Properties

Label 930.2.bg.a.691.1
Level $930$
Weight $2$
Character 930.691
Analytic conductor $7.426$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (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: \(7.42608738798\)
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 691.1
Root \(0.913545 - 0.406737i\) of defining polynomial
Character \(\chi\) \(=\) 930.691
Dual form 930.2.bg.a.751.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(3.57433 - 1.59139i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(3.57433 - 1.59139i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(-0.683591 + 6.50394i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(0.240636 - 0.267254i) q^{13} +(-0.408977 - 3.89116i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.671954 - 6.39322i) q^{17} +(0.669131 - 0.743145i) q^{18} +(3.78339 + 4.20188i) q^{19} +(0.104528 - 0.994522i) q^{20} +(3.82709 - 0.813473i) q^{21} +(5.97437 + 2.65996i) q^{22} +(1.08268 - 0.786610i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.179813 - 0.311445i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-3.82709 - 0.813473i) q^{28} +(-0.0381813 + 0.117510i) q^{29} +1.00000 q^{30} +(4.97437 + 2.50113i) q^{31} +1.00000 q^{32} +(-2.02090 + 6.21968i) q^{33} +(-6.28795 - 1.33655i) q^{34} +(3.16535 + 2.29976i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.144943 - 0.251049i) q^{37} +(5.16535 - 2.29976i) q^{38} +(0.290943 - 0.211383i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-9.06316 + 1.92643i) q^{41} +(0.408977 - 3.89116i) q^{42} +(-4.56694 - 5.07210i) q^{43} +(4.37595 - 4.85999i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.413545 - 1.27276i) q^{46} +(-0.671954 - 2.06806i) q^{47} +(0.104528 + 0.994522i) q^{48} +(5.55938 - 6.17432i) q^{49} +(0.669131 + 0.743145i) q^{50} +(0.671954 - 6.39322i) q^{51} +(-0.351767 + 0.0747703i) q^{52} +(-3.70353 - 1.64892i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-5.97437 + 2.65996i) q^{55} +(-1.95630 + 3.38840i) q^{56} +(2.82709 + 4.89667i) q^{57} +(0.0999601 + 0.0726252i) q^{58} +(4.86245 + 1.03355i) q^{59} +(0.309017 - 0.951057i) q^{60} +11.0795 q^{61} +(3.91588 - 3.95801i) q^{62} +3.91259 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.351767 + 0.0747703i) q^{65} +(5.29078 + 3.84398i) q^{66} +(-5.99448 - 10.3827i) q^{67} +(-3.21422 + 5.56718i) q^{68} +(1.22256 - 0.544320i) q^{69} +(3.16535 - 2.29976i) q^{70} +(7.88558 + 3.51089i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(1.61803 - 15.3946i) q^{73} +(-0.193972 - 0.215427i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(-0.591023 - 5.62321i) q^{76} +(7.90694 + 24.3351i) q^{77} +(-0.111130 - 0.342024i) q^{78} +(-0.678233 - 6.45295i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.968523 + 9.21488i) q^{82} +(-4.32157 + 0.918578i) q^{83} +(-3.57433 - 1.59139i) q^{84} +(5.20071 - 3.77854i) q^{85} +(-6.23511 + 2.77605i) q^{86} +(-0.0617787 + 0.107004i) q^{87} +(-3.26988 - 5.66360i) q^{88} +(-5.07794 - 3.68934i) q^{89} +(0.978148 + 0.207912i) q^{90} +(0.434808 - 1.33820i) q^{91} -1.33826 q^{92} +(4.34565 + 3.48070i) q^{93} -2.17449 q^{94} +(-1.74724 + 5.37745i) q^{95} +(0.978148 + 0.207912i) q^{96} +(11.0902 + 8.05748i) q^{97} +(-4.15418 - 7.19525i) q^{98} +(-3.26988 + 5.66360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 23 q^{11} - q^{12} - 17 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 11 q^{17} + q^{18} - q^{20} + 18 q^{21} + 22 q^{22} - 2 q^{23} - q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 18 q^{28} + 10 q^{29} + 8 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} - 19 q^{34} + 4 q^{35} - 4 q^{36} - q^{37} + 20 q^{38} + 6 q^{39} - q^{40} - 42 q^{41} - 2 q^{42} - 23 q^{43} + 17 q^{44} - q^{45} + 3 q^{46} + 11 q^{47} - q^{48} - 3 q^{49} + q^{50} - 11 q^{51} + 13 q^{52} + 2 q^{53} + 2 q^{54} - 22 q^{55} + 2 q^{56} + 10 q^{57} + 28 q^{59} - 2 q^{60} - 4 q^{61} + 14 q^{62} - 4 q^{63} - 2 q^{64} - 13 q^{65} - q^{66} - 20 q^{67} + q^{68} - q^{69} + 4 q^{70} + 42 q^{71} + q^{72} + 4 q^{73} - 41 q^{74} - q^{75} - 10 q^{76} + 52 q^{77} - 4 q^{78} - 42 q^{79} - q^{80} + q^{81} - 2 q^{82} + 6 q^{83} - 2 q^{84} + 22 q^{85} - 3 q^{86} - 10 q^{87} - 3 q^{88} + 16 q^{89} - q^{90} + 28 q^{91} - 2 q^{92} + 13 q^{93} + 6 q^{94} - q^{96} + 44 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{15}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) 0.978148 + 0.207912i 0.564734 + 0.120038i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 3.57433 1.59139i 1.35097 0.601490i 0.401647 0.915795i \(-0.368438\pi\)
0.949322 + 0.314304i \(0.101771\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 0.913545 + 0.406737i 0.304515 + 0.135579i
\(10\) 0.978148 0.207912i 0.309317 0.0657474i
\(11\) −0.683591 + 6.50394i −0.206110 + 1.96101i 0.0633279 + 0.997993i \(0.479829\pi\)
−0.269438 + 0.963018i \(0.586838\pi\)
\(12\) −0.669131 0.743145i −0.193161 0.214527i
\(13\) 0.240636 0.267254i 0.0667405 0.0741229i −0.708850 0.705359i \(-0.750786\pi\)
0.775590 + 0.631237i \(0.217452\pi\)
\(14\) −0.408977 3.89116i −0.109304 1.03996i
\(15\) 0.309017 + 0.951057i 0.0797878 + 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.671954 6.39322i −0.162973 1.55058i −0.704381 0.709822i \(-0.748775\pi\)
0.541408 0.840760i \(-0.317892\pi\)
\(18\) 0.669131 0.743145i 0.157716 0.175161i
\(19\) 3.78339 + 4.20188i 0.867968 + 0.963976i 0.999627 0.0273187i \(-0.00869689\pi\)
−0.131658 + 0.991295i \(0.542030\pi\)
\(20\) 0.104528 0.994522i 0.0233733 0.222382i
\(21\) 3.82709 0.813473i 0.835140 0.177514i
\(22\) 5.97437 + 2.65996i 1.27374 + 0.567105i
\(23\) 1.08268 0.786610i 0.225754 0.164020i −0.469159 0.883114i \(-0.655443\pi\)
0.694913 + 0.719094i \(0.255443\pi\)
\(24\) −0.913545 + 0.406737i −0.186477 + 0.0830248i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.179813 0.311445i −0.0352642 0.0610793i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) −3.82709 0.813473i −0.723252 0.153732i
\(29\) −0.0381813 + 0.117510i −0.00709010 + 0.0218211i −0.954539 0.298086i \(-0.903652\pi\)
0.947449 + 0.319907i \(0.103652\pi\)
\(30\) 1.00000 0.182574
