Properties

Label 99.2.m.a.58.1
Level $99$
Weight $2$
Character 99.58
Analytic conductor $0.791$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(4,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\), degree \(8\), 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: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{15})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 58.1
Root \(-0.978148 - 0.207912i\) of defining polynomial
Character \(\chi\) \(=\) 99.58
Dual form 99.2.m.a.70.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.39169 - 1.06485i) q^{2} +(0.360114 - 1.69420i) q^{3} +(3.24803 + 3.60730i) q^{4} +(2.95630 - 1.31623i) q^{5} +(-2.66535 + 3.66854i) q^{6} +(0.978148 - 0.207912i) q^{7} +(-2.30902 - 7.10642i) q^{8} +(-2.74064 - 1.22021i) q^{9} +O(q^{10})\) \(q+(-2.39169 - 1.06485i) q^{2} +(0.360114 - 1.69420i) q^{3} +(3.24803 + 3.60730i) q^{4} +(2.95630 - 1.31623i) q^{5} +(-2.66535 + 3.66854i) q^{6} +(0.978148 - 0.207912i) q^{7} +(-2.30902 - 7.10642i) q^{8} +(-2.74064 - 1.22021i) q^{9} -8.47214 q^{10} +(-2.38101 + 2.30885i) q^{11} +(7.28115 - 4.20378i) q^{12} +(-0.258409 - 2.45859i) q^{13} +(-2.56082 - 0.544320i) q^{14} +(-1.16535 - 5.48255i) q^{15} +(-1.03003 + 9.80012i) q^{16} +(1.50000 + 1.08981i) q^{17} +(5.25542 + 5.83674i) q^{18} +(0.309017 + 0.951057i) q^{19} +(14.3502 + 6.38910i) q^{20} -1.73205i q^{21} +(8.15323 - 2.98664i) q^{22} +(-1.19098 + 2.06284i) q^{23} +(-12.8712 + 1.35282i) q^{24} +(3.66157 - 4.06659i) q^{25} +(-2.00000 + 6.15537i) q^{26} +(-3.05422 + 4.20378i) q^{27} +(3.92705 + 2.85317i) q^{28} +(-1.81359 + 0.385489i) q^{29} +(-3.05093 + 14.3535i) q^{30} +(0.169131 + 1.60917i) q^{31} +(5.42705 - 9.39993i) q^{32} +(3.05422 + 4.86536i) q^{33} +(-2.42705 - 4.20378i) q^{34} +(2.61803 - 1.90211i) q^{35} +(-4.50000 - 13.8496i) q^{36} +(1.88197 - 5.79210i) q^{37} +(0.273659 - 2.60369i) q^{38} +(-4.25841 - 0.447577i) q^{39} +(-16.1798 - 17.9695i) q^{40} +(11.2214 + 2.38519i) q^{41} +(-1.84437 + 4.14253i) q^{42} +(2.42705 + 4.20378i) q^{43} +(-16.0623 - 1.08981i) q^{44} -9.70820 q^{45} +(5.04508 - 3.66547i) q^{46} +(-3.97749 + 4.41745i) q^{47} +(16.2324 + 5.27424i) q^{48} +(-5.48127 + 2.44042i) q^{49} +(-13.0877 + 5.82701i) q^{50} +(2.38653 - 2.14885i) q^{51} +(8.02957 - 8.91774i) q^{52} +(5.73607 - 4.16750i) q^{53} +(11.7812 - 6.80185i) q^{54} +(-4.00000 + 9.95959i) q^{55} +(-3.73607 - 6.47106i) q^{56} +(1.72256 - 0.181049i) q^{57} +(4.74803 + 1.00922i) q^{58} +(-0.413545 - 0.459289i) q^{59} +(15.9921 - 22.0113i) q^{60} +(-0.433364 + 4.12319i) q^{61} +(1.30902 - 4.02874i) q^{62} +(-2.93444 - 0.623735i) q^{63} +(-7.04508 + 5.11855i) q^{64} +(-4.00000 - 6.92820i) q^{65} +(-2.12388 - 14.8887i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(0.940756 + 8.95070i) q^{68} +(3.06598 + 2.76062i) q^{69} +(-8.28700 + 1.76146i) q^{70} +(11.3992 + 8.28199i) q^{71} +(-2.34315 + 22.2936i) q^{72} +(-2.11803 + 6.51864i) q^{73} +(-10.6688 + 11.8489i) q^{74} +(-5.57104 - 7.66788i) q^{75} +(-2.42705 + 4.20378i) q^{76} +(-1.84894 + 2.75344i) q^{77} +(9.70820 + 5.60503i) q^{78} +(-8.73560 - 3.88934i) q^{79} +(9.85410 + 30.3278i) q^{80} +(6.02218 + 6.68830i) q^{81} +(-24.2984 - 17.6538i) q^{82} +(1.48807 - 14.1581i) q^{83} +(6.24803 - 5.62575i) q^{84} +(5.86889 + 1.24747i) q^{85} +(-1.32837 - 12.6386i) q^{86} +3.21140i q^{87} +(21.9055 + 11.5893i) q^{88} -11.2361 q^{89} +(23.2190 + 10.3378i) q^{90} +(-0.763932 - 2.35114i) q^{91} +(-11.3096 + 2.40394i) q^{92} +(2.78716 + 0.292943i) q^{93} +(14.2169 - 6.32976i) q^{94} +(2.16535 + 2.40487i) q^{95} +(-13.9710 - 12.5796i) q^{96} +(5.48127 + 2.44042i) q^{97} +15.7082 q^{98} +(9.34277 - 3.42238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22} - 14 q^{23} - 39 q^{24} - 9 q^{25} - 16 q^{26} + 18 q^{28} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 30 q^{32} - 6 q^{34} + 12 q^{35} - 36 q^{36} + 24 q^{37} - 4 q^{38} - 24 q^{39} + 12 q^{40} + 3 q^{41} - 12 q^{42} + 6 q^{43} - 48 q^{44} - 24 q^{45} + 18 q^{46} + 23 q^{47} - 6 q^{49} - 24 q^{50} + 27 q^{51} + 12 q^{52} + 28 q^{53} + 54 q^{54} - 32 q^{55} - 12 q^{56} + 3 q^{57} + 6 q^{58} + 3 q^{59} + 6 q^{62} + 3 q^{63} - 34 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 42 q^{71} + 39 q^{72} - 8 q^{73} + 13 q^{74} - 6 q^{76} - 11 q^{77} + 24 q^{78} - 22 q^{79} + 52 q^{80} + 9 q^{81} - 96 q^{82} - 17 q^{83} + 18 q^{84} - 6 q^{85} + 21 q^{86} + 37 q^{88} - 72 q^{89} + 42 q^{90} - 24 q^{91} - 21 q^{92} + 9 q^{93} + 28 q^{94} - 4 q^{95} + 6 q^{97} + 72 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39169 1.06485i −1.69118 0.752963i −0.999528 0.0307347i \(-0.990215\pi\)
−0.691655 0.722228i \(-0.743118\pi\)
\(3\) 0.360114 1.69420i 0.207912 0.978148i
\(4\) 3.24803 + 3.60730i 1.62401 + 1.80365i
\(5\) 2.95630 1.31623i 1.32210 0.588635i 0.380313 0.924858i \(-0.375816\pi\)
0.941782 + 0.336223i \(0.109150\pi\)
\(6\) −2.66535 + 3.66854i −1.08813 + 1.49768i
\(7\) 0.978148 0.207912i 0.369705 0.0785832i −0.0193127 0.999813i \(-0.506148\pi\)
0.389018 + 0.921230i \(0.372814\pi\)
\(8\) −2.30902 7.10642i −0.816361 2.51250i
\(9\) −2.74064 1.22021i −0.913545 0.406737i
\(10\) −8.47214 −2.67912
\(11\) −2.38101 + 2.30885i −0.717902 + 0.696144i
\(12\) 7.28115 4.20378i 2.10189 1.21353i
\(13\) −0.258409 2.45859i −0.0716696 0.681891i −0.970088 0.242752i \(-0.921950\pi\)
0.898419 0.439140i \(-0.144717\pi\)
\(14\) −2.56082 0.544320i −0.684409 0.145476i
\(15\) −1.16535 5.48255i −0.300893 1.41559i
\(16\) −1.03003 + 9.80012i −0.257509 + 2.45003i
\(17\) 1.50000 + 1.08981i 0.363803 + 0.264319i 0.754637 0.656143i \(-0.227813\pi\)
−0.390833 + 0.920461i \(0.627813\pi\)
\(18\) 5.25542 + 5.83674i 1.23871 + 1.37573i
\(19\) 0.309017 + 0.951057i 0.0708934 + 0.218187i 0.980226 0.197884i \(-0.0634068\pi\)
−0.909332 + 0.416071i \(0.863407\pi\)
\(20\) 14.3502 + 6.38910i 3.20879 + 1.42865i
\(21\) 1.73205i 0.377964i
\(22\) 8.15323 2.98664i 1.73827 0.636754i
\(23\) −1.19098 + 2.06284i −0.248337 + 0.430133i −0.963065 0.269271i \(-0.913217\pi\)
0.714727 + 0.699403i \(0.246551\pi\)
\(24\) −12.8712 + 1.35282i −2.62733 + 0.276143i
\(25\) 3.66157 4.06659i 0.732315 0.813318i
\(26\) −2.00000 + 6.15537i −0.392232 + 1.20717i
\(27\) −3.05422 + 4.20378i −0.587785 + 0.809017i
\(28\) 3.92705 + 2.85317i 0.742143 + 0.539198i
\(29\) −1.81359 + 0.385489i −0.336774 + 0.0715836i −0.373195 0.927753i \(-0.621738\pi\)
0.0364206 + 0.999337i \(0.488404\pi\)
\(30\) −3.05093 + 14.3535i −0.557021 + 2.62058i
\(31\) 0.169131 + 1.60917i 0.0303768 + 0.289016i 0.999156 + 0.0410886i \(0.0130826\pi\)
−0.968779 + 0.247927i \(0.920251\pi\)
\(32\) 5.42705 9.39993i 0.959376 1.66169i
\(33\) 3.05422 + 4.86536i 0.531672 + 0.846950i
\(34\) −2.42705 4.20378i −0.416236 0.720942i
\(35\) 2.61803 1.90211i 0.442529 0.321516i
\(36\) −4.50000 13.8496i −0.750000 2.30826i
\(37\) 1.88197 5.79210i 0.309393 0.952215i −0.668608 0.743615i \(-0.733109\pi\)
0.978001 0.208599i \(-0.0668905\pi\)
\(38\) 0.273659 2.60369i 0.0443934 0.422375i
\(39\) −4.25841 0.447577i −0.681891 0.0716696i
\(40\) −16.1798 17.9695i −2.55825 2.84123i
\(41\) 11.2214 + 2.38519i 1.75249 + 0.372504i 0.968646 0.248447i \(-0.0799201\pi\)
0.783849 + 0.620951i \(0.213253\pi\)
\(42\) −1.84437 + 4.14253i −0.284593 + 0.639207i
\(43\) 2.42705 + 4.20378i 0.370122 + 0.641070i 0.989584 0.143957i \(-0.0459826\pi\)
−0.619462 + 0.785027i \(0.712649\pi\)
\(44\) −16.0623 1.08981i −2.42148 0.164296i
\(45\) −9.70820 −1.44721
\(46\) 5.04508 3.66547i 0.743857 0.540444i
\(47\) −3.97749 + 4.41745i −0.580177 + 0.644352i −0.959765 0.280804i \(-0.909399\pi\)
0.379588 + 0.925156i \(0.376066\pi\)
\(48\) 16.2324 + 5.27424i 2.34295 + 0.761271i
\(49\) −5.48127 + 2.44042i −0.783039 + 0.348631i
\(50\) −13.0877 + 5.82701i −1.85088 + 0.824063i
\(51\) 2.38653 2.14885i 0.334182 0.300899i
\(52\) 8.02957 8.91774i 1.11350 1.23667i
\(53\) 5.73607 4.16750i 0.787910 0.572450i −0.119433 0.992842i \(-0.538108\pi\)
0.907342 + 0.420393i \(0.138108\pi\)
\(54\) 11.7812 6.80185i 1.60321 0.925615i
\(55\) −4.00000 + 9.95959i −0.539360 + 1.34295i
