16.1238i −0.850980 + 0.850980i −0.990254 0.139274i \(-0.955523\pi\)
0.139274 + 0.990254i \(0.455523\pi\)
\(360\) −0.226884 0.193776i −0.0119578 0.0102129i
\(361\) 8.14222i 0.428538i
\(362\) −13.8629 −0.728616
\(363\) 4.76605 4.76605i 0.250153 0.250153i
\(364\) 11.8572 3.57319i 0.621486 0.187286i
\(365\) −5.84747 + 6.84655i −0.306071 + 0.358365i
\(366\) 32.8033 32.8033i 1.71465 1.71465i
\(367\) 6.58690 6.58690i 0.343833 0.343833i −0.513973 0.857806i \(-0.671827\pi\)
0.857806 + 0.513973i \(0.171827\pi\)
\(368\) 18.0394 18.0394i 0.940369 0.940369i
\(369\) 1.54565 + 1.54565i 0.0804635 + 0.0804635i
\(370\) −22.9454 + 26.8658i −1.19287 + 1.39668i
\(371\) 7.47470 + 7.47470i 0.388067 + 0.388067i
\(372\) 18.9692 0.983508
\(373\) −9.51823 9.51823i −0.492835 0.492835i 0.416363 0.909198i \(-0.363305\pi\)
−0.909198 + 0.416363i \(0.863305\pi\)
\(374\) 24.6507 1.27466
\(375\) 20.4480 4.90934i 1.05593 0.253517i
\(376\) 1.33156i 0.0686700i
\(377\) 4.45098 + 14.7701i 0.229237 + 0.760696i
\(378\) −10.7607 10.7607i −0.553469 0.553469i
\(379\) −5.31888 5.31888i −0.273213 0.273213i 0.557179 0.830392i \(-0.311884\pi\)
−0.830392 + 0.557179i \(0.811884\pi\)
\(380\) 1.22688 + 15.5884i 0.0629378 + 0.799669i
\(381\) 30.5312i 1.56416i
\(382\) 38.4645i 1.96802i
\(383\) 14.8685 0.759747 0.379874 0.925038i \(-0.375968\pi\)
0.379874 + 0.925038i \(0.375968\pi\)
\(384\) −2.63506 + 2.63506i −0.134470 + 0.134470i
\(385\) −1.08436 13.7776i −0.0552642 0.702170i
\(386\) 14.5957 0.742900
\(387\) 2.13974 + 2.13974i 0.108769 + 0.108769i
\(388\) 18.3306i 0.930597i
\(389\) 28.9078 1.46568 0.732841 0.680400i \(-0.238194\pi\)
0.732841 + 0.680400i \(0.238194\pi\)
\(390\) −28.6911 + 11.1691i −1.45283 + 0.565571i
\(391\) −21.6832 −1.09657
\(392\) 1.08692i 0.0548977i
\(393\) −2.40573 2.40573i −0.121353 0.121353i
\(394\) −8.96505 −0.451653
\(395\) −12.5435 + 14.6866i −0.631131 + 0.738964i
\(396\) 3.08188 3.08188i 0.154870 0.154870i
\(397\) −14.6060 −0.733052 −0.366526 0.930408i \(-0.619453\pi\)
−0.366526 + 0.930408i \(0.619453\pi\)
\(398\) 0.634411i 0.0318002i
\(399\) 10.0308i 0.502167i
\(400\) −2.92595 18.4730i −0.146297 0.923649i
\(401\) 8.22532 + 8.22532i 0.410753 + 0.410753i 0.882001 0.471248i \(-0.156196\pi\)
−0.471248 + 0.882001i \(0.656196\pi\)
\(402\) 15.7776 + 15.7776i 0.786914 + 0.786914i
\(403\) 8.10468 15.0963i 0.403723 0.752003i
\(404\) 1.74818i 0.0869750i
\(405\) 17.5544 + 14.9928i 0.872285 + 0.744997i
\(406\) −14.0588 −0.697727
\(407\) −21.0145 21.0145i −1.04165 1.04165i
\(408\) 1.48375 0.0734565
\(409\) 26.1042 + 26.1042i 1.29077 + 1.29077i 0.934312 + 0.356456i \(0.116015\pi\)
0.356456 + 0.934312i \(0.383985\pi\)