\(31\) 4.97437 + 2.50113i 0.893423 + 0.449216i
\(32\) 1.00000 0.176777
\(33\) −2.02090 + 6.21968i −0.351793 + 1.08271i
\(34\) −6.28795 1.33655i −1.07838 0.229216i
\(35\) 3.16535 + 2.29976i 0.535042 + 0.388731i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 0.144943 0.251049i 0.0238285 0.0412721i −0.853865 0.520494i \(-0.825748\pi\)
0.877694 + 0.479222i \(0.159081\pi\)
\(38\) 5.16535 2.29976i 0.837931 0.373071i
\(39\) 0.290943 0.211383i 0.0465882 0.0338483i
\(40\) −0.913545 0.406737i −0.144444 0.0643107i
\(41\) −9.06316 + 1.92643i −1.41543 + 0.300858i −0.851235 0.524785i \(-0.824146\pi\)
−0.564193 + 0.825643i \(0.690812\pi\)
\(42\) 0.408977 3.89116i 0.0631065 0.600419i
\(43\) −4.56694 5.07210i −0.696451 0.773488i 0.286356 0.958123i \(-0.407556\pi\)
−0.982807 + 0.184636i \(0.940889\pi\)
\(44\) 4.37595 4.85999i 0.659700 0.732671i
\(45\) 0.104528 + 0.994522i 0.0155822 + 0.148255i
\(46\) −0.413545 1.27276i −0.0609740 0.187659i
\(47\) −0.671954 2.06806i −0.0980146 0.301658i 0.890013 0.455935i \(-0.150695\pi\)
−0.988028 + 0.154277i \(0.950695\pi\)
\(48\) 0.104528 + 0.994522i 0.0150874 + 0.143547i
\(49\) 5.55938 6.17432i 0.794197 0.882045i
\(50\) 0.669131 + 0.743145i 0.0946294 + 0.105097i
\(51\) 0.671954 6.39322i 0.0940924 0.895229i
\(52\) −0.351767 + 0.0747703i −0.0487813 + 0.0103688i
\(53\) −3.70353 1.64892i −0.508719 0.226496i 0.136293 0.990669i \(-0.456481\pi\)
−0.645012 + 0.764172i \(0.723148\pi\)
\(54\) 0.809017 0.587785i 0.110093 0.0799874i
\(55\) −5.97437 + 2.65996i −0.805584 + 0.358669i
\(56\) −1.95630 + 3.38840i −0.261421 + 0.452794i
\(57\) 2.82709 + 4.89667i 0.374457 + 0.648579i
\(58\) 0.0999601 + 0.0726252i 0.0131254 + 0.00953616i
\(59\) 4.86245 + 1.03355i 0.633037 + 0.134556i 0.513244 0.858243i \(-0.328444\pi\)
0.119793 + 0.992799i \(0.461777\pi\)
\(60\) 0.309017 0.951057i 0.0398939 0.122781i
\(61\) 11.0795 1.41859 0.709294 0.704913i \(-0.249014\pi\)
0.709294 + 0.704913i \(0.249014\pi\)
\(62\) 3.91588 3.95801i 0.497317 0.502668i
\(63\) 3.91259 0.492940
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 0.351767 + 0.0747703i 0.0436313 + 0.00927412i
\(66\) 5.29078 + 3.84398i 0.651250 + 0.473161i
\(67\) −5.99448 10.3827i −0.732342 1.26845i −0.955880 0.293758i \(-0.905094\pi\)
0.223538 0.974695i \(-0.428239\pi\)
\(68\) −3.21422 + 5.56718i −0.389781 + 0.675120i
\(69\) 1.22256 0.544320i 0.147179 0.0655284i
\(70\) 3.16535 2.29976i 0.378332 0.274874i
\(71\) 7.88558 + 3.51089i 0.935846 + 0.416666i 0.817254 0.576278i \(-0.195495\pi\)
0.118592 + 0.992943i \(0.462162\pi\)
\(72\) −0.978148 + 0.207912i −0.115276 + 0.0245026i
\(73\) 1.61803 15.3946i 0.189377 1.80180i −0.326566 0.945174i \(-0.605892\pi\)
0.515943 0.856623i \(-0.327442\pi\)
\(74\) −0.193972 0.215427i −0.0225487 0.0250429i
\(75\) −0.669131 + 0.743145i −0.0772645 + 0.0858110i
\(76\) −0.591023 5.62321i −0.0677950 0.645026i
\(77\) 7.90694 + 24.3351i 0.901080 + 2.77324i
\(78\) −0.111130 0.342024i −0.0125830 0.0387266i
\(79\) −0.678233 6.45295i −0.0763072 0.726014i −0.964058 0.265691i \(-0.914400\pi\)
0.887751 0.460324i \(-0.152267\pi\)
\(80\) −0.669131 + 0.743145i −0.0748111 + 0.0830861i
\(81\) 0.669131 + 0.743145i 0.0743478 + 0.0825716i
\(82\) −0.968523 + 9.21488i −0.106955 + 1.01761i
\(83\) −4.32157 + 0.918578i −0.474354 + 0.100827i −0.438884 0.898544i \(-0.644626\pi\)
−0.0354697 + 0.999371i \(0.511293\pi\)
\(84\) −3.57433 1.59139i −0.389991 0.173635i
\(85\) 5.20071 3.77854i 0.564096 0.409840i
\(86\) −6.23511 + 2.77605i −0.672350 + 0.299349i
\(87\) −0.0617787 + 0.107004i −0.00662337 + 0.0114720i
\(88\) −3.26988 5.66360i −0.348570 0.603742i
\(89\) −5.07794 3.68934i −0.538261 0.391069i 0.285178 0.958475i \(-0.407947\pi\)
−0.823439 + 0.567405i \(0.807947\pi\)
\(90\) 0.978148 + 0.207912i 0.103106 + 0.0219158i
\(91\) 0.434808 1.33820i 0.0455802 0.140281i
\(92\) −1.33826 −0.139523
\(93\) 4.34565 + 3.48070i 0.450623 + 0.360932i
\(94\) −2.17449 −0.224281
\(95\) −1.74724 + 5.37745i −0.179263 + 0.551714i
\(96\) 0.978148 + 0.207912i 0.0998318 + 0.0212199i
\(97\) 11.0902 + 8.05748i 1.12604 + 0.818113i 0.985113 0.171907i \(-0.0549930\pi\)
0.140923 + 0.990021i \(0.454993\pi\)
\(98\) −4.15418 7.19525i −0.419636 0.726830i
\(99\) −3.26988 + 5.66360i −0.328635 + 0.569213i
\(100\) 0.913545 0.406737i 0.0913545 0.0406737i
\(101\) −6.98176 + 5.07255i −0.694711 + 0.504737i −0.878205 0.478284i \(-0.841259\pi\)
0.183494 + 0.983021i \(0.441259\pi\)
\(102\) −5.87266 2.61468i −0.581480 0.258892i
\(103\) −17.0119 + 3.61599i −1.67623 + 0.356294i −0.945312 0.326169i \(-0.894242\pi\)
−0.730920 + 0.682463i \(0.760909\pi\)
\(104\) −0.0375911 + 0.357655i −0.00368611 + 0.0350710i
\(105\) 2.61803 + 2.90762i 0.255494 + 0.283755i
\(106\) −2.71267 + 3.01273i −0.263478 + 0.292622i
\(107\) 0.619614 + 5.89523i 0.0599003 + 0.569914i 0.982774 + 0.184811i \(0.0591673\pi\)
−0.922874 + 0.385103i \(0.874166\pi\)
\(108\) −0.309017 0.951057i −0.0297352 0.0915155i
\(109\) 1.46458 + 4.50751i 0.140281 + 0.431741i 0.996374 0.0850809i \(-0.0271149\pi\)
−0.856093 + 0.516822i \(0.827115\pi\)
\(110\) 0.683591 + 6.50394i 0.0651779 + 0.620126i
\(111\) 0.193972 0.215427i 0.0184110 0.0204474i
\(112\) 2.61803 + 2.90762i 0.247381 + 0.274744i
\(113\) 1.23840 11.7826i 0.116499 1.10842i −0.767539 0.641002i \(-0.778519\pi\)
0.884039 0.467414i \(-0.154814\pi\)
\(114\) 5.53062 1.17557i 0.517990 0.110102i
\(115\) 1.22256 + 0.544320i 0.114005 + 0.0507581i
\(116\) 0.0999601 0.0726252i 0.00928106 0.00674308i
\(117\) 0.328534 0.146273i 0.0303730 0.0135229i
\(118\) 2.48554 4.30508i 0.228812 0.396315i
\(119\) −12.5759 21.7821i −1.15283 1.99676i
\(120\) −0.809017 0.587785i −0.0738528 0.0536572i
\(121\) −31.0743 6.60504i −2.82493 0.600458i
\(122\) 3.42376 10.5373i 0.309973 0.953998i
\(123\) −9.26564 −0.835454
\(124\) −2.55422 4.94732i −0.229376 0.444282i
\(125\) −1.00000 −0.0894427
\(126\) 1.20906 3.72109i 0.107711 0.331501i
\(127\) −6.17449 1.31243i −0.547897 0.116459i −0.0743576 0.997232i \(-0.523691\pi\)
−0.473540 + 0.880772i \(0.657024\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) −3.41259 5.91078i −0.300462 0.520415i