\(56\) −3.73607 6.47106i −0.499253 0.864732i
\(57\) 1.72256 0.181049i 0.228159 0.0239805i
\(58\) 4.74803 + 1.00922i 0.623447 + 0.132518i
\(59\) −0.413545 0.459289i −0.0538390 0.0597943i 0.715624 0.698486i \(-0.246143\pi\)
−0.769463 + 0.638692i \(0.779476\pi\)
\(60\) 15.9921 22.0113i 2.06457 2.84164i
\(61\) −0.433364 + 4.12319i −0.0554866 + 0.527920i 0.931110 + 0.364739i \(0.118842\pi\)
−0.986596 + 0.163180i \(0.947825\pi\)
\(62\) 1.30902 4.02874i 0.166245 0.511650i
\(63\) −2.93444 0.623735i −0.369705 0.0785832i
\(64\) −7.04508 + 5.11855i −0.880636 + 0.639819i
\(65\) −4.00000 6.92820i −0.496139 0.859338i
\(66\) −2.12388 14.8887i −0.261432 1.83268i
\(67\) −3.00000 + 5.19615i −0.366508 + 0.634811i −0.989017 0.147802i \(-0.952780\pi\)
0.622509 + 0.782613i \(0.286114\pi\)
\(68\) 0.940756 + 8.95070i 0.114083 + 1.08543i
\(69\) 3.06598 + 2.76062i 0.369101 + 0.332340i
\(70\) −8.28700 + 1.76146i −0.990486 + 0.210534i
\(71\) 11.3992 + 8.28199i 1.35283 + 0.982892i 0.998865 + 0.0476350i \(0.0151684\pi\)
0.353970 + 0.935257i \(0.384832\pi\)
\(72\) −2.34315 + 22.2936i −0.276143 + 2.62733i
\(73\) −2.11803 + 6.51864i −0.247897 + 0.762949i 0.747249 + 0.664544i \(0.231374\pi\)
−0.995146 + 0.0984051i \(0.968626\pi\)
\(74\) −10.6688 + 11.8489i −1.24022 + 1.37741i
\(75\) −5.57104 7.66788i −0.643288 0.885410i
\(76\) −2.42705 + 4.20378i −0.278402 + 0.482206i
\(77\) −1.84894 + 2.75344i −0.210707 + 0.313783i
\(78\) 9.70820 + 5.60503i 1.09924 + 0.634645i
\(79\) −8.73560 3.88934i −0.982832 0.437585i −0.148539 0.988907i \(-0.547457\pi\)
−0.834293 + 0.551322i \(0.814124\pi\)
\(80\) 9.85410 + 30.3278i 1.10172 + 3.39075i
\(81\) 6.02218 + 6.68830i 0.669131 + 0.743145i
\(82\) −24.2984 17.6538i −2.68331 1.94954i
\(83\) 1.48807 14.1581i 0.163337 1.55405i −0.539061 0.842267i \(-0.681221\pi\)
0.702398 0.711784i \(-0.252113\pi\)
\(84\) 6.24803 5.62575i 0.681716 0.613820i
\(85\) 5.86889 + 1.24747i 0.636570 + 0.135307i
\(86\) −1.32837 12.6386i −0.143242 1.36285i
\(87\) 3.21140i 0.344298i
\(88\) 21.9055 + 11.5893i 2.33513 + 1.23542i
\(89\) −11.2361 −1.19102 −0.595510 0.803348i \(-0.703050\pi\)
−0.595510 + 0.803348i \(0.703050\pi\)
\(90\) 23.2190 + 10.3378i 2.44750 + 1.08970i
\(91\) −0.763932 2.35114i −0.0800818 0.246467i
\(92\) −11.3096 + 2.40394i −1.17911 + 0.250628i
\(93\) 2.78716 + 0.292943i 0.289016 + 0.0303768i
\(94\) 14.2169 6.32976i 1.46636 0.652865i
\(95\) 2.16535 + 2.40487i 0.222160 + 0.246734i
\(96\) −13.9710 12.5796i −1.42591 1.28390i
\(97\) 5.48127 + 2.44042i 0.556539 + 0.247787i 0.665678 0.746239i \(-0.268143\pi\)
−0.109139 + 0.994027i \(0.534809\pi\)
\(98\) 15.7082 1.58677
\(99\) 9.34277 3.42238i 0.938983 0.343963i
\(100\) 26.5623 2.65623
\(101\) 0.431318 + 0.192035i 0.0429177 + 0.0191082i 0.428083 0.903739i \(-0.359189\pi\)
−0.385166 + 0.922847i \(0.625856\pi\)
\(102\) −7.99606 + 2.59808i −0.791728 + 0.257248i
\(103\) −3.85682 4.28344i −0.380024 0.422060i 0.522540 0.852615i \(-0.324984\pi\)
−0.902564 + 0.430555i \(0.858318\pi\)
\(104\) −16.8751 + 7.51329i −1.65474 + 0.736739i
\(105\) −2.27977 5.12045i −0.222483 0.499705i
\(106\) −18.1567 + 3.85932i −1.76353 + 0.374850i
\(107\) −4.64590 14.2986i −0.449136 1.38230i −0.877884 0.478874i \(-0.841045\pi\)
0.428748 0.903424i \(-0.358955\pi\)
\(108\) −25.0845 + 2.63649i −2.41376 + 0.253696i
\(109\) 13.8541 1.32698 0.663491 0.748184i \(-0.269074\pi\)
0.663491 + 0.748184i \(0.269074\pi\)
\(110\) 20.1722 19.5609i 1.92335 1.86506i
\(111\) −9.13525 5.27424i −0.867080 0.500609i
\(112\) 1.03003 + 9.80012i 0.0973291 + 0.926024i
\(113\) −12.4850 2.65377i −1.17449 0.249646i −0.420973 0.907073i \(-0.638311\pi\)
−0.753518 + 0.657427i \(0.771645\pi\)
\(114\) −4.31263 1.40126i −0.403915 0.131240i
\(115\) −0.805727 + 7.66598i −0.0751344 + 0.714856i
\(116\) −7.28115 5.29007i −0.676038 0.491170i
\(117\) −2.29180 + 7.05342i −0.211877 + 0.652089i
\(118\) 0.500000 + 1.53884i 0.0460287 + 0.141662i
\(119\) 1.69381 + 0.754131i 0.155271 + 0.0691311i
\(120\) −36.2705 + 20.9408i −3.31103 + 1.91162i
\(121\) 0.338426 10.9948i 0.0307660 0.999527i
\(122\) 5.42705 9.39993i 0.491342 0.851029i
\(123\) 8.08199 18.1524i 0.728728 1.63675i
\(124\) −5.25542 + 5.83674i −0.471951 + 0.524154i
\(125\) 0.472136 1.45309i 0.0422291 0.129968i
\(126\) 6.35410 + 4.61653i 0.566068 + 0.411273i
\(127\) −7.73607 5.62058i −0.686465 0.498746i 0.189031 0.981971i \(-0.439465\pi\)
−0.875496 + 0.483225i \(0.839465\pi\)
\(128\) 1.06635 0.226659i 0.0942527 0.0200340i
\(129\) 7.99606 2.59808i 0.704014 0.228748i
\(130\) 2.18927 + 20.8295i 0.192012 + 1.82687i
\(131\) −8.38197 + 14.5180i −0.732336 + 1.26844i 0.223547 + 0.974693i \(0.428236\pi\)
−0.955882 + 0.293750i \(0.905097\pi\)
\(132\) −7.63062 + 26.8203i −0.664160 + 2.33441i
\(133\) 0.500000 + 0.866025i 0.0433555 + 0.0750939i
\(134\) 12.7082 9.23305i 1.09782 0.797614i
\(135\) −3.49606 + 16.4477i −0.300893 + 1.41559i
\(136\) 4.28115 13.1760i 0.367106 1.12984i
\(137\) 0.667097 6.34700i 0.0569940 0.542261i −0.928353 0.371700i \(-0.878775\pi\)
0.985347 0.170562i \(-0.0545582\pi\)
\(138\) −4.39324 9.86737i −0.373977 0.839967i
\(139\) −2.48127 2.75573i −0.210459 0.233738i 0.628668 0.777674i \(-0.283600\pi\)
−0.839127 + 0.543935i \(0.816934\pi\)
\(140\) 15.3649 + 3.26592i 1.29857 + 0.276021i
\(141\) 6.05171 + 8.32946i 0.509646 + 0.701467i
\(142\) −18.4443 31.9464i −1.54781 2.68088i
\(143\) 6.29180 + 5.25731i 0.526146 + 0.439638i
\(144\) 14.7812 25.6017i 1.23176 2.13348i
\(145\) −4.85410 + 3.52671i −0.403111 + 0.292877i
\(146\) 12.0071 13.3352i 0.993711 1.10363i
\(147\) 2.16068 + 10.1652i 0.178210 + 0.838412i
\(148\) 27.0065 12.0241i 2.21992 0.988373i
\(149\) 6.55957 2.92051i 0.537381 0.239257i −0.120056 0.992767i \(-0.538307\pi\)
0.657437 + 0.753510i \(0.271641\pi\)
\(150\) 5.15907 + 24.2715i 0.421237 + 1.98176i
\(151\) −7.57873 + 8.41704i −0.616748 + 0.684969i −0.967896 0.251352i \(-0.919125\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(152\) 6.04508 4.39201i 0.490321 0.356239i
\(153\) −2.78115 4.81710i −0.224843 0.389439i
\(154\) 7.35410 4.61653i 0.592610 0.372010i
\(155\) 2.61803 + 4.53457i 0.210286 + 0.364225i
\(156\) −12.2169 16.8151i −0.978134 1.34629i
\(157\) −13.5514 2.88043i −1.08152 0.229883i −0.367508 0.930021i \(-0.619789\pi\)
−0.714008 + 0.700137i \(0.753122\pi\)
\(158\) 16.7513 + 18.6042i 1.33266 + 1.48007i
\(159\) −4.99494 11.2188i −0.396125 0.889711i
\(160\) 3.67152 34.9322i 0.290259 2.76163i
\(161\) −0.736068 + 2.26538i −0.0580103 + 0.178537i
\(162\) −7.28115 22.4091i −0.572061 1.76062i
\(163\) −5.89919 + 4.28601i −0.462060 + 0.335706i −0.794339 0.607475i \(-0.792182\pi\)
0.332279 + 0.943181i \(0.392182\pi\)
\(164\) 27.8435 + 48.2263i 2.17421 + 3.76584i
\(165\) 15.4331 + 10.3634i 1.20147 + 0.806789i
\(166\) −18.6353 + 32.2772i −1.44638 + 2.50520i
\(167\) 1.06996 + 10.1800i 0.0827960 + 0.787752i 0.954599 + 0.297895i \(0.0962844\pi\)
−0.871803 + 0.489857i \(0.837049\pi\)
\(168\) −12.3087 + 3.99933i −0.949636 + 0.308555i
\(169\) 6.73801 1.43221i 0.518309 0.110170i
\(170\) −12.7082 9.23305i −0.974675 0.708143i
\(171\) 0.313585 2.98357i 0.0239805 0.228159i
\(172\) −7.28115 + 22.4091i −0.555183 + 1.70868i
\(173\) −7.96923 + 8.85073i −0.605889 + 0.672908i −0.965563 0.260170i \(-0.916221\pi\)
0.359673 + 0.933078i \(0.382888\pi\)
\(174\) 3.41966 7.68068i 0.259244 0.582271i
\(175\) 2.73607 4.73901i 0.206827 0.358235i
\(176\) −20.1745 25.7124i −1.52071 1.93814i
\(177\) −0.927051 + 0.535233i −0.0696814 + 0.0402306i
\(178\) 26.8732 + 11.9647i 2.01423 + 0.896795i
\(179\) −7.09017 21.8213i −0.529944 1.63100i −0.754327 0.656499i \(-0.772036\pi\)
0.224382 0.974501i \(-0.427964\pi\)
\(180\) −31.5325 35.0204i −2.35030 2.61027i
\(181\) 17.0623 + 12.3965i 1.26823 + 0.921424i 0.999131 0.0416882i \(-0.0132736\pi\)
0.269101 + 0.963112i \(0.413274\pi\)
\(182\) −0.676522 + 6.43668i −0.0501472 + 0.477119i
\(183\) 6.82945 + 2.21902i 0.504847 + 0.164035i
\(184\) 17.4094 + 3.70049i 1.28344 + 0.272804i
\(185\) −2.06007 19.6002i −0.151459 1.44104i
\(186\) −6.35410 3.66854i −0.465905 0.268991i