\(410\) −1.44786 18.3960i −0.0715045 0.908515i
\(411\) 11.9235 + 11.9235i 0.588143 + 0.588143i
\(412\) 1.84162 1.84162i 0.0907303 0.0907303i
\(413\) −7.23655 + 7.23655i −0.356087 + 0.356087i
\(414\) −5.26565 + 5.26565i −0.258793 + 0.258793i
\(415\) −12.7319 10.8740i −0.624983 0.533782i
\(416\) 8.41726 + 27.9317i 0.412690 + 1.36946i
\(417\) −7.15298 + 7.15298i −0.350283 + 0.350283i
\(418\) −25.5486 −1.24962
\(419\) 22.8877i 1.11814i 0.829121 + 0.559070i \(0.188842\pi\)
−0.829121 + 0.559070i \(0.811158\pi\)
\(420\) −1.13344 14.4011i −0.0553060 0.702702i
\(421\) −24.6619 + 24.6619i −1.20195 + 1.20195i −0.228372 + 0.973574i \(0.573340\pi\)
−0.973574 + 0.228372i \(0.926660\pi\)
\(422\) 21.7614i 1.05933i
\(423\) 2.88611i 0.140327i
\(424\) 1.14592 1.14592i 0.0556510 0.0556510i
\(425\) −9.34371 + 12.8607i −0.453236 + 0.623835i
\(426\) 7.40725i 0.358883i
\(427\) 19.6607 0.951449
\(428\) 6.97090 6.97090i 0.336951 0.336951i
\(429\) −7.47252 24.7967i −0.360777 1.19719i
\(430\) −2.00435 25.4667i −0.0966583 1.22811i
\(431\) 16.5273 16.5273i 0.796093 0.796093i −0.186384 0.982477i \(-0.559677\pi\)
0.982477 + 0.186384i \(0.0596769\pi\)
\(432\) 12.2496 12.2496i 0.589361 0.589361i
\(433\) −25.0489 + 25.0489i −1.20378 + 1.20378i −0.230766 + 0.973009i \(0.574123\pi\)
−0.973009 + 0.230766i \(0.925877\pi\)
\(434\) 11.0419 + 11.0419i 0.530028 + 0.530028i
\(435\) 17.9389 1.41188i 0.860104 0.0676943i
\(436\) 10.7636 + 10.7636i 0.515481 + 0.515481i
\(437\) 22.4730 1.07503
\(438\) −10.8732 10.8732i −0.519540 0.519540i
\(439\) −18.1493 −0.866220 −0.433110 0.901341i \(-0.642584\pi\)
−0.433110 + 0.901341i \(0.642584\pi\)
\(440\) −2.11220 + 0.166240i −0.100695 + 0.00792520i
\(441\) 2.35586i 0.112184i
\(442\) 11.0088 20.5057i 0.523634 0.975359i
\(443\) −7.30257 7.30257i −0.346956 0.346956i 0.512019 0.858974i \(-0.328898\pi\)
−0.858974 + 0.512019i \(0.828898\pi\)
\(444\) −21.9655 21.9655i −1.04244 1.04244i
\(445\) 27.1068 2.13344i 1.28499 0.101135i
\(446\) 13.8410i 0.655391i
\(447\) 20.7105i 0.979572i
\(448\) −14.4785 −0.684047
\(449\) −3.27565 + 3.27565i −0.154588 + 0.154588i −0.780163 0.625576i \(-0.784864\pi\)
0.625576 + 0.780163i \(0.284864\pi\)
\(450\) 0.854075 + 5.39220i 0.0402615 + 0.254191i
\(451\) 15.5219 0.730899
\(452\) −19.6245 19.6245i −0.923057 0.923057i
\(453\) 4.94859i 0.232505i
\(454\) 9.26411 0.434786
\(455\) −11.9452 5.25091i −0.559997 0.246166i
\(456\) −1.53779 −0.0720136
\(457\) 13.8670i 0.648672i −0.945942 0.324336i \(-0.894859\pi\)
0.945942 0.324336i \(-0.105141\pi\)
\(458\) 27.5382 + 27.5382i 1.28678 + 1.28678i
\(459\) −14.7240 −0.687257
\(460\) 32.2643 2.53935i 1.50433 0.118398i