\(130\) 0.179813 0.311445i 0.0157706 0.0273155i
\(131\) 1.24382 0.553786i 0.108673 0.0483845i −0.351680 0.936120i \(-0.614389\pi\)
0.460353 + 0.887736i \(0.347723\pi\)
\(132\) 5.29078 3.84398i 0.460503 0.334575i
\(133\) 20.2099 + 8.99803i 1.75242 + 0.780228i
\(134\) −11.7270 + 2.49264i −1.01306 + 0.215332i
\(135\) −0.104528 + 0.994522i −0.00899638 + 0.0855948i
\(136\) 4.30146 + 4.77726i 0.368847 + 0.409646i
\(137\) −3.12437 + 3.46996i −0.266933 + 0.296459i −0.861678 0.507455i \(-0.830586\pi\)
0.594745 + 0.803914i \(0.297253\pi\)
\(138\) −0.139886 1.33093i −0.0119079 0.113296i
\(139\) 1.32794 + 4.08699i 0.112635 + 0.346654i 0.991446 0.130515i \(-0.0416630\pi\)
−0.878812 + 0.477169i \(0.841663\pi\)
\(140\) −1.20906 3.72109i −0.102184 0.314490i
\(141\) −0.227296 2.16258i −0.0191418 0.182122i
\(142\) 5.77583 6.41471i 0.484697 0.538310i
\(143\) 1.57370 + 1.74778i 0.131600 + 0.146156i
\(144\) −0.104528 + 0.994522i −0.00871071 + 0.0828768i
\(145\) −0.120857 + 0.0256890i −0.0100367 + 0.00213336i
\(146\) −14.1411 6.29602i −1.17033 0.521063i
\(147\) 6.72161 4.88353i 0.554389 0.402787i
\(148\) −0.264824 + 0.117907i −0.0217684 + 0.00969192i
\(149\) −8.75414 + 15.1626i −0.717167 + 1.24217i 0.244950 + 0.969536i \(0.421228\pi\)
−0.962118 + 0.272635i \(0.912105\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −9.13216 6.63491i −0.743165 0.539941i 0.150536 0.988605i \(-0.451900\pi\)
−0.893701 + 0.448664i \(0.851900\pi\)
\(152\) −5.53062 1.17557i −0.448593 0.0953514i
\(153\) 1.98649 6.11380i 0.160599 0.494272i
\(154\) 25.5874 2.06189
\(155\) 0.321142 + 5.55850i 0.0257948 + 0.446469i
\(156\) −0.359625 −0.0287931
\(157\) −2.18343 + 6.71989i −0.174256 + 0.536306i −0.999599 0.0283267i \(-0.990982\pi\)
0.825342 + 0.564633i \(0.190982\pi\)
\(158\) −6.34671 1.34903i −0.504917 0.107323i
\(159\) −3.27977 2.38289i −0.260103 0.188976i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 2.61803 4.53457i 0.206330 0.357374i
\(162\) 0.913545 0.406737i 0.0717749 0.0319562i
\(163\) −3.32916 + 2.41878i −0.260760 + 0.189453i −0.710482 0.703715i \(-0.751523\pi\)
0.449722 + 0.893169i \(0.351523\pi\)
\(164\) 8.46458 + 3.76867i 0.660973 + 0.294284i
\(165\) −6.39685 + 1.35969i −0.497994 + 0.105852i
\(166\) −0.461819 + 4.39391i −0.0358441 + 0.341034i
\(167\) −1.21944 1.35432i −0.0943629 0.104801i 0.694114 0.719865i \(-0.255797\pi\)
−0.788477 + 0.615065i \(0.789130\pi\)
\(168\) −2.61803 + 2.90762i −0.201986 + 0.224328i
\(169\) 1.34535 + 12.8002i 0.103489 + 0.984628i
\(170\) −1.98649 6.11380i −0.152357 0.468907i
\(171\) 1.74724 + 5.37745i 0.133615 + 0.411224i
\(172\) 0.713426 + 6.78779i 0.0543982 + 0.517564i
\(173\) −11.7519 + 13.0518i −0.893481 + 0.992311i −0.999998 0.00199962i \(-0.999363\pi\)
0.106517 + 0.994311i \(0.466030\pi\)
\(174\) 0.0826761 + 0.0918211i 0.00626766 + 0.00696094i
\(175\) −0.408977 + 3.89116i −0.0309158 + 0.294144i
\(176\) −6.39685 + 1.35969i −0.482181 + 0.102491i
\(177\) 4.54131 + 2.02192i 0.341345 + 0.151977i
\(178\) −5.07794 + 3.68934i −0.380608 + 0.276528i
\(179\) −20.4365 + 9.09894i −1.52750 + 0.680087i −0.986921 0.161207i \(-0.948461\pi\)
−0.540579 + 0.841293i \(0.681795\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 3.28444 + 5.68882i 0.244131 + 0.422847i 0.961887 0.273448i \(-0.0881641\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(182\) −1.13834 0.827053i −0.0843795 0.0613053i
\(183\) 10.8374 + 2.30356i 0.801124 + 0.170284i
\(184\) −0.413545 + 1.27276i −0.0304870 + 0.0938293i
\(185\) 0.289886 0.0213128
\(186\) 4.65323 3.05736i 0.341191 0.224177i
\(187\) 42.0404 3.07430
\(188\) −0.671954 + 2.06806i −0.0490073 + 0.150829i
\(189\) 3.82709 + 0.813473i 0.278380 + 0.0591715i
\(190\) 4.57433 + 3.32344i 0.331857 + 0.241108i
\(191\) 5.34391 + 9.25592i 0.386672 + 0.669735i 0.992000 0.126241i \(-0.0402914\pi\)
−0.605328 + 0.795976i \(0.706958\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −20.5322 + 9.14153i −1.47794 + 0.658021i −0.978107 0.208100i \(-0.933272\pi\)
−0.499833 + 0.866122i \(0.666605\pi\)
\(194\) 11.0902 8.05748i 0.796228 0.578493i
\(195\) 0.328534 + 0.146273i 0.0235268 + 0.0104748i
\(196\) −8.12681 + 1.72741i −0.580486 + 0.123386i
\(197\) 2.06040 19.6034i 0.146797 1.39668i −0.634692 0.772765i \(-0.718873\pi\)
0.781490 0.623918i \(-0.214460\pi\)
\(198\) 4.37595 + 4.85999i 0.310986 + 0.345384i
\(199\) 0.647664 0.719304i 0.0459117 0.0509901i −0.719752 0.694232i \(-0.755744\pi\)
0.765663 + 0.643242i \(0.222411\pi\)
\(200\) −0.104528 0.994522i −0.00739128 0.0703233i
\(201\) −3.70479 11.4022i −0.261316 0.804247i
\(202\) 2.66680 + 8.20755i 0.187635 + 0.577481i
\(203\) 0.0505322 + 0.480781i 0.00354666 + 0.0337442i
\(204\) −4.30146 + 4.77726i −0.301162 + 0.334475i
\(205\) −6.19992 6.88571i −0.433021 0.480919i
\(206\) −1.81795 + 17.2967i −0.126663 + 1.20512i
\(207\) 1.30902 0.278240i 0.0909830 0.0193390i
\(208\) 0.328534 + 0.146273i 0.0227797 + 0.0101422i
\(209\) −29.9150 + 21.7345i −2.06927 + 1.50341i
\(210\) 3.57433 1.59139i 0.246652 0.109817i
\(211\) 11.0195 19.0863i 0.758611 1.31395i −0.184949 0.982748i \(-0.559212\pi\)
0.943559 0.331204i \(-0.107455\pi\)
\(212\) 2.02701 + 3.51089i 0.139216 + 0.241129i
\(213\) 6.98331 + 5.07367i 0.478488 + 0.347642i
\(214\) 5.79817 + 1.23244i 0.396355 + 0.0842478i
\(215\) 2.10910 6.49113i 0.143839 0.442692i
\(216\) −1.00000 −0.0680414
\(217\) 21.7603 + 1.02368i 1.47719 + 0.0694920i
\(218\) 4.73948 0.320998
\(219\) 4.78339 14.7217i 0.323231 0.994804i
\(220\) 6.39685 + 1.35969i 0.431276 + 0.0916705i
\(221\) −1.87031 1.35886i −0.125810 0.0914067i
\(222\) −0.144943 0.251049i −0.00972794 0.0168493i
\(223\) 12.8028 22.1752i 0.857342 1.48496i −0.0171140 0.999854i \(-0.505448\pi\)
0.874456 0.485106i \(-0.161219\pi\)
\(224\) 3.57433 1.59139i 0.238820 0.106329i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) −10.8232 4.81882i −0.719952 0.320543i
\(227\) 6.51584 1.38498i 0.432472 0.0919247i 0.0134681 0.999909i \(-0.495713\pi\)
0.419003 + 0.907985i \(0.362380\pi\)
\(228\) 0.591023 5.62321i 0.0391415 0.372406i
\(229\) −10.6513 11.8295i −0.703857 0.781713i 0.280128 0.959963i \(-0.409623\pi\)
−0.983985 + 0.178250i \(0.942956\pi\)