\(187\) −6.08773 + 0.868416i −0.445179 + 0.0635049i
\(188\) −28.8541 −2.10440
\(189\) −2.11347 + 4.74692i −0.153732 + 0.345288i
\(190\) −2.61803 8.05748i −0.189932 0.584551i
\(191\) 11.6833 2.48335i 0.845371 0.179689i 0.235188 0.971950i \(-0.424429\pi\)
0.610183 + 0.792261i \(0.291096\pi\)
\(192\) 6.13483 + 13.7791i 0.442743 + 0.994418i
\(193\) −10.0490 + 4.47410i −0.723343 + 0.322053i −0.735175 0.677877i \(-0.762900\pi\)
0.0118325 + 0.999930i \(0.496234\pi\)
\(194\) −10.5108 11.6735i −0.754634 0.838106i
\(195\) −13.1782 + 4.28187i −0.943712 + 0.306631i
\(196\) −26.6067 11.8460i −1.90048 0.846146i
\(197\) 3.76393 0.268169 0.134085 0.990970i \(-0.457191\pi\)
0.134085 + 0.990970i \(0.457191\pi\)
\(198\) −25.9894 1.76336i −1.84698 0.125316i
\(199\) −13.8541 −0.982091 −0.491046 0.871134i \(-0.663385\pi\)
−0.491046 + 0.871134i \(0.663385\pi\)
\(200\) −37.3535 16.6309i −2.64129 1.17598i
\(201\) 7.72299 + 6.95381i 0.544738 + 0.490484i
\(202\) −0.827091 0.918578i −0.0581939 0.0646309i
\(203\) −1.69381 + 0.754131i −0.118882 + 0.0529296i
\(204\) 15.5031 + 1.62944i 1.08543 + 0.114083i
\(205\) 36.3133 7.71864i 2.53623 0.539093i
\(206\) 4.66312 + 14.3516i 0.324895 + 0.999924i
\(207\) 5.78115 4.20025i 0.401818 0.291938i
\(208\) 24.3607 1.68911
\(209\) −2.93162 1.55100i −0.202784 0.107285i
\(210\) 14.6742i 1.01261i
\(211\) −1.20499 11.4647i −0.0829549 0.789263i −0.954352 0.298685i \(-0.903452\pi\)
0.871397 0.490579i \(-0.163215\pi\)
\(212\) 33.6643 + 7.15557i 2.31208 + 0.491447i
\(213\) 18.1364 16.3301i 1.24268 1.11892i
\(214\) −4.11431 + 39.1451i −0.281249 + 2.67590i
\(215\) 12.7082 + 9.23305i 0.866692 + 0.629689i
\(216\) 36.9261 + 11.9980i 2.51250 + 0.816361i
\(217\) 0.500000 + 1.53884i 0.0339422 + 0.104463i
\(218\) −33.1348 14.7525i −2.24417 0.999168i
\(219\) 10.2812 + 5.93583i 0.694736 + 0.401106i
\(220\) −48.9194 + 17.9198i −3.29814 + 1.20816i
\(221\) 2.29180 3.96951i 0.154163 0.267018i
\(222\) 16.2324 + 22.3420i 1.08945 + 1.49950i
\(223\) 15.0598 16.7256i 1.00848 1.12003i 0.0157264 0.999876i \(-0.494994\pi\)
0.992755 0.120156i \(-0.0383394\pi\)
\(224\) 3.35410 10.3229i 0.224105 0.689725i
\(225\) −14.9971 + 6.67715i −0.999809 + 0.445144i
\(226\) 27.0344 + 19.6417i 1.79830 + 1.30654i
\(227\) 14.0677 2.99018i 0.933705 0.198465i 0.284150 0.958780i \(-0.408289\pi\)
0.649555 + 0.760315i \(0.274955\pi\)
\(228\) 6.24803 + 5.62575i 0.413786 + 0.372574i
\(229\) 1.27319 + 12.1136i 0.0841349 + 0.800490i 0.952495 + 0.304555i \(0.0985079\pi\)
−0.868360 + 0.495935i \(0.834825\pi\)
\(230\) 10.0902 17.4767i 0.665326 1.15238i
\(231\) 3.99904 + 4.12403i 0.263118 + 0.271341i
\(232\) 6.92705 + 11.9980i 0.454783 + 0.787708i
\(233\) −23.5623 + 17.1190i −1.54362 + 1.12150i −0.595603 + 0.803279i \(0.703087\pi\)
−0.948015 + 0.318225i \(0.896913\pi\)
\(234\) 12.9921 14.4292i 0.849321 0.943267i
\(235\) −5.94427 + 18.2946i −0.387762 + 1.19341i
\(236\) 0.313585 2.98357i 0.0204127 0.194214i
\(237\) −9.73513 + 13.3993i −0.632365 + 0.870376i
\(238\) −3.24803 3.60730i −0.210538 0.233827i
\(239\) −1.49448 0.317661i −0.0966697 0.0205478i 0.159323 0.987227i \(-0.449069\pi\)
−0.255993 + 0.966679i \(0.582402\pi\)
\(240\) 54.9300 5.77338i 3.54572 0.372670i
\(241\) −13.4164 23.2379i −0.864227 1.49688i −0.867813 0.496891i \(-0.834475\pi\)
0.00358606 0.999994i \(-0.498859\pi\)
\(242\) −12.5172 + 25.9358i −0.804637 + 1.66722i
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) −16.2812 + 11.8290i −1.04229 + 0.757271i
\(245\) −12.9921 + 14.4292i −0.830036 + 0.921848i
\(246\) −38.6593 + 34.8090i −2.46483 + 2.21934i
\(247\) 2.25841 1.00551i 0.143699 0.0639790i
\(248\) 11.0449 4.91752i 0.701353 0.312263i
\(249\) −23.4508 7.61962i −1.48613 0.482873i
\(250\) −2.67652 + 2.97258i −0.169278 + 0.188002i
\(251\) −0.354102 + 0.257270i −0.0223507 + 0.0162387i −0.598905 0.800820i \(-0.704397\pi\)
0.576554 + 0.817059i \(0.304397\pi\)
\(252\) −7.28115 12.6113i −0.458670 0.794439i
\(253\) −1.92705 7.66145i −0.121153 0.481671i
\(254\) 12.5172 + 21.6805i 0.785400 + 1.36035i
\(255\) 4.22693 9.49384i 0.264701 0.594528i
\(256\) 14.2441 + 3.02767i 0.890255 + 0.189230i
\(257\) −17.4577 19.3888i −1.08898 1.20944i −0.976439 0.215792i \(-0.930767\pi\)
−0.112544 0.993647i \(-0.535900\pi\)
\(258\) −21.8907 2.30080i −1.36285 0.143242i
\(259\) 0.636596 6.05681i 0.0395562 0.376352i
\(260\) 12.0000 36.9322i 0.744208 2.29044i
\(261\) 5.44076 + 1.15647i 0.336774 + 0.0715836i
\(262\) 35.5066 25.7970i 2.19360 1.59375i
\(263\) −0.354102 0.613323i −0.0218349 0.0378191i 0.854902 0.518790i \(-0.173617\pi\)
−0.876736 + 0.480971i \(0.840284\pi\)
\(264\) 27.5231 32.9388i 1.69393 2.02724i
\(265\) 11.4721 19.8703i 0.704728 1.22062i
\(266\) −0.273659 2.60369i −0.0167791 0.159643i
\(267\) −4.04626 + 19.0362i −0.247627 + 1.16499i
\(268\) −28.4882 + 6.05535i −1.74019 + 0.369889i
\(269\) −9.92705 7.21242i −0.605263 0.439749i 0.242480 0.970156i \(-0.422039\pi\)
−0.847743 + 0.530407i \(0.822039\pi\)
\(270\) 25.8758 35.6150i 1.57475 2.16746i
\(271\) 4.70820 14.4904i 0.286003 0.880227i −0.700093 0.714051i \(-0.746858\pi\)
0.986096 0.166175i \(-0.0531418\pi\)
\(272\) −12.2254 + 13.5776i −0.741271 + 0.823265i
\(273\) −4.25841 + 0.447577i −0.257731 + 0.0270886i
\(274\) −8.35410 + 14.4697i −0.504690 + 0.874148i
\(275\) 0.670897 + 18.1366i 0.0404566 + 1.09368i
\(276\) 20.0265i 1.20545i
\(277\) −13.4875 6.00503i −0.810387 0.360807i −0.0406537 0.999173i \(-0.512944\pi\)
−0.769733 + 0.638366i \(0.779611\pi\)
\(278\) 3.00000 + 9.23305i 0.179928 + 0.553762i
\(279\) 1.50000 4.61653i 0.0898027 0.276384i
\(280\) −19.5623 14.2128i −1.16907 0.849380i
\(281\) −0.661272 + 6.29158i −0.0394482 + 0.375324i 0.956932 + 0.290313i \(0.0937594\pi\)
−0.996380 + 0.0850115i \(0.972907\pi\)
\(282\) −5.60420 26.3657i −0.333725 1.57005i
\(283\) 16.6285 + 3.53450i 0.988462 + 0.210104i 0.673651 0.739050i \(-0.264725\pi\)
0.314812 + 0.949154i \(0.398059\pi\)
\(284\) 7.14924 + 68.0204i 0.424229 + 4.03627i
\(285\) 4.85410 2.80252i 0.287532 0.166007i
\(286\) −9.44980 19.2737i −0.558778 1.13968i
\(287\) 11.4721 0.677179
\(288\) −26.3435 + 19.1396i −1.55230 + 1.12781i
\(289\) −4.19098 12.8985i −0.246528 0.758736i
\(290\) 15.3649 3.26592i 0.902260 0.191781i
\(291\) 6.10844 8.40755i 0.358083 0.492859i
\(292\) −30.3941 + 13.5323i −1.77868 + 0.791920i
\(293\) −4.56324 5.06800i −0.266588 0.296075i 0.594957 0.803758i \(-0.297169\pi\)
−0.861544 + 0.507682i \(0.830502\pi\)
\(294\) 5.65674 26.6129i 0.329908 1.55209i
\(295\) −1.82709 0.813473i −0.106377 0.0473622i
\(296\) −45.5066 −2.64502
\(297\) −2.43375 17.0610i −0.141221 0.989978i
\(298\) −18.7984 −1.08896
\(299\) 5.37945 + 2.39509i 0.311102 + 0.138511i
\(300\) 9.56545 45.0019i 0.552261 2.59819i
\(301\) 3.24803 + 3.60730i 0.187213 + 0.207921i
\(302\) 27.0889 12.0607i 1.55879 0.694018i
\(303\) 0.480669 0.661585i 0.0276137 0.0380070i
\(304\) −9.63877 + 2.04878i −0.552821 + 0.117506i
\(305\) 4.14590 + 12.7598i 0.237393 + 0.730622i
\(306\) 1.52218 + 14.4825i 0.0870170 + 0.827911i
\(307\) 1.14590 0.0653999 0.0326999 0.999465i \(-0.489589\pi\)
0.0326999 + 0.999465i \(0.489589\pi\)
\(308\) −15.9379 + 2.27354i −0.908146 + 0.129547i
\(309\) −8.64590 + 4.99171i −0.491848 + 0.283969i
\(310\) −1.43290 13.6331i −0.0813831 0.774309i
\(311\) 7.02343 + 1.49288i 0.398262 + 0.0846533i 0.402689 0.915337i \(-0.368076\pi\)
−0.00442652 + 0.999990i \(0.501409\pi\)
\(312\) 6.65207 + 31.2955i 0.376599 + 1.77176i
\(313\) 0.571994 5.44216i 0.0323310 0.307609i −0.966391 0.257075i \(-0.917241\pi\)
0.998722 0.0505336i \(-0.0160922\pi\)
\(314\) 29.3435 + 21.3193i 1.65595 + 1.20312i
\(315\) −9.49606 + 2.01845i −0.535042 + 0.113727i
\(316\) −14.3435 44.1446i −0.806883 2.48333i
\(317\) 2.79155 + 1.24288i 0.156789 + 0.0698069i 0.483631 0.875272i \(-0.339318\pi\)
−0.326842 + 0.945079i \(0.605984\pi\)
\(318\) 32.1509i 1.80293i
\(319\) 3.42813 5.10515i 0.191938 0.285834i
\(320\) −14.0902 + 24.4049i −0.787664 + 1.36427i
\(321\) −25.8978 + 2.72196i −1.44547 + 0.151925i
\(322\) 4.17274 4.63430i 0.232538 0.258260i