\(461\) −6.02325 + 6.02325i −0.280531 + 0.280531i −0.833321 0.552790i \(-0.813563\pi\)
0.552790 + 0.833321i \(0.313563\pi\)
\(462\) 23.6026 1.09809
\(463\) 16.6916i 0.775723i 0.921718 + 0.387862i \(0.126786\pi\)
−0.921718 + 0.387862i \(0.873214\pi\)
\(464\) 16.0042i 0.742974i
\(465\) −15.1982 12.9804i −0.704801 0.601954i
\(466\) 1.35031 + 1.35031i 0.0625521 + 0.0625521i
\(467\) 5.68909 + 5.68909i 0.263260 + 0.263260i 0.826377 0.563117i \(-0.190398\pi\)
−0.563117 + 0.826377i \(0.690398\pi\)
\(468\) −1.18733 3.94000i −0.0548842 0.182127i
\(469\) 9.45633i 0.436653i
\(470\) 15.8232 18.5267i 0.729869 0.854572i
\(471\) −26.3158 −1.21257
\(472\) 1.10941 + 1.10941i 0.0510649 + 0.0510649i
\(473\) 21.4879 0.988015
\(474\) −23.3242 23.3242i −1.07131 1.07131i
\(475\) 9.68402 13.3291i 0.444333 0.611580i
\(476\) 7.72156 + 7.72156i 0.353917 + 0.353917i
\(477\) 2.48375 2.48375i 0.113723 0.113723i
\(478\) 19.2272 19.2272i 0.879433 0.879433i
\(479\) −7.93443 + 7.93443i −0.362533 + 0.362533i −0.864745 0.502212i \(-0.832520\pi\)
0.502212 + 0.864745i \(0.332520\pi\)
\(480\) 33.9243 2.67000i 1.54842 0.121868i
\(481\) −26.8658 + 8.09604i −1.22497 + 0.369148i
\(482\) −24.1754 + 24.1754i −1.10116 + 1.10116i
\(483\) −20.7613 −0.944671
\(484\) 7.60492i 0.345678i
\(485\) 12.5435 14.6866i 0.569570 0.666885i
\(486\) −7.93225 + 7.93225i −0.359814 + 0.359814i
\(487\) 18.1005i 0.820210i −0.912038 0.410105i \(-0.865492\pi\)
0.912038 0.410105i \(-0.134508\pi\)
\(488\) 3.01413i 0.136443i
\(489\) −10.0252 + 10.0252i −0.453357 + 0.453357i
\(490\) −12.9161 + 15.1229i −0.583488 + 0.683181i
\(491\) 26.3839i 1.19069i 0.803471 + 0.595344i \(0.202984\pi\)
−0.803471 + 0.595344i \(0.797016\pi\)
\(492\) 16.2244 0.731453
\(493\) −9.61845 + 9.61845i −0.433193 + 0.433193i
\(494\) −11.4097 + 21.2526i −0.513348 + 0.956199i
\(495\) −4.57812 + 0.360320i −0.205771 + 0.0161952i
\(496\) −12.5698 + 12.5698i −0.564400 + 0.564400i
\(497\) 2.21978 2.21978i 0.0995706 0.0995706i
\(498\) 20.2198 20.2198i 0.906070 0.906070i
\(499\) −10.6751 10.6751i −0.477882 0.477882i 0.426572 0.904454i \(-0.359721\pi\)
−0.904454 + 0.426572i \(0.859721\pi\)
\(500\) 12.3971 20.2307i 0.554417 0.904744i
\(501\) −25.1484 25.1484i −1.12355 1.12355i
\(502\) −29.5451 −1.31866
\(503\) 0.564102 + 0.564102i 0.0251521 + 0.0251521i 0.719571 0.694419i \(-0.244338\pi\)
−0.694419 + 0.719571i \(0.744338\pi\)
\(504\) 0.215958 0.00961955
\(505\) 1.19626 1.40065i 0.0532328 0.0623280i
\(506\) 52.8793i 2.35077i
\(507\) −23.9643 4.85793i −1.06429 0.215748i
\(508\) −24.3585 24.3585i −1.08073 1.08073i
\(509\) 21.2626 + 21.2626i 0.942448 + 0.942448i 0.998432 0.0559841i \(-0.0178296\pi\)
−0.0559841 + 0.998432i \(0.517830\pi\)