\(230\) 0.895472 0.994522i 0.0590456 0.0655768i
\(231\) 2.67461 + 25.4472i 0.175977 + 1.67431i
\(232\) −0.0381813 0.117510i −0.00250673 0.00771492i
\(233\) 4.22723 + 13.0101i 0.276935 + 0.852319i 0.988701 + 0.149902i \(0.0478958\pi\)
−0.711766 + 0.702417i \(0.752104\pi\)
\(234\) −0.0375911 0.357655i −0.00245741 0.0233807i
\(235\) 1.45502 1.61596i 0.0949148 0.105414i
\(236\) −3.32630 3.69423i −0.216524 0.240474i
\(237\) 0.678233 6.45295i 0.0440560 0.419164i
\(238\) −24.6022 + 5.22936i −1.59472 + 0.338969i
\(239\) −20.9688 9.33591i −1.35636 0.603890i −0.405665 0.914022i \(-0.632960\pi\)
−0.950694 + 0.310132i \(0.899627\pi\)
\(240\) −0.809017 + 0.587785i −0.0522218 + 0.0379414i
\(241\) −18.3358 + 8.16361i −1.18111 + 0.525864i −0.900880 0.434069i \(-0.857078\pi\)
−0.280230 + 0.959933i \(0.590411\pi\)
\(242\) −15.8842 + 27.5123i −1.02108 + 1.76856i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −8.96352 6.51238i −0.573831 0.416912i
\(245\) 8.12681 + 1.72741i 0.519203 + 0.110360i
\(246\) −2.86324 + 8.81214i −0.182553 + 0.561842i
\(247\) 2.03339 0.129381
\(248\) −5.49448 + 0.900404i −0.348900 + 0.0571757i
\(249\) −4.41811 −0.279987
\(250\) −0.309017 + 0.951057i −0.0195440 + 0.0601501i
\(251\) 26.9382 + 5.72590i 1.70033 + 0.361415i 0.952983 0.303024i \(-0.0979962\pi\)
0.747342 + 0.664439i \(0.231330\pi\)
\(252\) −3.16535 2.29976i −0.199398 0.144871i
\(253\) 4.37595 + 7.57938i 0.275114 + 0.476511i
\(254\) −3.15622 + 5.46673i −0.198039 + 0.343013i
\(255\) 5.87266 2.61468i 0.367760 0.163738i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −4.22112 1.87936i −0.263306 0.117231i 0.270838 0.962625i \(-0.412699\pi\)
−0.534144 + 0.845394i \(0.679366\pi\)
\(258\) −6.67603 + 1.41903i −0.415632 + 0.0883453i
\(259\) 0.118557 1.12799i 0.00736676 0.0700900i
\(260\) −0.240636 0.267254i −0.0149236 0.0165744i
\(261\) −0.0826761 + 0.0918211i −0.00511752 + 0.00568358i
\(262\) −0.142319 1.35408i −0.00879251 0.0836551i
\(263\) −3.54936 10.9238i −0.218863 0.673592i −0.998857 0.0478041i \(-0.984778\pi\)
0.779994 0.625788i \(-0.215222\pi\)
\(264\) −2.02090 6.21968i −0.124378 0.382795i
\(265\) −0.423761 4.03181i −0.0260314 0.247672i
\(266\) 14.8028 16.4402i 0.907620 1.00801i
\(267\) −4.19992 4.66448i −0.257031 0.285462i
\(268\) −1.25319 + 11.9233i −0.0765506 + 0.728330i
\(269\) −9.62931 + 2.04677i −0.587109 + 0.124794i −0.491882 0.870662i \(-0.663691\pi\)
−0.0952268 + 0.995456i \(0.530358\pi\)
\(270\) 0.913545 + 0.406737i 0.0555966 + 0.0247532i
\(271\) 7.02307 5.10256i 0.426621 0.309958i −0.353675 0.935368i \(-0.615068\pi\)
0.780296 + 0.625410i \(0.215068\pi\)
\(272\) 5.87266 2.61468i 0.356083 0.158538i
\(273\) 0.703533 1.21856i 0.0425798 0.0737503i
\(274\) 2.33465 + 4.04373i 0.141041 + 0.244291i
\(275\) −5.29078 3.84398i −0.319046 0.231800i
\(276\) −1.30902 0.278240i −0.0787936 0.0167481i
\(277\) −0.480771 + 1.47966i −0.0288868 + 0.0889043i −0.964460 0.264227i \(-0.914883\pi\)
0.935574 + 0.353131i \(0.114883\pi\)
\(278\) 4.29732 0.257736
\(279\) 3.52701 + 4.30815i 0.211157 + 0.257922i
\(280\) −3.91259 −0.233822
\(281\) 6.31303 19.4295i 0.376604 1.15907i −0.565786 0.824552i \(-0.691427\pi\)
0.942390 0.334516i \(-0.108573\pi\)
\(282\) −2.12697 0.452102i −0.126659 0.0269223i
\(283\) 7.86501 + 5.71426i 0.467526 + 0.339678i 0.796476 0.604670i \(-0.206695\pi\)
−0.328950 + 0.944347i \(0.606695\pi\)
\(284\) −4.31592 7.47539i −0.256103 0.443583i
\(285\) −2.82709 + 4.89667i −0.167462 + 0.290053i
\(286\) 2.14853 0.956589i 0.127046 0.0565643i
\(287\) −29.3290 + 21.3088i −1.73124 + 1.25782i
\(288\) 0.913545 + 0.406737i 0.0538312 + 0.0239672i
\(289\) −23.7932 + 5.05740i −1.39960 + 0.297494i
\(290\) −0.0129153 + 0.122881i −0.000758411 + 0.00721580i
\(291\) 9.17258 + 10.1872i 0.537706 + 0.597183i
\(292\) −10.3577 + 11.5034i −0.606139 + 0.673186i
\(293\) 0.109750 + 1.04420i 0.00641167 + 0.0610030i 0.997260 0.0739778i \(-0.0235694\pi\)
−0.990848 + 0.134981i \(0.956903\pi\)
\(294\) −2.56743 7.90172i −0.149735 0.460838i
\(295\) 1.53615 + 4.72778i 0.0894380 + 0.275262i
\(296\) 0.0303013 + 0.288298i 0.00176123 + 0.0167570i
\(297\) −4.37595 + 4.85999i −0.253919 + 0.282005i
\(298\) 11.7153 + 13.0112i 0.678651 + 0.753718i
\(299\) 0.0503067 0.478636i 0.00290931 0.0276803i
\(300\) 0.978148 0.207912i 0.0564734 0.0120038i
\(301\) −24.3954 10.8616i −1.40613 0.626049i
\(302\) −9.13216 + 6.63491i −0.525497 + 0.381796i
\(303\) −7.88383 + 3.51011i −0.452914 + 0.201651i
\(304\) −2.82709 + 4.89667i −0.162145 + 0.280843i
\(305\) 5.53976 + 9.59515i 0.317206 + 0.549417i
\(306\) −5.20071 3.77854i −0.297305 0.216005i
\(307\) −21.1069 4.48642i −1.20464 0.256053i −0.438500 0.898731i \(-0.644490\pi\)
−0.766136 + 0.642678i \(0.777823\pi\)
\(308\) 7.90694 24.3351i 0.450540 1.38662i
\(309\) −17.3920 −0.989394
\(310\) 5.38568 + 1.41224i 0.305886 + 0.0802101i
\(311\) 6.66523 0.377950 0.188975 0.981982i \(-0.439483\pi\)
0.188975 + 0.981982i \(0.439483\pi\)
\(312\) −0.111130 + 0.342024i −0.00629152 + 0.0193633i
\(313\) 22.1355 + 4.70504i 1.25117 + 0.265944i 0.785415 0.618969i \(-0.212450\pi\)
0.465755 + 0.884914i \(0.345783\pi\)
\(314\) 5.71628 + 4.15312i 0.322589 + 0.234374i
\(315\) 1.95630 + 3.38840i 0.110225 + 0.190915i
\(316\) −3.24425 + 5.61921i −0.182503 + 0.316105i
\(317\) 18.4001 8.19226i 1.03345 0.460123i 0.181307 0.983427i \(-0.441967\pi\)
0.852146 + 0.523303i \(0.175301\pi\)
\(318\) −3.27977 + 2.38289i −0.183921 + 0.133626i
\(319\) −0.738178 0.328658i −0.0413300 0.0184013i
\(320\) 0.978148 0.207912i 0.0546801 0.0116226i
\(321\) −0.619614 + 5.89523i −0.0345835 + 0.329040i
\(322\) −3.50361 3.89116i −0.195249 0.216846i
\(323\) 24.3212 27.0115i 1.35327 1.50296i
\(324\) −0.104528 0.994522i −0.00580714 0.0552512i
\(325\) 0.111130 + 0.342024i 0.00616440 + 0.0189721i
\(326\) 1.27163 + 3.91366i 0.0704288 + 0.216758i
\(327\) 0.495410 + 4.71351i 0.0273963 + 0.260658i
\(328\) 6.19992 6.88571i 0.342333 0.380200i
\(329\) −5.69289 6.32259i −0.313859 0.348576i
\(330\) −0.683591 + 6.50394i −0.0376305 + 0.358030i
\(331\) 10.1251 2.15216i 0.556528 0.118294i 0.0789428 0.996879i \(-0.474846\pi\)