\(323\) −0.572949 + 1.76336i −0.0318797 + 0.0981157i
\(324\) −4.56653 + 43.4476i −0.253696 + 2.41376i
\(325\) −10.9443 7.95148i −0.607079 0.441069i
\(326\) 18.6730 3.96907i 1.03420 0.219826i
\(327\) 4.98905 23.4716i 0.275895 1.29798i
\(328\) −8.96032 85.2518i −0.494751 4.70724i
\(329\) −2.97214 + 5.14789i −0.163859 + 0.283812i
\(330\) −25.8758 41.2200i −1.42441 2.26909i
\(331\) 6.20820 + 10.7529i 0.341234 + 0.591034i 0.984662 0.174472i \(-0.0558219\pi\)
−0.643428 + 0.765506i \(0.722489\pi\)
\(332\) 55.9058 40.6179i 3.06823 2.22920i
\(333\) −12.2254 + 13.5776i −0.669945 + 0.744050i
\(334\) 8.28115 25.4868i 0.453125 1.39457i
\(335\) −2.02957 + 19.3100i −0.110887 + 1.05502i
\(336\) 16.9743 + 1.78407i 0.926024 + 0.0973291i
\(337\) −1.69147 1.87857i −0.0921403 0.102332i 0.695311 0.718709i \(-0.255267\pi\)
−0.787451 + 0.616377i \(0.788600\pi\)
\(338\) −17.6403 3.74957i −0.959508 0.203950i
\(339\) −8.99204 + 20.1965i −0.488381 + 1.09692i
\(340\) 14.5623 + 25.2227i 0.789752 + 1.36789i
\(341\) −4.11803 3.44095i −0.223004 0.186338i
\(342\) −3.92705 + 6.80185i −0.212351 + 0.367802i
\(343\) −10.5172 + 7.64121i −0.567877 + 0.412586i
\(344\) 24.2697 26.9542i 1.30853 1.45328i
\(345\) 12.6976 + 4.12569i 0.683613 + 0.222119i
\(346\) 28.4847 12.6822i 1.53134 0.681799i
\(347\) 24.5639 10.9366i 1.31866 0.587105i 0.377795 0.925889i \(-0.376682\pi\)
0.940864 + 0.338784i \(0.110016\pi\)
\(348\) −11.5845 + 10.4307i −0.620993 + 0.559145i
\(349\) −7.26281 + 8.06617i −0.388769 + 0.431772i −0.905481 0.424388i \(-0.860489\pi\)
0.516711 + 0.856160i \(0.327156\pi\)
\(350\) −11.5902 + 8.42075i −0.619521 + 0.450108i
\(351\) 11.1246 + 6.42280i 0.593788 + 0.342824i
\(352\) 8.78115 + 34.9116i 0.468037 + 1.86079i
\(353\) −5.20820 9.02087i −0.277205 0.480133i 0.693484 0.720472i \(-0.256075\pi\)
−0.970689 + 0.240339i \(0.922741\pi\)
\(354\) 2.78716 0.292943i 0.148136 0.0155697i
\(355\) 44.6003 + 9.48010i 2.36714 + 0.503151i
\(356\) −36.4951 40.5319i −1.93423 2.14819i
\(357\) 1.88761 2.59808i 0.0999031 0.137505i
\(358\) −6.27891 + 59.7398i −0.331851 + 3.15735i
\(359\) −4.98936 + 15.3557i −0.263328 + 0.810441i 0.728746 + 0.684784i \(0.240104\pi\)
−0.992074 + 0.125656i \(0.959896\pi\)
\(360\) 22.4164 + 68.9906i 1.18145 + 3.63612i
\(361\) 14.5623 10.5801i 0.766437 0.556849i
\(362\) −27.6074 47.8174i −1.45101 2.51323i
\(363\) −18.5055 4.53274i −0.971288 0.237907i
\(364\) 6.00000 10.3923i 0.314485 0.544705i
\(365\) 2.31848 + 22.0588i 0.121355 + 1.15461i
\(366\) −13.9710 12.5796i −0.730277 0.657544i
\(367\) −0.692728 + 0.147244i −0.0361601 + 0.00768607i −0.225956 0.974137i \(-0.572551\pi\)
0.189796 + 0.981824i \(0.439217\pi\)
\(368\) −18.9894 13.7966i −0.989889 0.719196i
\(369\) −27.8435 20.2295i −1.44947 1.05310i
\(370\) −15.9443 + 49.0714i −0.828903 + 2.55110i
\(371\) 4.74425 5.26902i 0.246309 0.273554i
\(372\) 7.99606 + 11.0056i 0.414576 + 0.570615i
\(373\) −12.8262 + 22.2157i −0.664117 + 1.15029i 0.315406 + 0.948957i \(0.397859\pi\)
−0.979524 + 0.201328i \(0.935474\pi\)
\(374\) 15.4847 + 4.40554i 0.800696 + 0.227805i
\(375\) −2.29180 1.32317i −0.118348 0.0683282i
\(376\) 40.5764 + 18.0658i 2.09257 + 0.931671i
\(377\) 1.41641 + 4.35926i 0.0729487 + 0.224513i
\(378\) 10.1095 9.10265i 0.519978 0.468190i
\(379\) 7.11803 + 5.17155i 0.365629 + 0.265645i 0.755396 0.655269i \(-0.227445\pi\)
−0.389767 + 0.920913i \(0.627445\pi\)
\(380\) −1.64195 + 15.6222i −0.0842305 + 0.801400i
\(381\) −12.3083 + 11.0824i −0.630571 + 0.567769i
\(382\) −30.5872 6.50150i −1.56498 0.332646i
\(383\) −1.37412 13.0739i −0.0702143 0.668044i −0.971858 0.235566i \(-0.924306\pi\)
0.901644 0.432479i \(-0.142361\pi\)
\(384\) 1.88823i 0.0963583i
\(385\) −1.84187 + 10.5736i −0.0938706 + 0.538880i
\(386\) 28.7984 1.46580
\(387\) −1.52218 14.4825i −0.0773765 0.736188i
\(388\) 9.00000 + 27.6992i 0.456906 + 1.40621i
\(389\) −8.46340 + 1.79895i −0.429111 + 0.0912104i −0.417404 0.908721i \(-0.637060\pi\)
−0.0117074 + 0.999931i \(0.503727\pi\)
\(390\) 36.0778 + 3.79193i 1.82687 + 0.192012i
\(391\) −4.03459 + 1.79631i −0.204038 + 0.0908435i
\(392\) 29.9990 + 33.3173i 1.51518 + 1.68278i
\(393\) 21.5779 + 19.4289i 1.08846 + 0.980057i
\(394\) −9.00217 4.00802i −0.453523 0.201921i
\(395\) −30.9443 −1.55698
\(396\) 42.6911 + 22.5862i 2.14531 + 1.13500i
\(397\) 38.1246 1.91342 0.956710 0.291044i \(-0.0940026\pi\)
0.956710 + 0.291044i \(0.0940026\pi\)
\(398\) 33.1348 + 14.7525i 1.66090 + 0.739478i
\(399\) 1.64728 0.535233i 0.0824671 0.0267952i
\(400\) 36.0815 + 40.0726i 1.80408 + 2.00363i
\(401\) −5.08142 + 2.26239i −0.253754 + 0.112979i −0.529672 0.848203i \(-0.677685\pi\)
0.275918 + 0.961181i \(0.411018\pi\)
\(402\) −11.0662 24.8552i −0.551934 1.23966i
\(403\) 3.91259 0.831647i 0.194900 0.0414273i
\(404\) 0.708204 + 2.17963i 0.0352345 + 0.108441i
\(405\) 26.6067 + 11.8460i 1.32210 + 0.588635i
\(406\) 4.85410 0.240905
\(407\) 8.89210 + 18.1362i 0.440765 + 0.898979i
\(408\) −20.7812 11.9980i −1.02882 0.593990i
\(409\) −0.913855 8.69475i −0.0451872 0.429928i −0.993606 0.112906i \(-0.963984\pi\)
0.948418 0.317021i \(-0.102683\pi\)
\(410\) −95.0696 20.2077i −4.69515 0.997985i
\(411\) −10.5129 3.41584i −0.518562 0.168491i
\(412\) 2.92457 27.8254i 0.144083 1.37086i
\(413\) −0.500000 0.363271i −0.0246034 0.0178754i
\(414\) −18.2994 + 3.88965i −0.899366 + 0.191166i
\(415\) −14.2361 43.8141i −0.698821 2.15075i
\(416\) −24.5130 10.9139i −1.20185 0.535097i
\(417\) −5.56231 + 3.21140i −0.272387 + 0.157263i
\(418\) 5.35995 + 6.83126i 0.262164 + 0.334128i
\(419\) 1.54508 2.67617i 0.0754823 0.130739i −0.825814 0.563943i \(-0.809284\pi\)
0.901296 + 0.433204i \(0.142617\pi\)
\(420\) 11.0662 24.8552i 0.539978 1.21281i
\(421\) 3.85682 4.28344i 0.187970 0.208762i −0.641793 0.766878i \(-0.721809\pi\)
0.829763 + 0.558116i \(0.188476\pi\)
\(422\) −9.32624 + 28.7032i −0.453994 + 1.39725i
\(423\) 16.2911 7.25326i 0.792100 0.352666i
\(424\) −42.8607 31.1401i −2.08150 1.51230i
\(425\) 9.92419 2.10945i 0.481394 0.102323i
\(426\) −60.7657 + 19.7440i −2.94411 + 0.956599i
\(427\) 0.433364 + 4.12319i 0.0209720 + 0.199535i
\(428\) 36.4894 63.2014i 1.76378 3.05496i
\(429\) 11.1727 8.76634i 0.539423 0.423243i
\(430\) −20.5623 35.6150i −0.991602 1.71751i
\(431\) −19.4721 + 14.1473i −0.937940 + 0.681453i −0.947924 0.318497i \(-0.896822\pi\)
0.00998408 + 0.999950i \(0.496822\pi\)
\(432\) −38.0516 34.2618i −1.83076 1.64842i
\(433\) −8.57295 + 26.3848i −0.411990 + 1.26797i 0.502926 + 0.864329i \(0.332257\pi\)
−0.914916 + 0.403644i \(0.867743\pi\)
\(434\) 0.442790 4.21286i 0.0212546 0.202224i
\(435\) 4.22693 + 9.49384i 0.202666 + 0.455195i
\(436\) 44.9985 + 49.9759i 2.15504 + 2.39341i
\(437\) −2.32991 0.495239i −0.111455 0.0236905i
\(438\) −18.2686 25.1446i −0.872907 1.20145i
\(439\) −6.35410 11.0056i −0.303265 0.525270i 0.673609 0.739088i \(-0.264743\pi\)
−0.976873 + 0.213818i \(0.931410\pi\)
\(440\) 80.0132 + 5.42882i 3.81448 + 0.258809i
\(441\) 18.0000 0.857143
\(442\) −9.70820 + 7.05342i −0.461772 + 0.335497i
\(443\) 2.16535 2.40487i 0.102879 0.114259i −0.689506 0.724280i \(-0.742172\pi\)
0.792385 + 0.610021i \(0.208839\pi\)
\(444\) −10.6458 50.0845i −0.505227 2.37691i
\(445\) −33.2171 + 14.7892i −1.57464 + 0.701076i
\(446\) −53.8288 + 23.9661i −2.54887 + 1.13483i
\(447\) −2.58574 12.1649i −0.122301 0.575382i
\(448\) −5.82693 + 6.47146i −0.275296 + 0.305748i
\(449\) 1.19098 0.865300i 0.0562060 0.0408360i −0.559328 0.828947i \(-0.688941\pi\)
0.615533 + 0.788111i \(0.288941\pi\)
\(450\) 42.9787 2.02604
\(451\) −32.2254 + 20.2295i −1.51744 + 0.952568i
\(452\) −30.9787 53.6567i −1.45712 2.52380i
\(453\) 11.5309 + 15.8710i 0.541771 + 0.745684i
\(454\) −36.8297 7.82839i −1.72850 0.367405i
\(455\) −5.35304 5.94516i −0.250955 0.278713i
\(456\) −5.26403 11.8232i −0.246511 0.553673i
\(457\) 0.104528 0.994522i 0.00488964 0.0465218i −0.991805 0.127761i \(-0.959221\pi\)
0.996695 + 0.0812390i \(0.0258877\pi\)
\(458\) 9.85410 30.3278i 0.460452 1.41713i
\(459\) −9.16267 + 2.97713i −0.427677 + 0.138961i
\(460\) −30.2705 + 21.9928i −1.41137 + 1.02542i