\(510\) −20.6441 17.6317i −0.914138 0.780743i
\(511\) 6.51686i 0.288289i
\(512\) 32.1217i 1.41959i
\(513\) 15.2603 0.673757
\(514\) −26.4482 + 26.4482i −1.16658 + 1.16658i
\(515\) −2.73572 + 0.215315i −0.120550 + 0.00948789i
\(516\) 22.4604 0.988763
\(517\) 14.4916 + 14.4916i 0.637340 + 0.637340i
\(518\) 25.5720i 1.12357i
\(519\) −7.47145 −0.327960
\(520\) −0.805001 + 1.83128i −0.0353016 + 0.0803068i
\(521\) −0.104827 −0.00459254 −0.00229627 0.999997i \(-0.500731\pi\)
−0.00229627 + 0.999997i \(0.500731\pi\)
\(522\) 4.67157i 0.204469i
\(523\) −5.70495 5.70495i −0.249460 0.249460i 0.571289 0.820749i \(-0.306444\pi\)
−0.820749 + 0.571289i \(0.806444\pi\)
\(524\) −3.83869 −0.167694
\(525\) −8.94641 + 12.3138i −0.390453 + 0.537420i
\(526\) −22.4211 + 22.4211i −0.977605 + 0.977605i
\(527\) 15.1088 0.658150
\(528\) 26.8685i 1.16930i
\(529\) 23.5136i 1.02233i
\(530\) −29.5610 + 2.32660i −1.28405 + 0.101061i
\(531\) 2.40462 + 2.40462i 0.104351 + 0.104351i
\(532\) −8.00279 8.00279i −0.346965 0.346965i
\(533\) 6.93195 12.9119i 0.300256 0.559278i
\(534\) 46.4371i 2.00953i
\(535\) −10.3552 + 0.815007i −0.447696 + 0.0352358i
\(536\) 1.44972 0.0626185
\(537\) 28.8121 + 28.8121i 1.24333 + 1.24333i
\(538\) 3.58502 0.154561
\(539\) −11.8291 11.8291i −0.509517 0.509517i
\(540\) 21.9090 1.72435i 0.942814 0.0742040i
\(541\) 18.8179 + 18.8179i 0.809047 + 0.809047i 0.984490 0.175443i \(-0.0561358\pi\)
−0.175443 + 0.984490i \(0.556136\pi\)
\(542\) 25.1854 25.1854i 1.08181 1.08181i
\(543\) −9.08111 + 9.08111i −0.389708 + 0.389708i
\(544\) −18.1895 + 18.1895i −0.779866 + 0.779866i
\(545\) −1.25843 15.9892i −0.0539052 0.684903i
\(546\) 10.5407 19.6338i 0.451100 0.840250i
\(547\) 13.3103 13.3103i 0.569108 0.569108i −0.362770 0.931879i \(-0.618169\pi\)
0.931879 + 0.362770i \(0.118169\pi\)
\(548\) 19.0257 0.812737
\(549\) 6.53301i 0.278822i
\(550\) 31.3636 + 22.7867i 1.33735 + 0.971627i
\(551\) 9.96876 9.96876i 0.424683 0.424683i
\(552\) 3.18285i 0.135471i
\(553\) 13.9794i 0.594464i
\(554\) 23.7967 23.7967i 1.01102 1.01102i
\(555\) 2.56811 + 32.6297i 0.109010 + 1.38505i
\(556\) 11.4136i 0.484046i
\(557\) −37.1686 −1.57489 −0.787443 0.616388i \(-0.788595\pi\)
−0.787443 + 0.616388i \(0.788595\pi\)
\(558\) 3.66908 3.66908i 0.155325 0.155325i
\(559\) 9.59629 17.8747i 0.405880 0.756021i
\(560\) 10.2938 + 8.79171i 0.434994 + 0.371517i
\(561\) 16.1479 16.1479i 0.681765 0.681765i
\(562\) −25.4179 + 25.4179i −1.07219 + 1.07219i
\(563\) −30.1782 + 30.1782i −1.27186 + 1.27186i −0.326747 + 0.945112i \(0.605953\pi\)
−0.945112 + 0.326747i \(0.894047\pi\)
\(564\) 15.1475 + 15.1475i 0.637823 + 0.637823i
\(565\) 2.29441 + 29.1521i 0.0965264 + 1.22644i