0.477585 + 0.878585i \(0.341512\pi\)
\(332\) 4.03615 + 1.79701i 0.221512 + 0.0986237i
\(333\) 0.234523 0.170391i 0.0128518 0.00933735i
\(334\) −1.66486 + 0.741245i −0.0910973 + 0.0405591i
\(335\) 5.99448 10.3827i 0.327513 0.567270i
\(336\) 1.95630 + 3.38840i 0.106725 + 0.184853i
\(337\) 9.68375 + 7.03566i 0.527507 + 0.383257i 0.819425 0.573187i \(-0.194293\pi\)
−0.291917 + 0.956444i \(0.594293\pi\)
\(338\) 12.5894 + 2.67596i 0.684774 + 0.145553i
\(339\) 3.66109 11.2677i 0.198843 0.611975i
\(340\) −6.42843 −0.348631
\(341\) −19.6676 + 30.6432i −1.06506 + 1.65942i
\(342\) 5.65418 0.305743
\(343\) 1.58189 4.86854i 0.0854138 0.262877i
\(344\) 6.67603 + 1.41903i 0.359948 + 0.0765092i
\(345\) 1.08268 + 0.786610i 0.0582893 + 0.0423497i
\(346\) 8.78148 + 15.2100i 0.472095 + 0.817693i
\(347\) −3.80126 + 6.58398i −0.204062 + 0.353446i −0.949834 0.312756i \(-0.898748\pi\)
0.745771 + 0.666202i \(0.232081\pi\)
\(348\) 0.112875 0.0502553i 0.00605075 0.00269397i
\(349\) 4.47660 3.25244i 0.239627 0.174099i −0.461490 0.887145i \(-0.652685\pi\)
0.701117 + 0.713046i \(0.252685\pi\)
\(350\) 3.57433 + 1.59139i 0.191056 + 0.0850636i
\(351\) 0.351767 0.0747703i 0.0187759 0.00399094i
\(352\) −0.683591 + 6.50394i −0.0364355 + 0.346661i
\(353\) −7.07640 7.85914i −0.376639 0.418300i 0.524787 0.851234i \(-0.324145\pi\)
−0.901426 + 0.432934i \(0.857478\pi\)
\(354\) 3.32630 3.69423i 0.176791 0.196346i
\(355\) 0.902273 + 8.58456i 0.0478877 + 0.455621i
\(356\) 1.93960 + 5.96948i 0.102799 + 0.316382i
\(357\) −7.77234 23.9208i −0.411356 1.26602i
\(358\) 2.33836 + 22.2480i 0.123586 + 1.17585i
\(359\) −0.339568 + 0.377128i −0.0179217 + 0.0199041i −0.752039 0.659119i \(-0.770930\pi\)
0.734117 + 0.679023i \(0.237596\pi\)
\(360\) −0.669131 0.743145i −0.0352663 0.0391672i
\(361\) −1.35571 + 12.8987i −0.0713532 + 0.678880i
\(362\) 6.42534 1.36575i 0.337708 0.0717821i
\(363\) −29.0219 12.9214i −1.52326 0.678198i
\(364\) −1.13834 + 0.827053i −0.0596653 + 0.0433494i
\(365\) 14.1411 6.29602i 0.740179 0.329549i
\(366\) 5.53976 9.59515i 0.289568 0.501546i
\(367\) 9.95630 + 17.2448i 0.519714 + 0.900172i 0.999737 + 0.0229158i \(0.00729497\pi\)
−0.480023 + 0.877256i \(0.659372\pi\)
\(368\) 1.08268 + 0.786610i 0.0564384 + 0.0410049i
\(369\) −9.06316 1.92643i −0.471809 0.100286i
\(370\) 0.0895797 0.275698i 0.00465703 0.0143329i
\(371\) −15.8617 −0.823500
\(372\) −1.46980 5.37026i −0.0762056 0.278435i
\(373\) −22.9573 −1.18869 −0.594343 0.804212i \(-0.702588\pi\)
−0.594343 + 0.804212i \(0.702588\pi\)
\(374\) 12.9912 39.9828i 0.671759 2.06746i
\(375\) −0.978148 0.207912i −0.0505113 0.0107365i
\(376\) 1.75920 + 1.27813i 0.0907237 + 0.0659147i
\(377\) 0.0222172 + 0.0384813i 0.00114424 + 0.00198189i
\(378\) 1.95630 3.38840i 0.100621 0.174281i
\(379\) −0.791547 + 0.352419i −0.0406590 + 0.0181026i −0.426965 0.904268i \(-0.640417\pi\)
0.386306 + 0.922371i \(0.373751\pi\)
\(380\) 4.57433 3.32344i 0.234658 0.170489i
\(381\) −5.76669 2.56750i −0.295437 0.131537i
\(382\) 10.4543 2.22212i 0.534887 0.113694i
\(383\) 2.59614 24.7006i 0.132657 1.26214i −0.702322 0.711860i \(-0.747853\pi\)
0.834978 0.550283i \(-0.185480\pi\)
\(384\) −0.669131 0.743145i −0.0341464 0.0379235i
\(385\) −17.1213 + 19.0151i −0.872583 + 0.969102i
\(386\) 2.34931 + 22.3522i 0.119577 + 1.13770i
\(387\) −2.10910 6.49113i −0.107211 0.329963i
\(388\) −4.23607 13.0373i −0.215054 0.661867i
\(389\) 1.86655 + 17.7590i 0.0946379 + 0.900419i 0.934103 + 0.357005i \(0.116202\pi\)
−0.839465 + 0.543414i \(0.817131\pi\)
\(390\) 0.240636 0.267254i 0.0121851 0.0135329i
\(391\) −5.75648 6.39322i −0.291118 0.323319i
\(392\) −0.868460 + 8.26285i −0.0438639 + 0.417337i
\(393\) 1.33178 0.283079i 0.0671796 0.0142795i
\(394\) −18.0072 8.01733i −0.907191 0.403907i
\(395\) 5.24931 3.81384i 0.264121 0.191895i
\(396\) 5.97437 2.65996i 0.300223 0.133668i
\(397\) −19.4006 + 33.6028i −0.973688 + 1.68648i −0.289491 + 0.957181i \(0.593486\pi\)
−0.684197 + 0.729297i \(0.739847\pi\)
\(398\) −0.483960 0.838243i −0.0242587 0.0420173i
\(399\) 17.8975 + 13.0033i 0.895995 + 0.650978i
\(400\) −0.978148 0.207912i −0.0489074 0.0103956i
\(401\) 5.97226 18.3807i 0.298240 0.917890i −0.683873 0.729601i \(-0.739706\pi\)
0.982114 0.188289i \(-0.0602941\pi\)
\(402\) −11.9890 −0.597955
\(403\) 1.86545 0.727556i 0.0929247 0.0362421i
\(404\) 8.62993 0.429355
\(405\) −0.309017 + 0.951057i −0.0153552 + 0.0472584i
\(406\) 0.472866 + 0.100511i 0.0234679 + 0.00498826i
\(407\) 1.53372 + 1.11431i 0.0760238 + 0.0552345i
\(408\) 3.21422 + 5.56718i 0.159127 + 0.275617i
\(409\) 14.1030 24.4272i 0.697350 1.20784i −0.272033 0.962288i \(-0.587696\pi\)
0.969382 0.245557i \(-0.0789708\pi\)
\(410\) −8.46458 + 3.76867i −0.418036 + 0.186122i
\(411\) −3.77754 + 2.74454i −0.186332 + 0.135378i
\(412\) 15.8883 + 7.07394i 0.782762 + 0.348508i
\(413\) 19.0248 4.04384i 0.936148 0.198984i
\(414\) 0.139886 1.33093i 0.00687504 0.0654116i
\(415\) −2.95630 3.28330i −0.145119 0.161171i
\(416\) 0.240636 0.267254i 0.0117982 0.0131032i
\(417\) 0.449192 + 4.27378i 0.0219970 + 0.209288i
\(418\) 11.4265 + 35.1672i 0.558889 + 1.72008i
\(419\) −10.7147 32.9765i −0.523449 1.61101i −0.767363 0.641212i \(-0.778432\pi\)
0.243915 0.969797i \(-0.421568\pi\)
\(420\) −0.408977 3.89116i −0.0199560 0.189869i
\(421\) 25.5097 28.3314i 1.24327 1.38079i 0.346645 0.937997i \(-0.387321\pi\)
0.896624 0.442793i \(-0.146012\pi\)
\(422\) −14.7469 16.3781i −0.717868 0.797273i
\(423\) 0.227296 2.16258i 0.0110515 0.105148i
\(424\) 3.96543 0.842879i 0.192578 0.0409338i
\(425\) 5.87266 + 2.61468i 0.284866 + 0.126831i
\(426\) 6.98331 5.07367i 0.338342 0.245820i
\(427\) 39.6019 17.6319i 1.91647 0.853267i
\(428\) 2.96385 5.13354i 0.143263 0.248139i
\(429\) 1.17593 + 2.03677i 0.0567745 + 0.0983364i
\(430\) −5.52169 4.01174i −0.266279 0.193463i
\(431\) 35.2948 + 7.50215i 1.70009 + 0.361366i 0.952910 0.303254i \(-0.0980729\pi\)
0.747182 + 0.664619i \(0.231406\pi\)
\(432\) −0.309017 + 0.951057i −0.0148676 + 0.0457577i
\(433\) 13.0958 0.629346 0.314673 0.949200i \(-0.398105\pi\)
0.314673 + 0.949200i \(0.398105\pi\)
\(434\) 7.69789 20.3790i 0.369510 0.978221i