\(461\) 11.4271 + 19.7922i 0.532211 + 0.921816i 0.999293 + 0.0376022i \(0.0119720\pi\)
−0.467082 + 0.884214i \(0.654695\pi\)
\(462\) −5.17301 14.1218i −0.240670 0.657006i
\(463\) −8.50000 + 14.7224i −0.395029 + 0.684209i −0.993105 0.117230i \(-0.962599\pi\)
0.598076 + 0.801439i \(0.295932\pi\)
\(464\) −1.90979 18.1704i −0.0886597 0.843541i
\(465\) 8.62526 2.80252i 0.399987 0.129964i
\(466\) 74.5830 15.8531i 3.45499 0.734381i
\(467\) 4.23607 + 3.07768i 0.196022 + 0.142418i 0.681467 0.731849i \(-0.261342\pi\)
−0.485445 + 0.874267i \(0.661342\pi\)
\(468\) −32.8876 + 14.6425i −1.52023 + 0.676851i
\(469\) −1.85410 + 5.70634i −0.0856145 + 0.263494i
\(470\) 33.6979 37.4253i 1.55437 1.72630i
\(471\) −9.76006 + 21.9214i −0.449720 + 1.01009i
\(472\) −2.30902 + 3.99933i −0.106281 + 0.184084i
\(473\) −15.4847 4.40554i −0.711988 0.202567i
\(474\) 37.5517 21.6805i 1.72480 0.995817i
\(475\) 4.99904 + 2.22572i 0.229372 + 0.102123i
\(476\) 2.78115 + 8.55951i 0.127474 + 0.392324i
\(477\) −20.8057 + 4.42239i −0.952627 + 0.202487i
\(478\) 3.23607 + 2.35114i 0.148014 + 0.107539i
\(479\) 1.69713 16.1471i 0.0775439 0.737781i −0.884805 0.465962i \(-0.845708\pi\)
0.962348 0.271819i \(-0.0876251\pi\)
\(480\) −57.8600 18.7999i −2.64094 0.858092i
\(481\) −14.7267 3.13026i −0.671481 0.142728i
\(482\) 7.34304 + 69.8644i 0.334466 + 3.18224i
\(483\) 3.57295 + 2.06284i 0.162575 + 0.0938626i
\(484\) 40.7607 34.4906i 1.85276 1.56775i
\(485\) 19.4164 0.881654
\(486\) −40.5875 + 4.26592i −1.84109 + 0.193506i
\(487\) 10.5000 + 32.3157i 0.475800 + 1.46436i 0.844875 + 0.534963i \(0.179675\pi\)
−0.369075 + 0.929400i \(0.620325\pi\)
\(488\) 30.3018 6.44084i 1.37170 0.291563i
\(489\) 5.13699 + 11.5379i 0.232303 + 0.521760i
\(490\) 46.4381 20.6756i 2.09786 0.934027i
\(491\) −5.57134 6.18760i −0.251431 0.279243i 0.604196 0.796836i \(-0.293495\pi\)
−0.855627 + 0.517594i \(0.826828\pi\)
\(492\) 91.7318 29.8055i 4.13559 1.34373i
\(493\) −3.14049 1.39824i −0.141441 0.0629734i
\(494\) −6.47214 −0.291195
\(495\) 23.1153 22.4148i 1.03896 1.00747i
\(496\) −15.9443 −0.715919
\(497\) 12.8720 + 5.73099i 0.577389 + 0.257070i
\(498\) 47.9733 + 43.1953i 2.14973 + 1.93563i
\(499\) 7.75094 + 8.60829i 0.346980 + 0.385360i 0.891221 0.453569i \(-0.149849\pi\)
−0.544242 + 0.838928i \(0.683183\pi\)
\(500\) 6.77523 3.01652i 0.302997 0.134903i
\(501\) 17.6323 + 1.85323i 0.787752 + 0.0827960i
\(502\) 1.12086 0.238246i 0.0500263 0.0106334i
\(503\) −5.70820 17.5680i −0.254516 0.783320i −0.993925 0.110063i \(-0.964895\pi\)
0.739408 0.673257i \(-0.235105\pi\)
\(504\) 2.34315 + 22.2936i 0.104372 + 0.993036i
\(505\) 1.52786 0.0679891
\(506\) −3.54939 + 20.3759i −0.157789 + 0.905818i
\(507\) 11.9313i 0.529888i
\(508\) −4.85184 46.1621i −0.215265 2.04811i
\(509\) 4.71434 + 1.00206i 0.208959 + 0.0444157i 0.311202 0.950344i \(-0.399268\pi\)
−0.102243 + 0.994760i \(0.532602\pi\)
\(510\) −20.2190 + 18.2053i −0.895314 + 0.806145i
\(511\) −0.716449 + 6.81655i −0.0316938 + 0.301547i
\(512\) −32.6074 23.6907i −1.44106 1.04699i
\(513\) −4.94183 1.60570i −0.218187 0.0708934i
\(514\) 21.1074 + 64.9619i 0.931007 + 2.86535i
\(515\) −17.0399 7.58665i −0.750867 0.334308i
\(516\) 35.3435 + 20.4056i 1.55591 + 0.898304i
\(517\) −0.728782 19.7014i −0.0320518 0.866469i
\(518\) −7.97214 + 13.8081i −0.350276 + 0.606695i
\(519\) 12.1251 + 16.6888i 0.532232 + 0.732555i
\(520\) −39.9987 + 44.4230i −1.75406 + 1.94808i
\(521\) 1.34752 4.14725i 0.0590361 0.181694i −0.917190 0.398451i \(-0.869548\pi\)
0.976226 + 0.216757i \(0.0695478\pi\)
\(522\) −11.7812 8.55951i −0.515647 0.374640i
\(523\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(524\) −79.5956 + 16.9186i −3.47715 + 0.739091i
\(525\) −7.04354 6.34203i −0.307405 0.276789i
\(526\) 0.193806 + 1.84395i 0.00845036 + 0.0803998i
\(527\) −1.50000 + 2.59808i −0.0653410 + 0.113174i
\(528\) −50.8271 + 24.9203i −2.21196 + 1.08451i
\(529\) 8.66312 + 15.0050i 0.376657 + 0.652390i
\(530\) −48.5967 + 35.3076i −2.11091 + 1.53366i
\(531\) 0.572949 + 1.76336i 0.0248639 + 0.0765231i
\(532\) −1.50000 + 4.61653i −0.0650332 + 0.200152i
\(533\) 2.96450 28.2053i 0.128407 1.22171i
\(534\) 29.9481 41.2200i 1.29598 1.78376i
\(535\) −32.5549 36.1558i −1.40747 1.56315i
\(536\) 43.8531 + 9.32127i 1.89417 + 0.402617i
\(537\) −39.5229 + 4.15403i −1.70554 + 0.179260i
\(538\) 16.0623 + 27.8207i 0.692495 + 1.19944i
\(539\) 7.41641 18.4661i 0.319447 0.795391i
\(540\) −70.6869 + 40.8111i −3.04188 + 1.75623i
\(541\) 18.6803 13.5721i 0.803131 0.583508i −0.108700 0.994075i \(-0.534669\pi\)
0.911831 + 0.410566i \(0.134669\pi\)
\(542\) −26.6906 + 29.6430i −1.14646 + 1.27327i
\(543\) 27.1465 24.4428i 1.16497 1.04894i
\(544\) 18.3847 8.18542i 0.788240 0.350947i
\(545\) 40.9568 18.2351i 1.75440 0.781108i
\(546\) 10.6614 + 3.46410i 0.456266 + 0.148250i
\(547\) −11.1569 + 12.3910i −0.477036 + 0.529802i −0.932846 0.360275i \(-0.882683\pi\)
0.455810 + 0.890077i \(0.349349\pi\)
\(548\) 25.0623 18.2088i 1.07061 0.777843i
\(549\) 6.21885 10.7714i 0.265414 0.459710i
\(550\) 17.7082 44.0916i 0.755080 1.88007i
\(551\) −0.927051 1.60570i −0.0394937 0.0684051i
\(552\) 12.5388 28.1625i 0.533685 1.19868i
\(553\) −9.35335 1.98812i −0.397745 0.0845433i
\(554\) 25.8636 + 28.7244i 1.09884 + 1.22038i
\(555\) −33.9486 3.56814i −1.44104 0.151459i
\(556\) 1.88151 17.9014i 0.0797939 0.759188i
\(557\) 9.47214 29.1522i 0.401347 1.23522i −0.522560 0.852603i \(-0.675023\pi\)
0.923907 0.382617i \(-0.124977\pi\)
\(558\) −8.50345 + 9.44404i −0.359980 + 0.399798i
\(559\) 9.70820 7.05342i 0.410613 0.298328i
\(560\) 15.9443 + 27.6163i 0.673768 + 1.16700i
\(561\) −0.721004 + 10.6266i −0.0304408 + 0.448654i
\(562\) 8.28115 14.3434i 0.349319 0.605039i
\(563\) −4.42207 42.0732i −0.186368 1.77317i −0.543781 0.839227i \(-0.683008\pi\)
0.357413 0.933947i \(-0.383659\pi\)
\(564\) −10.3908 + 48.8847i −0.437530 + 2.05842i
\(565\) −40.4023 + 8.58778i −1.69974 + 0.361291i
\(566\) −36.0066 26.1603i −1.51347 1.09960i
\(567\) 7.28115 + 5.29007i 0.305780 + 0.222162i
\(568\) 32.5344 100.131i 1.36511 4.20139i
\(569\) 9.50274 10.5539i 0.398376 0.442441i −0.510267 0.860016i \(-0.670453\pi\)
0.908642 + 0.417575i \(0.137120\pi\)
\(570\) −14.5938 + 1.53387i −0.611266 + 0.0642467i
\(571\) 13.7361 23.7916i 0.574837 0.995646i −0.421223 0.906957i \(-0.638399\pi\)
0.996059 0.0886889i \(-0.0282677\pi\)
\(572\) 1.47123 + 39.7723i 0.0615152 + 1.66296i
\(573\) 20.6881i 0.864257i
\(574\) −27.4378 12.2161i −1.14523 0.509890i
\(575\) 4.02786 + 12.3965i 0.167974 + 0.516969i
\(576\) 25.5537 5.43161i 1.06474 0.226317i
\(577\) −6.94427 5.04531i −0.289094 0.210039i 0.433780 0.901019i \(-0.357179\pi\)
−0.722874 + 0.690980i \(0.757179\pi\)
\(578\) −3.71145 + 35.3121i −0.154376 + 1.46879i
\(579\) 3.96125 + 18.6362i 0.164624 + 0.774495i
\(580\) −28.4882 6.05535i −1.18291 0.251435i
\(581\) −1.48807 14.1581i −0.0617357 0.587376i
\(582\) −23.5623 + 13.6037i −0.976689 + 0.563892i
\(583\) −4.03552 + 23.1666i −0.167134 + 0.959462i
\(584\) 51.2148 2.11928
\(585\) 2.50868 + 23.8685i 0.103721 + 0.986842i
\(586\) 5.51722 + 16.9803i 0.227914 + 0.701448i
\(587\) 13.1232 2.78943i 0.541654 0.115132i 0.0710433 0.997473i \(-0.477367\pi\)
0.470610 + 0.882341i \(0.344034\pi\)
\(588\) −29.6510 + 40.8111i −1.22279 + 1.68302i
\(589\) −1.47815 + 0.658114i −0.0609060 + 0.0271171i
\(590\) 3.50361 + 3.89116i 0.144241 + 0.160196i
\(591\) 1.35544 6.37686i 0.0557555 0.262309i
\(592\) 54.8247 + 24.4095i 2.25328 + 1.00323i
\(593\) 6.94427 0.285167 0.142584 0.989783i \(-0.454459\pi\)
0.142584 + 0.989783i \(0.454459\pi\)
\(594\) −12.3466 + 43.3962i −0.506587 + 1.78057i
\(595\) 6.00000 0.245976
\(596\) 31.8408 + 14.1764i 1.30425 + 0.580690i
\(597\) −4.98905 + 23.4716i −0.204188 + 0.960630i
\(598\) −10.3156 11.4566i −0.421836 0.468496i
\(599\) 28.6494 12.7555i 1.17058 0.521177i 0.272996 0.962015i \(-0.411985\pi\)
0.897587 + 0.440838i \(0.145319\pi\)
\(600\) −41.6276 + 57.2954i −1.69944 + 2.33908i
\(601\) 8.34151 1.77304i 0.340257 0.0723239i −0.0346141 0.999401i \(-0.511020\pi\)