\(566\) −26.1013 26.1013i −1.09712 1.09712i
\(567\) −16.7091 −0.701715
\(568\) −0.340308 0.340308i −0.0142790 0.0142790i
\(569\) 37.6216 1.57718 0.788589 0.614920i \(-0.210812\pi\)
0.788589 + 0.614920i \(0.210812\pi\)
\(570\) 21.3960 + 18.2738i 0.896181 + 0.765406i
\(571\) 21.9027i 0.916599i −0.888798 0.458299i \(-0.848459\pi\)
0.888798 0.458299i \(-0.151541\pi\)
\(572\) −25.7451 13.8216i −1.07646 0.577911i
\(573\) 25.1969 + 25.1969i 1.05261 + 1.05261i
\(574\) 9.44415 + 9.44415i 0.394191 + 0.394191i
\(575\) −27.5880 20.0436i −1.15050 0.835875i
\(576\) 4.81104i 0.200460i
\(577\) 0.139587i 0.00581108i 0.999996 + 0.00290554i \(0.000924863\pi\)
−0.999996 + 0.00290554i \(0.999075\pi\)
\(578\) −13.9928 −0.582024
\(579\) 9.56115 9.56115i 0.397348 0.397348i
\(580\) 13.1856 15.4385i 0.547504 0.641049i
\(581\) 12.1188 0.502771
\(582\) 23.3242 + 23.3242i 0.966817 + 0.966817i
\(583\) 24.9426i 1.03302i
\(584\) −0.999081 −0.0413422
\(585\) −1.74481 + 3.96923i −0.0721390 + 0.164107i
\(586\) 37.1530 1.53478
\(587\) 2.38675i 0.0985115i 0.998786 + 0.0492558i \(0.0156849\pi\)
−0.998786 + 0.0492558i \(0.984315\pi\)
\(588\) −12.3645 12.3645i −0.509902 0.509902i
\(589\) −15.6591 −0.645221
\(590\) −2.25247 28.6192i −0.0927327 1.17823i
\(591\) −5.87272 + 5.87272i −0.241571 + 0.241571i
\(592\) 29.1105 1.19643
\(593\) 35.9052i 1.47445i −0.675647 0.737225i \(-0.736136\pi\)
0.675647 0.737225i \(-0.263864\pi\)
\(594\) 35.9076i 1.47331i
\(595\) −0.902771 11.4703i −0.0370100 0.470238i
\(596\) −16.5233 16.5233i −0.676821 0.676821i
\(597\) −0.415582 0.415582i −0.0170087 0.0170087i
\(598\) 43.9877 + 23.6154i 1.79879 + 0.965705i
\(599\) 31.9707i 1.30629i −0.757233 0.653144i \(-0.773449\pi\)
0.757233 0.653144i \(-0.226551\pi\)
\(600\) 1.88780 + 1.37155i 0.0770691 + 0.0559932i
\(601\) 44.8777 1.83060 0.915299 0.402775i \(-0.131954\pi\)
0.915299 + 0.402775i \(0.131954\pi\)
\(602\) 13.0741 + 13.0741i 0.532860 + 0.532860i
\(603\) 3.14222 0.127961
\(604\) −3.94810 3.94810i −0.160646 0.160646i
\(605\) −5.20397 + 6.09311i −0.211572 + 0.247720i
\(606\) 2.22440 + 2.22440i 0.0903601 + 0.0903601i
\(607\) −25.9355 + 25.9355i −1.05269 + 1.05269i −0.0541565 + 0.998532i \(0.517247\pi\)
−0.998532 + 0.0541565i \(0.982753\pi\)
\(608\) 18.8519 18.8519i 0.764547 0.764547i
\(609\) −9.20947 + 9.20947i −0.373186 + 0.373186i
\(610\) −35.8174 + 41.9371i −1.45020 + 1.69798i
\(611\) 18.5267 5.58305i 0.749509 0.225866i
\(612\) 2.56578 2.56578i 0.103715 0.103715i
\(613\) 3.63491 0.146812 0.0734062 0.997302i \(-0.476613\pi\)
0.0734062 + 0.997302i \(0.476613\pi\)
\(614\) 38.4474i 1.55161i
\(615\) −12.9991 11.1022i −0.524174 0.447684i