\(435\) −0.123557 −0.00592413
\(436\) 1.46458 4.50751i 0.0701406 0.215871i
\(437\) 7.40142 + 1.57322i 0.354058 + 0.0752573i
\(438\) −12.5231 9.09854i −0.598375 0.434745i
\(439\) −0.0397897 0.0689178i −0.00189906 0.00328927i 0.865074 0.501644i \(-0.167271\pi\)
−0.866973 + 0.498354i \(0.833938\pi\)
\(440\) 3.26988 5.66360i 0.155885 0.270002i
\(441\) 7.59007 3.37932i 0.361432 0.160920i
\(442\) −1.87031 + 1.35886i −0.0889615 + 0.0646343i
\(443\) 3.50650 + 1.56119i 0.166599 + 0.0741746i 0.488342 0.872653i \(-0.337602\pi\)
−0.321743 + 0.946827i \(0.604269\pi\)
\(444\) −0.283551 + 0.0602707i −0.0134567 + 0.00286032i
\(445\) 0.656092 6.24230i 0.0311017 0.295913i
\(446\) −17.1335 19.0287i −0.811297 0.901036i
\(447\) −11.7153 + 13.0112i −0.554116 + 0.615408i
\(448\) −0.408977 3.89116i −0.0193223 0.183840i
\(449\) 11.0453 + 33.9939i 0.521259 + 1.60427i 0.771597 + 0.636112i \(0.219458\pi\)
−0.250337 + 0.968159i \(0.580542\pi\)
\(450\) 0.309017 + 0.951057i 0.0145672 + 0.0448332i
\(451\) −6.33391 60.2631i −0.298252 2.83768i
\(452\) −7.92754 + 8.80442i −0.372880 + 0.414125i
\(453\) −7.55313 8.38860i −0.354877 0.394131i
\(454\) 0.696307 6.62492i 0.0326793 0.310923i
\(455\) 1.37632 0.292546i 0.0645228 0.0137148i
\(456\) −5.16535 2.29976i −0.241890 0.107696i
\(457\) −9.26052 + 6.72816i −0.433189 + 0.314730i −0.782923 0.622119i \(-0.786272\pi\)
0.349734 + 0.936849i \(0.386272\pi\)
\(458\) −14.5419 + 6.47448i −0.679499 + 0.302533i
\(459\) 3.21422 5.56718i 0.150027 0.259854i
\(460\) −0.669131 1.15897i −0.0311984 0.0540372i
\(461\) 21.1526 + 15.3683i 0.985175 + 0.715771i 0.958859 0.283882i \(-0.0916226\pi\)
0.0263155 + 0.999654i \(0.491623\pi\)
\(462\) 25.0283 + 5.31992i 1.16442 + 0.247505i
\(463\) 1.78903 5.50608i 0.0831434 0.255889i −0.900839 0.434152i \(-0.857048\pi\)
0.983983 + 0.178263i \(0.0570479\pi\)
\(464\) −0.123557 −0.00573601
\(465\) −0.841551 + 5.50380i −0.0390260 + 0.255233i
\(466\) 13.6796 0.633696
\(467\) 7.39216 22.7507i 0.342068 1.05278i −0.621066 0.783758i \(-0.713300\pi\)
0.963135 0.269020i \(-0.0866997\pi\)
\(468\) −0.351767 0.0747703i −0.0162604 0.00345626i
\(469\) −37.9493 27.5717i −1.75233 1.27315i
\(470\) −1.08724 1.88316i −0.0501508 0.0868638i
\(471\) −3.53286 + 6.11909i −0.162785 + 0.281953i
\(472\) −4.54131 + 2.02192i −0.209031 + 0.0930664i
\(473\) 36.1105 26.2358i 1.66036 1.20632i
\(474\) −5.92754 2.63911i −0.272261 0.121218i
\(475\) −5.53062 + 1.17557i −0.253762 + 0.0539389i
\(476\) −2.62908 + 25.0140i −0.120504 + 1.14652i
\(477\) −2.71267 3.01273i −0.124205 0.137943i
\(478\) −15.3587 + 17.0576i −0.702490 + 0.780194i
\(479\) −0.853456 8.12009i −0.0389954 0.371016i −0.996565 0.0828143i \(-0.973609\pi\)
0.957570 0.288202i \(-0.0930575\pi\)
\(480\) 0.309017 + 0.951057i 0.0141046 + 0.0434096i
\(481\) −0.0322151 0.0991480i −0.00146888 0.00452076i
\(482\) 2.09799 + 19.9610i 0.0955608 + 0.909200i
\(483\) 3.50361 3.89116i 0.159420 0.177054i
\(484\) 21.2573 + 23.6086i 0.966239 + 1.07312i
\(485\) −1.43290 + 13.6331i −0.0650645 + 0.619048i
\(486\) 0.978148 0.207912i 0.0443697 0.00943107i
\(487\) 5.73441 + 2.55312i 0.259851 + 0.115693i 0.532528 0.846413i \(-0.321242\pi\)
−0.272677 + 0.962106i \(0.587909\pi\)
\(488\) −8.96352 + 6.51238i −0.405760 + 0.294802i
\(489\) −3.75930 + 1.67375i −0.170001 + 0.0756895i
\(490\) 4.15418 7.19525i 0.187667 0.325048i
\(491\) −6.21487 10.7645i −0.280473 0.485794i 0.691028 0.722828i \(-0.257158\pi\)
−0.971501 + 0.237034i \(0.923825\pi\)
\(492\) 7.49606 + 5.44620i 0.337948 + 0.245534i
\(493\) 0.776924 + 0.165140i 0.0349909 + 0.00743754i
\(494\) 0.628351 1.93387i 0.0282709 0.0870088i
\(495\) −6.53976 −0.293940
\(496\) −0.841551 + 5.50380i −0.0377868 + 0.247128i
\(497\) 33.7729 1.51492
\(498\) −1.36527 + 4.20188i −0.0611793 + 0.188291i
\(499\) 18.9682 + 4.03181i 0.849133 + 0.180489i 0.611872 0.790957i \(-0.290417\pi\)
0.237261 + 0.971446i \(0.423750\pi\)
\(500\) 0.809017 + 0.587785i 0.0361803 + 0.0262866i
\(501\) −0.911210 1.57826i −0.0407099 0.0705116i
\(502\) 13.7700 23.8504i 0.614586 1.06449i
\(503\) −28.3442 + 12.6196i −1.26380 + 0.562682i −0.925640 0.378405i \(-0.876473\pi\)
−0.338164 + 0.941087i \(0.609806\pi\)
\(504\) −3.16535 + 2.29976i −0.140996 + 0.102440i
\(505\) −7.88383 3.51011i −0.350826 0.156198i
\(506\) 8.56066 1.81962i 0.380568 0.0808922i
\(507\) −1.34535 + 12.8002i −0.0597491 + 0.568475i
\(508\) 4.22384 + 4.69105i 0.187403 + 0.208132i
\(509\) 25.9928 28.8679i 1.15211 1.27955i 0.197963 0.980209i \(-0.436567\pi\)
0.954147 0.299338i \(-0.0967659\pi\)
\(510\) −0.671954 6.39322i −0.0297546 0.283096i
\(511\) −18.7154 57.6002i −0.827922 2.54808i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) 0.591023 + 5.62321i 0.0260943 + 0.248271i
\(514\) −3.09178 + 3.43377i −0.136372 + 0.151457i
\(515\) −11.6375 12.9247i −0.512809 0.569532i
\(516\) −0.713426 + 6.78779i −0.0314068 + 0.298816i
\(517\) 13.9099 2.95664i 0.611756 0.130033i
\(518\) −1.03615 0.461323i −0.0455257 0.0202694i
\(519\) −14.2087 + 10.3232i −0.623694 + 0.453140i
\(520\) −0.328534 + 0.146273i −0.0144072 + 0.00641449i
\(521\) 1.79699 3.11248i 0.0787275 0.136360i −0.823974 0.566628i \(-0.808248\pi\)
0.902701 + 0.430268i \(0.141581\pi\)
\(522\) 0.0617787 + 0.107004i 0.00270398 + 0.00468343i
\(523\) 16.6923 + 12.1277i 0.729903 + 0.530306i 0.889533 0.456871i \(-0.151030\pi\)
−0.159630 + 0.987177i \(0.551030\pi\)
\(524\) −1.33178 0.283079i −0.0581792 0.0123664i
\(525\) −1.20906 + 3.72109i −0.0527676 + 0.162402i
\(526\) −11.4860 −0.500813
\(527\) 12.6477 33.4829i 0.550943 1.45854i
\(528\) −6.53976 −0.284607
\(529\) −6.55396 + 20.1710i −0.284955 + 0.877001i
\(530\) −3.96543 0.842879i −0.172247 0.0366123i
\(531\) 4.02169 + 2.92193i 0.174526 + 0.126801i
\(532\) −11.0612 19.1586i −0.479566 0.830633i
\(533\) −1.66608 + 2.88573i −0.0721659 + 0.124995i
\(534\) −5.73403 + 2.55296i −0.248136 + 0.110477i
\(535\) −4.79561 + 3.48422i −0.207332 + 0.150636i
\(536\) 10.9525 + 4.87635i 0.473074 + 0.210626i
\(537\) −21.8817 + 4.65111i −0.944267 + 0.200710i
\(538\) −1.02902 + 9.79050i −0.0443643 + 0.422099i
\(539\) 36.3570 + 40.3786i 1.56601 + 1.73923i