0.374871 + 0.927077i \(0.377687\pi\)
\(602\) −3.92705 12.0862i −0.160055 0.492598i
\(603\) 14.5623 10.5801i 0.593023 0.430856i
\(604\) −54.9787 −2.23705
\(605\) −13.4712 32.9493i −0.547681 1.33958i
\(606\) −1.85410 + 1.07047i −0.0753177 + 0.0434847i
\(607\) 3.17938 + 30.2498i 0.129047 + 1.22780i 0.846956 + 0.531663i \(0.178433\pi\)
−0.717909 + 0.696137i \(0.754900\pi\)
\(608\) 10.6169 + 2.25669i 0.430573 + 0.0915211i
\(609\) 0.667687 + 3.14122i 0.0270561 + 0.127289i
\(610\) 3.67152 34.9322i 0.148656 1.41436i
\(611\) 11.8885 + 8.63753i 0.480959 + 0.349437i
\(612\) 8.34346 25.6785i 0.337264 1.03799i
\(613\) 4.06231 + 12.5025i 0.164075 + 0.504971i 0.998967 0.0454430i \(-0.0144699\pi\)
−0.834892 + 0.550414i \(0.814470\pi\)
\(614\) −2.74064 1.22021i −0.110603 0.0492437i
\(615\) 64.3017i 2.59290i
\(616\) 23.8363 + 6.78164i 0.960393 + 0.273240i
\(617\) −21.0795 + 36.5108i −0.848630 + 1.46987i 0.0338015 + 0.999429i \(0.489239\pi\)
−0.882431 + 0.470441i \(0.844095\pi\)
\(618\) 25.9938 2.73205i 1.04562 0.109899i
\(619\) 4.97679 5.52728i 0.200034 0.222160i −0.634779 0.772694i \(-0.718909\pi\)
0.834813 + 0.550533i \(0.185576\pi\)
\(620\) −7.85410 + 24.1724i −0.315428 + 0.970789i
\(621\) −5.03420 11.3070i −0.202016 0.453735i
\(622\) −15.2082 11.0494i −0.609793 0.443041i
\(623\) −10.9905 + 2.33611i −0.440326 + 0.0935943i
\(624\) 8.77261 41.2719i 0.351186 1.65220i
\(625\) 2.34315 + 22.2936i 0.0937261 + 0.891744i
\(626\) −7.16312 + 12.4069i −0.286296 + 0.495879i
\(627\) −3.68343 + 4.40822i −0.147102 + 0.176047i
\(628\) −33.6246 58.2395i −1.34177 2.32401i
\(629\) 9.13525 6.63715i 0.364246 0.264641i
\(630\) 24.8610 + 5.28437i 0.990486 + 0.210534i
\(631\) 7.69098 23.6704i 0.306173 0.942304i −0.673064 0.739585i \(-0.735022\pi\)
0.979237 0.202720i \(-0.0649780\pi\)
\(632\) −7.46865 + 71.0594i −0.297087 + 2.82659i
\(633\) −19.8575 2.08710i −0.789263 0.0829549i
\(634\) −5.35304 5.94516i −0.212597 0.236112i
\(635\) −30.2681 6.43368i −1.20115 0.255313i
\(636\) 24.2460 54.4573i 0.961415 2.15937i
\(637\) 7.41641 + 12.8456i 0.293849 + 0.508961i
\(638\) −13.6353 + 8.55951i −0.539825 + 0.338874i
\(639\) −21.1353 36.6073i −0.836098 1.44816i
\(640\) 2.85410 2.07363i 0.112818 0.0819673i
\(641\) 23.7212 26.3451i 0.936933 1.04057i −0.0621633 0.998066i \(-0.519800\pi\)
0.999096 0.0425035i \(-0.0135334\pi\)
\(642\) 64.8380 + 21.0671i 2.55895 + 0.831454i
\(643\) −0.133284 + 0.0593421i −0.00525623 + 0.00234022i −0.409363 0.912372i \(-0.634249\pi\)
0.404107 + 0.914712i \(0.367582\pi\)
\(644\) −10.5627 + 4.70281i −0.416228 + 0.185317i
\(645\) 20.2190 18.2053i 0.796124 0.716833i
\(646\) 3.24803 3.60730i 0.127792 0.141927i
\(647\) −14.7082 + 10.6861i −0.578239 + 0.420115i −0.838089 0.545534i \(-0.816327\pi\)
0.259850 + 0.965649i \(0.416327\pi\)
\(648\) 33.6246 58.2395i 1.32090 2.28787i
\(649\) 2.04508 + 0.138757i 0.0802766 + 0.00544670i
\(650\) 17.7082 + 30.6715i 0.694573 + 1.20304i
\(651\) 2.78716 0.292943i 0.109238 0.0114813i
\(652\) −34.6217 7.35906i −1.35589 0.288203i
\(653\) 29.0140 + 32.2233i 1.13540 + 1.26099i 0.961069 + 0.276307i \(0.0891108\pi\)
0.174335 + 0.984686i \(0.444223\pi\)
\(654\) −36.9261 + 50.8244i −1.44392 + 1.98739i
\(655\) −5.67059 + 53.9520i −0.221568 + 2.10808i
\(656\) −34.9336 + 107.515i −1.36393 + 4.19774i
\(657\) 13.7589 15.2808i 0.536785 0.596160i
\(658\) 12.5902 9.14729i 0.490816 0.356599i
\(659\) 18.4894 + 32.0245i 0.720243 + 1.24750i 0.960902 + 0.276888i \(0.0893031\pi\)
−0.240659 + 0.970610i \(0.577364\pi\)
\(660\) 12.7433 + 89.3324i 0.496032 + 3.47726i
\(661\) 8.85410 15.3358i 0.344385 0.596492i −0.640857 0.767660i \(-0.721421\pi\)
0.985242 + 0.171168i \(0.0547542\pi\)
\(662\) −3.39786 32.3285i −0.132062 1.25648i
\(663\) −5.89984 5.31224i −0.229131 0.206310i
\(664\) −104.049 + 22.1164i −4.03790 + 0.858281i
\(665\) 2.61803 + 1.90211i 0.101523 + 0.0737608i
\(666\) 43.6975 19.4554i 1.69324 0.753880i
\(667\) 1.36475 4.20025i 0.0528431 0.162634i
\(668\) −33.2470 + 36.9246i −1.28637 + 1.42865i
\(669\) −22.9134 31.5375i −0.885882 1.21931i
\(670\) 25.4164 44.0225i 0.981922 1.70074i
\(671\) −8.48797 10.8179i −0.327675 0.417621i
\(672\) −16.2812 9.39993i −0.628059 0.362610i
\(673\) −8.62176 3.83866i −0.332345 0.147969i 0.233779 0.972290i \(-0.424891\pi\)
−0.566123 + 0.824320i \(0.691557\pi\)
\(674\) 2.04508 + 6.29412i 0.0787737 + 0.242441i
\(675\) 5.91177 + 27.8127i 0.227544 + 1.07051i
\(676\) 27.0517 + 19.6542i 1.04045 + 0.755930i
\(677\) −2.50286 + 23.8131i −0.0961926 + 0.915212i 0.834893 + 0.550412i \(0.185529\pi\)
−0.931086 + 0.364800i \(0.881137\pi\)
\(678\) 43.0124 38.7286i 1.65188 1.48736i
\(679\) 5.86889 + 1.24747i 0.225227 + 0.0478735i
\(680\) −4.68631 44.5872i −0.179712 1.70984i
\(681\) 24.9103i 0.954565i
\(682\) 6.18497 + 12.6148i 0.236835 + 0.483046i
\(683\) −14.4721 −0.553761 −0.276880 0.960904i \(-0.589301\pi\)
−0.276880 + 0.960904i \(0.589301\pi\)
\(684\) 11.7812 8.55951i 0.450464 0.327281i
\(685\) −6.38197 19.6417i −0.243842 0.750470i
\(686\) 33.2907 7.07616i 1.27105 0.270169i
\(687\) 20.9814 + 2.20523i 0.800490 + 0.0841349i
\(688\) −43.6975 + 19.4554i −1.66595 + 0.741729i
\(689\) −11.7284 13.0257i −0.446818 0.496241i
\(690\) −25.9754 23.3884i −0.988867 0.890380i
\(691\) −31.6057 14.0718i −1.20234 0.535315i −0.294911 0.955525i \(-0.595290\pi\)
−0.907427 + 0.420210i \(0.861957\pi\)
\(692\) −57.8115 −2.19766
\(693\) 8.42705 5.29007i 0.320117 0.200953i
\(694\) −70.3951 −2.67216
\(695\) −10.9625 4.88084i −0.415833 0.185141i
\(696\) 22.8216 7.41517i 0.865049 0.281071i
\(697\) 14.2327 + 15.8071i 0.539104 + 0.598735i
\(698\) 25.9597 11.5580i 0.982588 0.437477i
\(699\) 20.5180 + 46.0841i 0.776060 + 1.74306i
\(700\) 25.9819 5.52261i 0.982022 0.208735i
\(701\) 12.8926 + 39.6794i 0.486947 + 1.49867i 0.829141 + 0.559040i \(0.188830\pi\)
−0.342194 + 0.939629i \(0.611170\pi\)
\(702\) −19.7673 27.2074i −0.746070 1.02688i
\(703\) 6.09017 0.229695
\(704\) 4.95645 28.4534i 0.186803 1.07238i
\(705\) 28.8541 + 16.6589i 1.08671 + 0.627411i
\(706\) 2.85054 + 27.1211i 0.107282 + 1.02072i
\(707\) 0.461819 + 0.0981626i 0.0173685 + 0.00369178i
\(708\) −4.94183 1.60570i −0.185726 0.0603459i
\(709\) 3.16053 30.0704i 0.118696 1.12932i −0.759330 0.650706i \(-0.774473\pi\)
0.878026 0.478613i \(-0.158860\pi\)
\(710\) −96.5755 70.1662i −3.62441 2.63329i
\(711\) 19.1953 + 21.3185i 0.719880 + 0.799508i
\(712\) 25.9443 + 79.8483i 0.972303 + 2.99244i
\(713\) −3.52090 1.56760i −0.131859 0.0587072i
\(714\) −7.28115 + 4.20378i −0.272490 + 0.157322i
\(715\) 25.5202 + 7.26073i 0.954402 + 0.271536i
\(716\) 55.6869 96.4526i 2.08112 3.60460i
\(717\) −1.07636 + 2.41755i −0.0401975 + 0.0902851i
\(718\) 28.2845 31.4131i 1.05557 1.17233i
\(719\) 9.14590 28.1482i 0.341084 1.04975i −0.622562 0.782570i \(-0.713908\pi\)
0.963647 0.267180i \(-0.0860917\pi\)
\(720\) 9.99978 95.1416i 0.372670 3.54572i
\(721\) −4.66312 3.38795i −0.173664 0.126174i
\(722\) −46.0948 + 9.79776i −1.71547 + 0.364635i
\(723\) −44.2011 + 14.3618i −1.64386 + 0.534122i
\(724\) 10.7010 + 101.813i 0.397699 + 3.78385i
\(725\) −5.07295 + 8.78661i −0.188405 + 0.326326i
\(726\) 39.4328 + 30.5465i 1.46349 + 1.13369i
\(727\) 17.4164 + 30.1661i 0.645939 + 1.11880i 0.984084 + 0.177705i \(0.0568672\pi\)
−0.338145 + 0.941094i \(0.609799\pi\)
\(728\) −14.9443 + 10.8576i −0.553872 + 0.402411i
\(729\) −8.34346 25.6785i −0.309017 0.951057i
\(730\) 17.9443 55.2268i 0.664147 2.04404i
\(731\) −0.940756 + 8.95070i −0.0347951 + 0.331053i
\(732\) 14.1776 + 31.8433i 0.524018 + 1.17696i
\(733\) 26.4493 + 29.3749i 0.976927 + 1.08499i 0.996366 + 0.0851767i \(0.0271455\pi\)
−0.0194385 + 0.999811i \(0.506188\pi\)
\(734\) 1.81359 + 0.385489i 0.0669407 + 0.0142287i
\(735\) 19.7673 + 27.2074i 0.729129 + 1.00356i
\(736\) 12.9271 + 22.3903i 0.476497 + 0.825318i
\(737\) −4.85410 19.2986i −0.178803 0.710875i
\(738\) 45.0517 + 78.0318i 1.65837 + 2.87239i
\(739\) 19.8541 14.4248i 0.730345 0.530627i −0.159328 0.987226i \(-0.550933\pi\)
0.889673 + 0.456599i \(0.150933\pi\)
\(740\) 64.0128 71.0934i 2.35316 2.61345i