\(616\) 1.08436 1.08436i 0.0436902 0.0436902i
\(617\) 29.1618i 1.17401i 0.809583 + 0.587005i \(0.199693\pi\)
−0.809583 + 0.587005i \(0.800307\pi\)
\(618\) 4.68661i 0.188523i
\(619\) 28.1188 28.1188i 1.13019 1.13019i 0.140045 0.990145i \(-0.455275\pi\)
0.990145 0.140045i \(-0.0447247\pi\)
\(620\) −22.4816 + 1.76941i −0.902883 + 0.0710612i
\(621\) 31.5850i 1.26746i
\(622\) 35.2326 1.41270
\(623\) −13.9161 + 13.9161i −0.557536 + 0.557536i
\(624\) 22.3506 + 11.9992i 0.894741 + 0.480354i
\(625\) −23.7763 + 7.72572i −0.951053 + 0.309029i
\(626\) −11.2595 + 11.2595i −0.450019 + 0.450019i
\(627\) −16.7360 + 16.7360i −0.668373 + 0.668373i
\(628\) −20.9954 + 20.9954i −0.837807 + 0.837807i
\(629\) −17.4953 17.4953i −0.697584 0.697584i
\(630\) −3.00474 2.56627i −0.119712 0.102243i
\(631\) −15.9754 15.9754i −0.635971 0.635971i 0.313588 0.949559i \(-0.398469\pi\)
−0.949559 + 0.313588i \(0.898469\pi\)
\(632\) −2.14314 −0.0852495
\(633\) 14.2552 + 14.2552i 0.566592 + 0.566592i
\(634\) −68.0131 −2.70114
\(635\) 2.84789 + 36.1844i 0.113015 + 1.43593i
\(636\) 26.0714i 1.03380i
\(637\) −15.1229 + 4.55730i −0.599189 + 0.180567i
\(638\) 23.4567 + 23.4567i 0.928658 + 0.928658i
\(639\) −0.737604 0.737604i −0.0291792 0.0291792i
\(640\) 2.87718 3.36876i 0.113730 0.133162i
\(641\) 40.6941i 1.60732i 0.595088 + 0.803661i \(0.297117\pi\)
−0.595088 + 0.803661i \(0.702883\pi\)
\(642\) 17.7397i 0.700131i
\(643\) −3.29115 −0.129790 −0.0648952 0.997892i \(-0.520671\pi\)
−0.0648952 + 0.997892i \(0.520671\pi\)
\(644\) −16.5638 + 16.5638i −0.652706 + 0.652706i
\(645\) −17.9954 15.3694i −0.708567 0.605170i
\(646\) −21.2701 −0.836861
\(647\) 34.7828 + 34.7828i 1.36745 + 1.36745i 0.864052 + 0.503403i \(0.167919\pi\)
0.503403 + 0.864052i \(0.332081\pi\)
\(648\) 2.56162i 0.100630i
\(649\) 24.1479 0.947888
\(650\) 32.9618 15.9135i 1.29287 0.624179i
\(651\) 14.4664 0.566982
\(652\) 15.9967i 0.626481i
\(653\) −9.10093 9.10093i −0.356147 0.356147i 0.506243 0.862391i \(-0.331034\pi\)
−0.862391 + 0.506243i \(0.831034\pi\)
\(654\) 27.3914 1.07109
\(655\) 3.07558 + 2.62678i 0.120173 + 0.102637i
\(656\) −10.7510 + 10.7510i −0.419755 + 0.419755i
\(657\) −2.16547 −0.0844830
\(658\) 17.6345i 0.687465i
\(659\) 1.05740i 0.0411906i −0.999788 0.0205953i \(-0.993444\pi\)
0.999788 0.0205953i \(-0.00655616\pi\)
\(660\) −22.1367 + 25.9189i −0.861669 + 1.00889i
\(661\) −6.24812 6.24812i −0.243024 0.243024i 0.575076 0.818100i \(-0.304972\pi\)
−0.818100 + 0.575076i \(0.804972\pi\)
\(662\) −38.0046 38.0046i −1.47709 1.47709i
\(663\) −6.22115 20.6441i −0.241609 0.801752i
\(664\) 1.85789i 0.0721002i
\(665\) 0.935651 + 11.8881i 0.0362830 + 0.461001i
\(666\) −8.49727 −0.329263