\(540\) 0.669131 0.743145i 0.0287948 0.0319799i
\(541\) −3.03330 28.8600i −0.130412 1.24079i −0.842500 0.538696i \(-0.818917\pi\)
0.712088 0.702090i \(-0.247750\pi\)
\(542\) −2.68257 8.25611i −0.115226 0.354630i
\(543\) 2.02990 + 6.24738i 0.0871112 + 0.268101i
\(544\) −0.671954 6.39322i −0.0288098 0.274107i
\(545\) −3.17133 + 3.52212i −0.135845 + 0.150871i
\(546\) −0.941512 1.04565i −0.0402930 0.0447499i
\(547\) 0.0950011 0.903875i 0.00406195 0.0386469i −0.992303 0.123832i \(-0.960482\pi\)
0.996365 + 0.0851853i \(0.0271482\pi\)
\(548\) 4.56726 0.970801i 0.195104 0.0414706i
\(549\) 10.1216 + 4.50645i 0.431981 + 0.192331i
\(550\) −5.29078 + 3.84398i −0.225600 + 0.163908i
\(551\) −0.638218 + 0.284153i −0.0271890 + 0.0121053i
\(552\) −0.669131 + 1.15897i −0.0284801 + 0.0493290i
\(553\) −12.6934 21.9856i −0.539779 0.934925i
\(554\) 1.25868 + 0.914481i 0.0534760 + 0.0388526i
\(555\) 0.283551 + 0.0602707i 0.0120361 + 0.00255835i
\(556\) 1.32794 4.08699i 0.0563174 0.173327i
\(557\) −8.79350 −0.372593 −0.186296 0.982494i \(-0.559648\pi\)
−0.186296 + 0.982494i \(0.559648\pi\)
\(558\) 5.18720 2.02309i 0.219592 0.0856444i
\(559\) −2.45451 −0.103815
\(560\) −1.20906 + 3.72109i −0.0510920 + 0.157245i
\(561\) 41.1217 + 8.74069i 1.73616 + 0.369032i
\(562\) −16.5277 12.0081i −0.697181 0.506531i
\(563\) −1.07072 1.85453i −0.0451253 0.0781593i 0.842581 0.538570i \(-0.181035\pi\)
−0.887706 + 0.460411i \(0.847702\pi\)
\(564\) −1.08724 + 1.88316i −0.0457813 + 0.0792955i
\(565\) 10.8232 4.81882i 0.455338 0.202729i
\(566\) 7.86501 5.71426i 0.330591 0.240188i
\(567\) 3.57433 + 1.59139i 0.150108 + 0.0668323i
\(568\) −8.44321 + 1.79466i −0.354269 + 0.0753023i
\(569\) 0.615920 5.86009i 0.0258207 0.245668i −0.973997 0.226562i \(-0.927251\pi\)
0.999817 0.0191057i \(-0.00608189\pi\)
\(570\) 3.78339 + 4.20188i 0.158469 + 0.175997i
\(571\) 7.26052 8.06363i 0.303843 0.337452i −0.571816 0.820382i \(-0.693761\pi\)
0.875659 + 0.482930i \(0.160427\pi\)
\(572\) −0.245837 2.33898i −0.0102790 0.0977977i
\(573\) 3.30272 + 10.1647i 0.137973 + 0.424637i
\(574\) 11.2027 + 34.4783i 0.467591 + 1.43910i
\(575\) 0.139886 + 1.33093i 0.00583367 + 0.0555036i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) −2.00756 2.22962i −0.0835757 0.0928202i 0.699906 0.714235i \(-0.253225\pi\)
−0.783482 + 0.621414i \(0.786558\pi\)
\(578\) −2.54263 + 24.1915i −0.105759 + 1.00623i
\(579\) −21.9842 + 4.67288i −0.913630 + 0.194198i
\(580\) 0.112875 + 0.0502553i 0.00468689 + 0.00208674i
\(581\) −13.9849 + 10.1606i −0.580191 + 0.421533i
\(582\) 12.5231 5.57563i 0.519098 0.231117i
\(583\) 13.2562 22.9604i 0.549014 0.950921i
\(584\) 7.73968 + 13.4055i 0.320270 + 0.554724i
\(585\) 0.290943 + 0.211383i 0.0120290 + 0.00873959i
\(586\) 1.02701 + 0.218298i 0.0424254 + 0.00901780i
\(587\) −3.64951 + 11.2320i −0.150631 + 0.463596i −0.997692 0.0679003i \(-0.978370\pi\)
0.847061 + 0.531496i \(0.178370\pi\)
\(588\) −8.30836 −0.342631
\(589\) 8.31052 + 30.3644i 0.342429 + 1.25114i
\(590\) 4.97108 0.204656
\(591\) 6.09115 18.7466i 0.250556 0.771133i
\(592\) 0.283551 + 0.0602707i 0.0116539 + 0.00247711i
\(593\) −34.8529 25.3221i −1.43124 1.03986i −0.989785 0.142571i \(-0.954463\pi\)
−0.441453 0.897284i \(-0.645537\pi\)
\(594\) 3.26988 + 5.66360i 0.134165 + 0.232380i
\(595\) 12.5759 21.7821i 0.515562 0.892980i
\(596\) 15.9946 7.12126i 0.655165 0.291698i
\(597\) 0.783063 0.568929i 0.0320486 0.0232847i
\(598\) −0.439665 0.195751i −0.0179792 0.00800486i
\(599\) 14.6485 3.11364i 0.598523 0.127220i 0.101319 0.994854i \(-0.467694\pi\)
0.497203 + 0.867634i \(0.334360\pi\)
\(600\) 0.104528 0.994522i 0.00426736 0.0406012i
\(601\) −8.44923 9.38382i −0.344651 0.382774i 0.545752 0.837947i \(-0.316244\pi\)
−0.890403 + 0.455173i \(0.849577\pi\)
\(602\) −17.8686 + 19.8450i −0.728268 + 0.808823i
\(603\) −1.25319 11.9233i −0.0510337 0.485553i
\(604\) 3.48818 + 10.7355i 0.141932 + 0.436821i
\(605\) −9.81700 30.2136i −0.399118 1.22836i
\(606\) 0.902073 + 8.58266i 0.0366442 + 0.348647i
\(607\) −30.4720 + 33.8426i −1.23682 + 1.37363i −0.334596 + 0.942362i \(0.608600\pi\)
−0.902224 + 0.431267i \(0.858067\pi\)
\(608\) 3.78339 + 4.20188i 0.153437 + 0.170409i
\(609\) −0.0505322 + 0.480781i −0.00204767 + 0.0194822i
\(610\) 10.8374 2.30356i 0.438794 0.0932685i
\(611\) −0.714394 0.318069i −0.0289013 0.0128677i
\(612\) −5.20071 + 3.77854i −0.210226 + 0.152738i
\(613\) −0.442000 + 0.196791i −0.0178522 + 0.00794831i −0.415643 0.909528i \(-0.636444\pi\)
0.397791 + 0.917476i \(0.369777\pi\)
\(614\) −10.7892 + 18.6875i −0.435418 + 0.754166i
\(615\) −4.63282 8.02428i −0.186813 0.323570i
\(616\) −20.7006 15.0399i −0.834053 0.605975i
\(617\) 27.9990 + 5.95137i 1.12720 + 0.239593i 0.733528 0.679659i \(-0.237872\pi\)
0.393669 + 0.919252i \(0.371205\pi\)
\(618\) −5.37441 + 16.5407i −0.216190 + 0.665366i
\(619\) −22.8790 −0.919583 −0.459791 0.888027i \(-0.652076\pi\)
−0.459791 + 0.888027i \(0.652076\pi\)
\(620\) 3.00739 4.68568i 0.120780 0.188181i
\(621\) 1.33826 0.0537026
\(622\) 2.05967 6.33901i 0.0825852 0.254171i
\(623\) −24.0214 5.10591i −0.962398 0.204564i
\(624\) 0.290943 + 0.211383i 0.0116470 + 0.00846207i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 11.3150 19.5981i 0.452238 0.783299i
\(627\) −33.7802 + 15.0399i −1.34905 + 0.600636i
\(628\) 5.71628 4.15312i 0.228105 0.165728i
\(629\) −1.70240 0.757959i −0.0678792 0.0302218i
\(630\) 3.82709 0.813473i 0.152475 0.0324096i
\(631\) 2.43562 23.1734i 0.0969606 0.922519i −0.832606 0.553865i \(-0.813152\pi\)
0.929567 0.368653i \(-0.120181\pi\)
\(632\) 4.34165 + 4.82189i 0.172702 + 0.191805i
\(633\) 14.7469 16.3781i 0.586137 0.650971i
\(634\) −2.10535 20.0311i −0.0836142 0.795536i
\(635\) −1.95065 6.00348i −0.0774091 0.238241i
\(636\) 1.25276 + 3.85560i 0.0496752 + 0.152885i
\(637\) −0.312320 2.97153i −0.0123746 0.117736i
\(638\) −0.540682 + 0.600488i −0.0214058 + 0.0237735i
\(639\) 5.77583 + 6.41471i 0.228488 + 0.253762i
\(640\) 0.104528 0.994522i 0.00413185 0.0393119i
\(641\) 27.1660 5.77430i 1.07299 0.228071i 0.362647 0.931926i \(-0.381873\pi\)
0.710343 + 0.703855i \(0.248540\pi\)
\(642\) 5.41523 + 2.41101i 0.213722 + 0.0951552i