\(741\) −0.890250 4.18830i −0.0327041 0.153861i
\(742\) −16.9575 + 7.54997i −0.622530 + 0.277168i
\(743\) 2.15659 0.960175i 0.0791176 0.0352254i −0.366796 0.930301i \(-0.619545\pi\)
0.445914 + 0.895076i \(0.352879\pi\)
\(744\) −4.35383 20.4832i −0.159619 0.750950i
\(745\) 15.5480 17.2678i 0.569633 0.632642i
\(746\) 54.3328 39.4751i 1.98927 1.44529i
\(747\) −21.3541 + 36.9864i −0.781306 + 1.35326i
\(748\) −22.9058 19.1396i −0.837518 0.699815i
\(749\) −7.51722 13.0202i −0.274673 0.475748i
\(750\) 4.07230 + 5.60503i 0.148699 + 0.204667i
\(751\) −48.1730 10.2395i −1.75786 0.373644i −0.787689 0.616073i \(-0.788723\pi\)
−0.970169 + 0.242429i \(0.922056\pi\)
\(752\) −39.1946 43.5301i −1.42928 1.58738i
\(753\) 0.308350 + 0.692567i 0.0112369 + 0.0252385i
\(754\) 1.25434 11.9343i 0.0456804 0.434620i
\(755\) −11.3262 + 34.8586i −0.412204 + 1.26863i
\(756\) −23.9882 + 7.79423i −0.872441 + 0.283473i
\(757\) −8.89919 + 6.46564i −0.323446 + 0.234998i −0.737645 0.675189i \(-0.764062\pi\)
0.414198 + 0.910187i \(0.364062\pi\)
\(758\) −11.5172 19.9484i −0.418324 0.724559i
\(759\) −13.6740 + 0.505819i −0.496335 + 0.0183601i
\(760\) 12.0902 20.9408i 0.438557 0.759602i
\(761\) 4.17891 + 39.7597i 0.151485 + 1.44129i 0.761123 + 0.648608i \(0.224648\pi\)
−0.609637 + 0.792680i \(0.708685\pi\)
\(762\) 41.2387 13.3993i 1.49392 0.485404i
\(763\) 13.5514 2.88043i 0.490592 0.104279i
\(764\) 46.9058 + 34.0790i 1.69699 + 1.23294i
\(765\) −14.5623 10.5801i −0.526501 0.382526i
\(766\) −10.6353 + 32.7319i −0.384267 + 1.18265i
\(767\) −1.02234 + 1.13542i −0.0369146 + 0.0409978i
\(768\) 10.2590 23.0420i 0.370189 0.831458i
\(769\) −4.39919 + 7.61962i −0.158639 + 0.274770i −0.934378 0.356283i \(-0.884044\pi\)
0.775739 + 0.631054i \(0.217377\pi\)
\(770\) 15.6645 23.3275i 0.564509 0.840664i
\(771\) −39.1353 + 22.5947i −1.40942 + 0.813730i
\(772\) −48.7789 21.7178i −1.75559 0.781639i
\(773\) −2.36475 7.27794i −0.0850540 0.261769i 0.899480 0.436961i \(-0.143945\pi\)
−0.984534 + 0.175192i \(0.943945\pi\)
\(774\) −11.7812 + 36.2587i −0.423465 + 1.30329i
\(775\) 7.16312 + 5.20431i 0.257307 + 0.186944i
\(776\) 4.68631 44.5872i 0.168229 1.60059i
\(777\) −10.0322 3.25966i −0.359903 0.116940i
\(778\) 22.1575 + 4.70971i 0.794384 + 0.168851i
\(779\) 1.19916 + 11.4093i 0.0429645 + 0.408780i
\(780\) −58.2492 33.6302i −2.08566 1.20415i
\(781\) −46.2635 + 6.59949i −1.65544 + 0.236148i
\(782\) 11.5623 0.413467
\(783\) 3.91858 8.80128i 0.140039 0.314532i
\(784\) −18.2705 56.2308i −0.652518 2.00824i
\(785\) −43.8531 + 9.32127i −1.56518 + 0.332690i
\(786\) −30.9190 69.4452i −1.10284 2.47703i
\(787\) 32.8876 14.6425i 1.17232 0.521949i 0.274186 0.961677i \(-0.411592\pi\)
0.898131 + 0.439727i \(0.144925\pi\)
\(788\) 12.2254 + 13.5776i 0.435510 + 0.483683i
\(789\) −1.16661 + 0.379054i −0.0415324 + 0.0134947i
\(790\) 74.0092 + 32.9510i 2.63313 + 1.17234i
\(791\) −12.7639 −0.453833
\(792\) −45.8935 58.4913i −1.63076 2.07840i
\(793\) 10.2492 0.363961
\(794\) −91.1824 40.5970i −3.23594 1.44073i
\(795\) −29.5331 26.5917i −1.04743 0.943110i
\(796\) −44.9985 49.9759i −1.59493 1.77135i
\(797\) −8.46903 + 3.77066i −0.299989 + 0.133563i −0.551211 0.834366i \(-0.685834\pi\)
0.251223 + 0.967929i \(0.419167\pi\)
\(798\) −4.50973 0.473991i −0.159643 0.0167791i
\(799\) −10.7804 + 2.29145i −0.381385 + 0.0810658i
\(800\) −18.3541 56.4881i −0.648915 1.99716i
\(801\) 30.7940 + 13.7104i 1.08805 + 0.484432i
\(802\) 14.5623 0.514213
\(803\) −10.0075 20.4112i −0.353157 0.720295i
\(804\) 50.4453i 1.77907i
\(805\) 0.805727 + 7.66598i 0.0283981 + 0.270190i
\(806\) −10.2433 2.17728i −0.360805 0.0766914i
\(807\) −15.7942 + 14.2211i −0.555981 + 0.500608i
\(808\) 0.368762 3.50854i 0.0129730 0.123430i
\(809\) 5.59017 + 4.06150i 0.196540 + 0.142795i 0.681703 0.731629i \(-0.261240\pi\)
−0.485163 + 0.874424i \(0.661240\pi\)
\(810\) −51.0207 56.6642i −1.79268 1.99098i
\(811\) −15.9721 49.1572i −0.560858 1.72614i −0.679950 0.733259i \(-0.737998\pi\)
0.119092 0.992883i \(-0.462002\pi\)
\(812\) −8.22191 3.66063i −0.288532 0.128463i
\(813\) −22.8541 13.1948i −0.801528 0.462763i
\(814\) −1.95481 52.8450i −0.0685159 1.85222i
\(815\) −11.7984 + 20.4354i −0.413279 + 0.715820i
\(816\) 18.6007 + 25.6017i 0.651156 + 0.896239i
\(817\) −3.24803 + 3.60730i −0.113634 + 0.126203i
\(818\) −7.07295 + 21.7683i −0.247300 + 0.761111i
\(819\) −0.775226 + 7.37578i −0.0270886 + 0.257731i
\(820\) 145.790 + 105.923i 5.09122 + 3.69899i
\(821\) 12.9260 2.74751i 0.451121 0.0958887i 0.0232522 0.999730i \(-0.492598\pi\)
0.427869 + 0.903841i \(0.359265\pi\)
\(822\) 21.5062 + 19.3643i 0.750115 + 0.675407i
\(823\) 5.82309 + 55.4030i 0.202980 + 1.93123i 0.339531 + 0.940595i \(0.389732\pi\)
−0.136550 + 0.990633i \(0.543602\pi\)
\(824\) −21.5344 + 37.2987i −0.750188 + 1.29936i
\(825\) 30.9687 + 5.39461i 1.07819 + 0.187816i
\(826\) 0.809017 + 1.40126i 0.0281493 + 0.0487560i
\(827\) 22.6246 16.4377i 0.786735 0.571596i −0.120258 0.992743i \(-0.538372\pi\)
0.906993 + 0.421146i \(0.138372\pi\)
\(828\) 33.9289 + 7.21182i 1.17911 + 0.250628i
\(829\) −7.27458 + 22.3888i −0.252656 + 0.777597i 0.741626 + 0.670814i \(0.234055\pi\)
−0.994282 + 0.106783i \(0.965945\pi\)
\(830\) −12.6072 + 119.949i −0.437601 + 4.16350i
\(831\) −15.0308 + 20.6881i −0.521412 + 0.717662i
\(832\) 14.4050 + 15.9983i 0.499402 + 0.554642i
\(833\) −10.8815 2.31294i −0.377022 0.0801385i
\(834\) 16.7230 1.75766i 0.579070 0.0608627i
\(835\) 16.5623 + 28.6868i 0.573162 + 0.992746i
\(836\) −3.92705 15.6129i −0.135820 0.539985i
\(837\) −7.28115 4.20378i −0.251673 0.145304i
\(838\) −6.54508 + 4.75528i −0.226096 + 0.164269i
\(839\) −20.5478 + 22.8206i −0.709389 + 0.787856i −0.984841 0.173459i \(-0.944506\pi\)
0.275452 + 0.961315i \(0.411172\pi\)
\(840\) −31.1241 + 28.0242i −1.07388 + 0.966928i
\(841\) −23.3523 + 10.3971i −0.805253 + 0.358522i
\(842\) −13.7856 + 6.13773i −0.475082 + 0.211520i
\(843\) 10.4211 + 3.38601i 0.358921 + 0.116620i
\(844\) 37.4428 41.5845i 1.28884 1.43140i
\(845\) 18.0344 13.1028i 0.620404 0.450750i
\(846\) −46.6869 −1.60513
\(847\) −1.95492 10.8249i −0.0671717 0.371948i
\(848\) 34.9336 + 60.5068i 1.19963 + 2.07781i
\(849\) 11.9763 26.8992i 0.411026 0.923179i
\(850\) −25.9819 5.52261i −0.891170 0.189424i
\(851\) 9.70680 + 10.7805i 0.332745 + 0.369550i
\(852\) 117.815 + 12.3828i 4.03627 + 0.424229i
\(853\) 5.80784 55.2579i 0.198857 1.89200i −0.207430 0.978250i \(-0.566510\pi\)
0.406287 0.913746i \(-0.366823\pi\)
\(854\) 3.35410 10.3229i 0.114775 0.353241i
\(855\) −3.00000 9.23305i −0.102598 0.315764i
\(856\) −90.8845 + 66.0314i −3.10637 + 2.25691i
\(857\) 9.68034 + 16.7668i 0.330674 + 0.572744i 0.982644 0.185500i \(-0.0593906\pi\)
−0.651970 + 0.758245i \(0.726057\pi\)
\(858\) −36.0565 + 9.06914i −1.23095 + 0.309615i
\(859\) 6.21885 10.7714i 0.212184 0.367514i −0.740214 0.672372i \(-0.765276\pi\)
0.952398 + 0.304858i \(0.0986089\pi\)
\(860\) 7.97021 + 75.8315i 0.271782 + 2.58583i
\(861\) 4.13127 19.4361i 0.140793 0.662381i
\(862\) 61.6362 13.1012i 2.09934 0.446228i
\(863\) 33.5344 + 24.3642i 1.14153 + 0.829367i 0.987331 0.158674i \(-0.0507217\pi\)
0.154195 + 0.988041i \(0.450722\pi\)
\(864\) 22.9398 + 51.5236i 0.780427 + 1.75287i
\(865\) −11.9098 + 36.6547i −0.404946 + 1.24630i
\(866\) 48.5998 53.9755i 1.65149 1.83416i
\(867\) −23.3619 + 2.45544i −0.793412 + 0.0833910i
\(868\) −3.92705 + 6.80185i −0.133293 + 0.230870i
\(869\) 29.7795 10.9086i 1.01020 0.370050i
\(870\) 27.2074i 0.922417i
\(871\) 13.5505 + 6.03305i 0.459140 + 0.204422i
\(872\) −31.9894 98.4531i −1.08330 3.33404i
\(873\) −12.0444 13.3766i −0.407640 0.452730i
\(874\) 5.04508 + 3.66547i 0.170653 + 0.123986i
\(875\) 0.159705 1.51949i 0.00539902 0.0513683i
\(876\) 11.9812 + 56.3669i 0.404806 + 1.90446i
\(877\) 36.7752 + 7.81680i 1.24181 + 0.263955i 0.781557 0.623834i \(-0.214426\pi\)
0.460252 + 0.887788i \(0.347759\pi\)
\(878\) 3.47772 + 33.0883i 0.117367 + 1.11667i
\(879\) −10.2295 + 5.90600i −0.345032 + 0.199204i
\(880\) −93.4851 49.4592i −3.15138 1.66727i