\(667\) −20.6329 20.6329i −0.798910 0.798910i
\(668\) −40.1279 −1.55259
\(669\) −9.06679 9.06679i −0.350543 0.350543i
\(670\) −20.1707 17.2273i −0.779262 0.665549i
\(671\) −32.8033 32.8033i −1.26636 1.26636i
\(672\) −17.4160 + 17.4160i −0.671838 + 0.671838i
\(673\) 8.47252 8.47252i 0.326592 0.326592i −0.524697 0.851289i \(-0.675821\pi\)
0.851289 + 0.524697i \(0.175821\pi\)
\(674\) 25.0854 25.0854i 0.966254 0.966254i
\(675\) −18.7336 13.6106i −0.721056 0.523871i
\(676\) −22.9950 + 15.2435i −0.884424 + 0.586288i
\(677\) −0.782203 + 0.782203i −0.0300625 + 0.0300625i −0.721978 0.691916i \(-0.756767\pi\)
0.691916 + 0.721978i \(0.256767\pi\)
\(678\) −49.9409 −1.91797
\(679\) 13.9794i 0.536479i
\(680\) −1.75848 + 0.138401i −0.0674348 + 0.00530744i
\(681\) 6.06862 6.06862i 0.232550 0.232550i
\(682\) 36.8461i 1.41091i
\(683\) 16.4856i 0.630803i −0.948958 0.315401i \(-0.897861\pi\)
0.948958 0.315401i \(-0.102139\pi\)
\(684\) −2.65923 + 2.65923i −0.101678 + 0.101678i
\(685\) −15.2435 13.0191i −0.582424 0.497434i
\(686\) 37.3964i 1.42780i
\(687\) 36.0788 1.37649
\(688\) −14.8832 + 14.8832i −0.567416 + 0.567416i
\(689\) −20.7485 11.1391i −0.790455 0.424367i
\(690\) 37.8224 44.2846i 1.43987 1.68589i
\(691\) 31.1593 31.1593i 1.18535 1.18535i 0.207018 0.978337i \(-0.433624\pi\)
0.978337 0.207018i \(-0.0663758\pi\)
\(692\) −5.96089 + 5.96089i −0.226599 + 0.226599i
\(693\) 2.35031 2.35031i 0.0892810 0.0892810i
\(694\) 1.95410 + 1.95410i 0.0741766 + 0.0741766i
\(695\) 7.81023 9.14466i 0.296259 0.346877i
\(696\) 1.41188 + 1.41188i 0.0535171 + 0.0535171i
\(697\) 12.9226 0.489478
\(698\) −12.5854 12.5854i −0.476363 0.476363i
\(699\) 1.76909 0.0669133
\(700\) 2.68661 + 16.9619i 0.101544 + 0.641101i
\(701\) 16.2976i 0.615554i 0.951459 + 0.307777i \(0.0995850\pi\)
−0.951459 + 0.307777i \(0.900415\pi\)
\(702\) 29.8698 + 16.0360i 1.12736 + 0.605240i
\(703\) 18.1325 + 18.1325i 0.683881 + 0.683881i
\(704\) 24.1570 + 24.1570i 0.910451 + 0.910451i
\(705\) −1.77097 22.5015i −0.0666987 0.847454i
\(706\) 7.89852i 0.297265i
\(707\) 1.33320i 0.0501401i
\(708\) 25.2407 0.948605
\(709\) −1.04907 + 1.04907i −0.0393988 + 0.0393988i −0.726532 0.687133i \(-0.758869\pi\)
0.687133 + 0.726532i \(0.258869\pi\)
\(710\) 0.690934 + 8.77880i 0.0259303 + 0.329463i
\(711\) −4.64517 −0.174208
\(712\) 2.13344 + 2.13344i 0.0799539 + 0.0799539i
\(713\) 32.4105i 1.21378i
\(714\) 19.6500 0.735384
\(715\) 11.1691 + 28.6911i 0.417702 + 1.07299i
\(716\) 45.9739 1.71812
\(717\) 25.1903i 0.940748i
\(718\) 32.7364 + 32.7364i 1.22171 + 1.22171i
\(719\) 48.2826 1.80064 0.900319 0.435232i \(-0.143333\pi\)
0.900319 + 0.435232i \(0.143333\pi\)
\(720\) 2.92137 3.42051i 0.108873 0.127475i
\(721\) 1.40447 1.40447i 0.0523050 0.0523050i
\(722\) −16.5313 −0.615232
\(723\) 31.6731i 1.17793i
\(724\) 14.4902i 0.538526i
\(725\) −21.1288 + 3.34661i −0.784704 + 0.124290i
\(726\) −9.67661 9.67661i −0.359133 0.359133i
\(727\) −13.9089 13.9089i −0.515851 0.515851i 0.400462 0.916313i \(-0.368850\pi\)
−0.916313 + 0.400462i \(0.868850\pi\)
\(728\) −0.417762 1.38629i −0.0154833 0.0513794i
\(729\) 20.5801i 0.762227i
\(730\) 13.9007 + 11.8722i 0.514488 + 0.439412i
\(731\) 17.8895 0.661666
\(732\) −34.2878 34.2878i −1.26731 1.26731i
\(733\) 38.3390 1.41608 0.708041 0.706171i \(-0.249579\pi\)
0.708041 + 0.706171i \(0.249579\pi\)
\(734\) −13.3735 13.3735i −0.493626 0.493626i
\(735\) 1.44560 + 18.3674i 0.0533218 + 0.677491i
\(736\) −39.0189 39.0189i −1.43826 1.43826i
\(737\) 15.7776 15.7776i 0.581175 0.581175i
\(738\) 3.13817 3.13817i 0.115518 0.115518i
\(739\) −14.1532 + 14.1532i −0.520633 + 0.520633i −0.917763 0.397130i \(-0.870006\pi\)
0.397130 + 0.917763i \(0.370006\pi\)
\(740\) 28.0816 + 23.9838i 1.03230 + 0.881662i
\(741\) 6.44773 + 21.3960i 0.236863 + 0.786003i
\(742\) 15.1760 15.1760i 0.557130 0.557130i
\(743\) 19.6941 0.722508 0.361254 0.932467i \(-0.382349\pi\)
0.361254 + 0.932467i \(0.382349\pi\)
\(744\) 2.21780i 0.0813084i
\(745\) 1.93183 + 24.5453i 0.0707769 + 0.899270i
\(746\) −19.3251 + 19.3251i −0.707541 + 0.707541i
\(747\) 4.02692i 0.147337i
\(748\) 25.7663i 0.942111i
\(749\) 5.31617 5.31617i 0.194249 0.194249i
\(750\) −9.96754 41.5161i −0.363963 1.51595i
\(751\) 31.6564i 1.15516i 0.816334 + 0.577580i \(0.196003\pi\)
−0.816334 + 0.577580i \(0.803997\pi\)
\(752\) −20.0747 −0.732047
\(753\) −19.3540 + 19.3540i −0.705300 + 0.705300i
\(754\) 29.9880 9.03693i 1.09210 0.329105i
\(755\) 0.461595 + 5.86489i 0.0167992 + 0.213445i
\(756\) −11.2477 + 11.2477i −0.409073 + 0.409073i
\(757\) −7.76808 + 7.76808i −0.282335 + 0.282335i −0.834040 0.551704i \(-0.813978\pi\)
0.551704 + 0.834040i \(0.313978\pi\)
\(758\) −10.7990 + 10.7990i −0.392239 + 0.392239i
\(759\) 34.6395 + 34.6395i 1.25733 + 1.25733i
\(760\) 1.82253 0.143442i 0.0661101 0.00520319i
\(761\) 20.3483 + 20.3483i 0.737626 + 0.737626i 0.972118 0.234492i \(-0.0753427\pi\)
−0.234492 + 0.972118i \(0.575343\pi\)
\(762\) −61.9881 −2.24559
\(763\) 8.20855 + 8.20855i 0.297169 + 0.297169i
\(764\) 40.2053 1.45458
\(765\) −3.81145 + 0.299980i −0.137803 + 0.0108458i
\(766\) 30.1879i 1.09073i
\(767\) 10.7842 20.0875i 0.389396 0.725316i
\(768\) −18.4462 18.4462i −0.665620 0.665620i
\(769\) −30.9403 30.9403i −1.11573 1.11573i −0.992360 0.123374i \(-0.960628\pi\)
−0.123374 0.992360i \(-0.539372\pi\)
\(770\) −27.9729 + 2.20160i −1.00807