\(881\) 24.1803 0.814656 0.407328 0.913282i \(-0.366461\pi\)
0.407328 + 0.913282i \(0.366461\pi\)
\(882\) −43.0505 19.1673i −1.44958 0.645397i
\(883\) −1.34346 4.13474i −0.0452110 0.139145i 0.925903 0.377762i \(-0.123306\pi\)
−0.971114 + 0.238616i \(0.923306\pi\)
\(884\) 21.7630 4.62587i 0.731970 0.155585i
\(885\) −2.03615 + 2.80252i −0.0684444 + 0.0942056i
\(886\) −7.73968 + 3.44593i −0.260020 + 0.115768i
\(887\) 16.7513 + 18.6042i 0.562454 + 0.624668i 0.955550 0.294829i \(-0.0952627\pi\)
−0.393096 + 0.919497i \(0.628596\pi\)
\(888\) −16.3875 + 77.0973i −0.549930 + 2.58722i
\(889\) −8.73560 3.88934i −0.292983 0.130444i
\(890\) 95.1935 3.19089
\(891\) −29.7812 2.02063i −0.997706 0.0676935i
\(892\) 109.249 3.65793
\(893\) −5.43036 2.41775i −0.181720 0.0809070i
\(894\) −6.76955 + 31.8482i −0.226408 + 1.06516i
\(895\) −49.6824 55.1779i −1.66070 1.84439i
\(896\) 0.995920 0.443412i 0.0332713 0.0148134i
\(897\) 5.99497 8.25137i 0.200166 0.275505i
\(898\) −3.76988 + 0.801313i −0.125803 + 0.0267402i
\(899\) −0.927051 2.85317i −0.0309189 0.0951585i
\(900\) −72.7976 32.4116i −2.42659 1.08039i
\(901\) 13.1459 0.437953
\(902\) 98.6147 14.0674i 3.28351 0.468393i
\(903\) 7.28115 4.20378i 0.242302 0.139893i
\(904\) 9.96928 + 94.8514i 0.331573 + 3.15471i
\(905\) 66.7578 + 14.1898i 2.21910 + 0.471685i
\(906\) −10.6783 50.2373i −0.354761 1.66902i
\(907\) 4.32919 41.1895i 0.143749 1.36768i −0.650233 0.759734i \(-0.725329\pi\)
0.793982 0.607941i \(-0.208004\pi\)
\(908\) 56.4787 + 41.0342i 1.87431 + 1.36177i
\(909\) −0.947762 1.05260i −0.0314353 0.0349124i
\(910\) 6.47214 + 19.9192i 0.214549 + 0.660315i
\(911\) 2.90539 + 1.29356i 0.0962597 + 0.0428576i 0.454302 0.890848i \(-0.349889\pi\)
−0.358042 + 0.933706i \(0.616556\pi\)
\(912\) 17.0678i 0.565172i
\(913\) 29.1458 + 37.1463i 0.964584 + 1.22936i
\(914\) −1.30902 + 2.26728i −0.0432984 + 0.0749951i
\(915\) 23.1106 2.42902i 0.764013 0.0803010i
\(916\) −39.5621 + 43.9381i −1.30717 + 1.45176i
\(917\) −5.18034 + 15.9434i −0.171070 + 0.526499i
\(918\) 25.0845 + 2.63649i 0.827911 + 0.0870170i
\(919\) −45.1976 32.8380i −1.49093 1.08322i −0.973824 0.227303i \(-0.927009\pi\)
−0.517106 0.855922i \(-0.672991\pi\)
\(920\) 56.3381 11.9750i 1.85741 0.394805i
\(921\) 0.412653 1.94138i 0.0135974 0.0639707i
\(922\) −6.25423 59.5050i −0.205972 1.95969i
\(923\) 17.4164 30.1661i 0.573268 0.992929i
\(924\) −1.88761 + 27.8207i −0.0620979 + 0.915235i
\(925\) −16.6631 28.8614i −0.547880 0.948956i
\(926\) 36.0066 26.1603i 1.18325 0.859681i
\(927\) 5.34346 + 16.4455i 0.175502 + 0.540140i
\(928\) −6.21885 + 19.1396i −0.204144 + 0.628290i
\(929\) 1.53965 14.6488i 0.0505143 0.480612i −0.939796 0.341737i \(-0.888985\pi\)
0.990310 0.138875i \(-0.0443485\pi\)
\(930\) −23.6132 2.48185i −0.774309 0.0813831i
\(931\) −4.01478 4.45887i −0.131579 0.146134i
\(932\) −138.284 29.3933i −4.52966 0.962809i
\(933\) 5.05847 11.3615i 0.165607 0.371959i
\(934\) −6.85410 11.8717i −0.224273 0.388452i
\(935\) −16.8541 + 10.5801i −0.551188 + 0.346007i
\(936\) 55.4164 1.81134
\(937\) −4.88197 + 3.54696i −0.159487 + 0.115874i −0.664666 0.747140i \(-0.731426\pi\)
0.505179 + 0.863014i \(0.331426\pi\)
\(938\) 10.5108 11.6735i 0.343191 0.381152i
\(939\) −9.01413 2.92887i −0.294165 0.0955800i
\(940\) −85.3012 + 37.9786i −2.78222 + 1.23872i
\(941\) −38.5142 + 17.1476i −1.25553 + 0.558997i −0.923255 0.384187i \(-0.874482\pi\)
−0.332272 + 0.943184i \(0.607815\pi\)
\(942\) 46.6861 42.0364i 1.52112 1.36962i
\(943\) −18.2848 + 20.3074i −0.595436 + 0.661298i
\(944\) 4.92705 3.57971i 0.160362 0.116510i
\(945\) 16.8151i 0.546995i
\(946\) 32.3435 + 27.0256i 1.05158 + 0.878678i
\(947\) −11.6459 20.1713i −0.378441 0.655479i 0.612395 0.790552i \(-0.290206\pi\)
−0.990836 + 0.135073i \(0.956873\pi\)
\(948\) −79.9552 + 8.40363i −2.59682 + 0.272937i
\(949\) 16.5740 + 3.52291i 0.538015 + 0.114359i
\(950\) −9.58612 10.6465i −0.311015 0.345417i
\(951\) 3.11096 4.28187i 0.100880 0.138849i
\(952\) 1.44815 13.7782i 0.0469347 0.446554i
\(953\) −14.6803 + 45.1814i −0.475543 + 1.46357i 0.369681 + 0.929159i \(0.379467\pi\)
−0.845224 + 0.534412i \(0.820533\pi\)
\(954\) 54.4700 + 11.5780i 1.76353 + 0.374850i
\(955\) 31.2705 22.7194i 1.01189 0.735181i
\(956\) −3.70820 6.42280i −0.119932 0.207728i
\(957\) −7.41464 7.64638i −0.239681 0.247172i
\(958\) −21.2533 + 36.8118i −0.686663 + 1.18933i
\(959\) −0.667097 6.34700i −0.0215417 0.204955i
\(960\) 36.2727 + 32.6601i 1.17070 + 1.05410i
\(961\) 27.7618 5.90094i 0.895540 0.190353i
\(962\) 31.8885 + 23.1684i 1.02813 + 0.746979i
\(963\) −4.71458 + 44.8562i −0.151925 + 1.44547i
\(964\) 40.2492 123.874i 1.29634 3.98972i
\(965\) −23.8189 + 26.4535i −0.766757 + 0.851570i
\(966\) −6.34878 8.73834i −0.204269 0.281152i
\(967\) 16.2426 28.1331i 0.522328 0.904699i −0.477334 0.878722i \(-0.658397\pi\)
0.999663 0.0259773i \(-0.00826976\pi\)
\(968\) −78.9151 + 22.9822i −2.53643 + 0.738675i
\(969\) 2.78115 + 1.60570i 0.0893435 + 0.0515825i
\(970\) −46.4381 20.6756i −1.49104 0.663853i
\(971\) −7.50000 23.0826i −0.240686 0.740757i −0.996316 0.0857575i \(-0.972669\pi\)
0.755630 0.654999i \(-0.227331\pi\)
\(972\) 71.9645 + 23.3827i 2.30826 + 0.750000i
\(973\) −3.00000 2.17963i −0.0961756 0.0698757i
\(974\) 9.29858 88.4701i 0.297946 2.83477i
\(975\) −17.4126 + 15.6784i −0.557649 + 0.502110i
\(976\) −39.9613 8.49405i −1.27913 0.271888i
\(977\) −2.11525 20.1252i −0.0676727 0.643863i −0.974811 0.223031i \(-0.928405\pi\)
0.907139 0.420832i \(-0.138262\pi\)
\(978\) 33.0651i 1.05731i
\(979\) 26.7532 25.9424i 0.855036 0.829122i
\(980\) −94.2492 −3.01068
\(981\) −37.9691 16.9049i −1.21226 0.539732i
\(982\) 6.73607 + 20.7315i 0.214957 + 0.661568i
\(983\) −50.6119 + 10.7579i −1.61427 + 0.343124i −0.924582 0.380983i \(-0.875586\pi\)
−0.689688 + 0.724106i \(0.742252\pi\)
\(984\) −147.660 15.5197i −4.70724 0.494751i
\(985\) 11.1273 4.95419i 0.354545 0.157854i
\(986\) 6.02218 + 6.68830i 0.191785 + 0.212999i
\(987\) 7.65126 + 6.88922i 0.243542 + 0.219286i
\(988\) 10.9625 + 4.88084i 0.348765 + 0.155280i
\(989\) −11.5623 −0.367660
\(990\) −79.1532 + 28.9949i −2.51565 + 0.921519i
\(991\) −28.5967 −0.908406 −0.454203 0.890898i \(-0.650076\pi\)
−0.454203 + 0.890898i \(0.650076\pi\)
\(992\) 16.0440 + 7.14323i 0.509396 + 0.226798i
\(993\) 20.4533 6.64567i 0.649065 0.210894i
\(994\) −24.6833 27.4135i −0.782905 0.869504i
\(995\) −40.9568 + 18.2351i −1.29842 + 0.578093i
\(996\) −48.6825 109.343i −1.54256 3.46466i
\(997\) −9.40786 + 1.99970i −0.297950 + 0.0633312i −0.354461 0.935071i \(-0.615336\pi\)
0.0565113 + 0.998402i \(0.482002\pi\)
\(998\) −9.37132 28.8420i −0.296644 0.912976i
\(999\) 18.6007 + 25.6017i 0.588501 + 0.810002i
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 99.2.m.a.58.1 yes 8
3.2 odd 2 297.2.n.a.91.1 8
9.2 odd 6 297.2.n.a.289.1 8
9.4 even 3 891.2.f.b.487.1 4
9.5 odd 6 891.2.f.a.487.1 4
9.7 even 3 inner 99.2.m.a.25.1 yes 8
11.2 odd 10 1089.2.e.d.364.1 4
11.4 even 5 inner 99.2.m.a.4.1 8
11.9 even 5 1089.2.e.g.364.2 4
33.26 odd 10 297.2.n.a.37.1 8
99.4 even 15 891.2.f.b.730.1 4
99.13 odd 30 9801.2.a.bc.1.2 2
99.31 even 15 9801.2.a.n.1.1 2
99.59 odd 30 891.2.f.a.730.1 4
99.68 even 30 9801.2.a.m.1.1 2
99.70 even 15 inner 99.2.m.a.70.1 yes 8
99.79 odd 30 1089.2.e.d.727.1 4
99.86 odd 30 9801.2.a.bb.1.2 2
99.92 odd 30 297.2.n.a.235.1 8
99.97 even 15 1089.2.e.g.727.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.a.4.1 8 11.4 even 5 inner
99.2.m.a.25.1 yes 8 9.7 even 3 inner
99.2.m.a.58.1 yes 8 1.1 even 1 trivial
99.2.m.a.70.1 yes 8 99.70 even 15 inner
297.2.n.a.37.1 8 33.26 odd 10
297.2.n.a.91.1 8 3.2 odd 2
297.2.n.a.235.1 8 99.92 odd 30
297.2.n.a.289.1 8 9.2 odd 6
891.2.f.a.487.1 4 9.5 odd 6
891.2.f.a.730.1 4 99.59 odd 30
891.2.f.b.487.1 4 9.4 even 3
891.2.f.b.730.1 4 99.4 even 15
1089.2.e.d.364.1 4 11.2 odd 10
1089.2.e.d.727.1 4 99.79 odd 30
1089.2.e.g.364.2 4 11.9 even 5
1089.2.e.g.727.2 4 99.97 even 15
9801.2.a.m.1.1 2 99.68 even 30
9801.2.a.n.1.1 2 99.31 even 15
9801.2.a.bb.1.2 2 99.86 odd 30
9801.2.a.bc.1.2 2 99.13 odd 30