\(643\) −11.1260 + 8.08351i −0.438766 + 0.318782i −0.785145 0.619313i \(-0.787411\pi\)
0.346378 + 0.938095i \(0.387411\pi\)
\(644\) −4.78339 + 2.12970i −0.188492 + 0.0839220i
\(645\) 3.41259 5.91078i 0.134371 0.232737i
\(646\) −18.1738 31.4779i −0.715037 1.23848i
\(647\) −19.4489 14.1305i −0.764617 0.555527i 0.135706 0.990749i \(-0.456670\pi\)
−0.900323 + 0.435222i \(0.856670\pi\)
\(648\) −0.978148 0.207912i −0.0384253 0.00816754i
\(649\) −10.0460 + 30.9185i −0.394342 + 1.21366i
\(650\) 0.359625 0.0141057
\(651\) 21.0720 + 5.52554i 0.825875 + 0.216563i
\(652\) 4.11507 0.161158
\(653\) −5.55548 + 17.0980i −0.217403 + 0.669097i 0.781572 + 0.623816i \(0.214418\pi\)
−0.998974 + 0.0452811i \(0.985582\pi\)
\(654\) 4.63591 + 0.985393i 0.181278 + 0.0385319i
\(655\) 1.10151 + 0.800291i 0.0430394 + 0.0312699i
\(656\) −4.63282 8.02428i −0.180881 0.313295i
\(657\) 7.73968 13.4055i 0.301954 0.522999i
\(658\) −7.77234 + 3.46047i −0.302997 + 0.134903i
\(659\) −11.8810 + 8.63209i −0.462820 + 0.336258i −0.794636 0.607086i \(-0.792339\pi\)
0.331816 + 0.943344i \(0.392339\pi\)
\(660\) 5.97437 + 2.65996i 0.232552 + 0.103539i
\(661\) −32.0485 + 6.81212i −1.24654 + 0.264961i −0.783509 0.621380i \(-0.786572\pi\)
−0.463033 + 0.886341i \(0.653239\pi\)
\(662\) 1.08201 10.2946i 0.0420535 0.400112i
\(663\) −1.54691 1.71802i −0.0600772 0.0667225i
\(664\) 2.95630 3.28330i 0.114727 0.127417i
\(665\) 2.31243 + 22.0013i 0.0896722 + 0.853174i
\(666\) −0.0895797 0.275698i −0.00347114 0.0106831i
\(667\) 0.0510966 + 0.157259i 0.00197847 + 0.00608910i
\(668\) 0.190495 + 1.81244i 0.00737047 + 0.0701253i
\(669\) 17.1335 19.0287i 0.662421 0.735693i
\(670\) −8.02218 8.90953i −0.309924 0.344205i
\(671\) −7.57386 + 72.0605i −0.292386 + 2.78186i
\(672\) 3.82709 0.813473i 0.147633 0.0313804i
\(673\) 17.8755 + 7.95869i 0.689050 + 0.306785i 0.721229 0.692697i \(-0.243578\pi\)
−0.0321783 + 0.999482i \(0.510244\pi\)
\(674\) 9.68375 7.03566i 0.373004 0.271003i
\(675\) −0.913545 + 0.406737i −0.0351624 + 0.0156553i
\(676\) 6.43533 11.1463i 0.247513 0.428705i
\(677\) −20.9236 36.2407i −0.804157 1.39284i −0.916858 0.399213i \(-0.869284\pi\)
0.112701 0.993629i \(-0.464050\pi\)
\(678\) −9.58485 6.96380i −0.368104 0.267443i
\(679\) 52.4625 + 11.1513i 2.01333 + 0.427946i
\(680\) −1.98649 + 6.11380i −0.0761786 + 0.234454i
\(681\) 6.66141 0.255266
\(682\) 23.0658 + 28.1743i 0.883236 + 1.07885i
\(683\) 47.2560 1.80820 0.904101 0.427319i \(-0.140542\pi\)
0.904101 + 0.427319i \(0.140542\pi\)
\(684\) 1.74724 5.37745i 0.0668073 0.205612i
\(685\) −4.56726 0.970801i −0.174506 0.0370924i
\(686\) −4.14143 3.00893i −0.158121 0.114881i
\(687\) −7.95906 13.7855i −0.303657 0.525949i
\(688\) 3.41259 5.91078i 0.130104 0.225346i
\(689\) −1.33188 + 0.592993i −0.0507408 + 0.0225912i
\(690\) 1.08268 0.786610i 0.0412168 0.0299457i
\(691\) 31.8600 + 14.1850i 1.21201 + 0.539623i 0.910369 0.413798i \(-0.135798\pi\)
0.301644 + 0.953421i \(0.402465\pi\)
\(692\) 17.1792 3.65154i 0.653054 0.138811i
\(693\) −2.67461 + 25.4472i −0.101600 + 0.966661i
\(694\) 5.08708 + 5.64977i 0.193103 + 0.214462i
\(695\) −2.87547 + 3.19353i −0.109073 + 0.121137i
\(696\) −0.0129153 0.122881i −0.000489552 0.00465778i
\(697\) 18.4061 + 56.6483i 0.697182 + 2.14571i
\(698\) −1.70991 5.26256i −0.0647210 0.199191i
\(699\) 1.42991 + 13.6047i 0.0540841 + 0.514576i
\(700\) 2.61803 2.90762i 0.0989524 0.109898i
\(701\) −15.9898 17.7585i −0.603926 0.670728i 0.361207 0.932485i \(-0.382365\pi\)
−0.965134 + 0.261757i \(0.915698\pi\)
\(702\) 0.0375911 0.357655i 0.00141878 0.0134988i
\(703\) 1.60325 0.340781i 0.0604677 0.0128528i
\(704\) 5.97437 + 2.65996i 0.225168 + 0.100251i
\(705\) 1.75920 1.27813i 0.0662552 0.0481373i
\(706\) −9.66121 + 4.30145i −0.363604 + 0.161887i
\(707\) −16.8827 + 29.2417i −0.634939 + 1.09975i
\(708\) −2.48554 4.30508i −0.0934123 0.161795i
\(709\) 25.8657 + 18.7925i 0.971406 + 0.705767i 0.955771 0.294110i \(-0.0950233\pi\)
0.0156341 + 0.999878i \(0.495023\pi\)
\(710\) 8.44321 + 1.79466i 0.316868 + 0.0673524i
\(711\) 2.00506 6.17093i 0.0751955 0.231428i
\(712\) 6.27668 0.235229
\(713\) 7.35304 1.20498i 0.275374 0.0451267i
\(714\) −25.1518 −0.941283
\(715\) −0.726766 + 2.23676i −0.0271795 + 0.0836499i
\(716\) 21.8817 + 4.65111i 0.817759 + 0.173820i
\(717\) −18.5695 13.4916i −0.693492 0.503851i
\(718\) 0.253738 + 0.439487i 0.00946942 + 0.0164015i
\(719\) −17.7032 + 30.6628i −0.660218 + 1.14353i 0.320340 + 0.947303i \(0.396203\pi\)
−0.980558 + 0.196229i \(0.937131\pi\)
\(720\) −0.913545 + 0.406737i −0.0340458 + 0.0151582i
\(721\) −55.0517 + 39.9974i −2.05023 + 1.48958i
\(722\) 11.8485 + 5.27528i 0.440955 + 0.196326i
\(723\) −19.6324 + 4.17299i −0.730136 + 0.155195i
\(724\) 0.686636 6.53290i 0.0255186 0.242793i
\(725\) −0.0826761 0.0918211i −0.00307051 0.00341015i
\(726\) −21.2573 + 23.6086i −0.788931 + 0.876197i
\(727\) 0.0524849 + 0.499361i 0.00194656 + 0.0185203i 0.995452 0.0952638i \(-0.0303695\pi\)
−0.993506 + 0.113784i \(0.963703\pi\)
\(728\) 0.434808 + 1.33820i 0.0161150 + 0.0495970i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −1.61803 15.3946i −0.0598861 0.569778i
\(731\) −29.3582 + 32.6056i −1.08585 + 1.20596i
\(732\) −7.41365 8.23369i −0.274016 0.304326i
\(733\) −4.46738 + 42.5042i −0.165006 + 1.56993i 0.528155 + 0.849148i \(0.322884\pi\)
−0.693161 + 0.720782i \(0.743783\pi\)
\(734\) 19.4775 4.14006i 0.718926 0.152812i
\(735\) 7.59007 + 3.37932i 0.279964 + 0.124648i
\(736\) 1.08268 0.786610i 0.0399080 0.0289948i
\(737\) 71.6264 31.8901i 2.63839 1.17469i
\(738\) −4.63282 + 8.02428i −0.170536 + 0.295378i
\(739\) −4.13367 7.15973i −0.152060 0.263375i 0.779925 0.625873i \(-0.215257\pi\)
−0.931984 + 0.362498i \(0.881924\pi\)
\(740\) −0.234523 0.170391i −0.00862122 0.00626369i
\(741\) 1.98895 + 0.422765i 0.0730660 + 0.0155307i
\(742\) −4.90154 + 15.0854i −0.179941 + 0.553802i
\(743\) 5.90833 0.216756 0.108378 0.994110i \(-0.465434\pi\)
0.108378 + 0.994110i \(0.465434\pi\)
\(744\) −5.56161 0.261638i −0.203899 0.00959211i
\(745\) −17.5083 −0.641454
\(746\) −7.09421 + 21.8337i −0.259737 + 0.799390i
\(747\) −4.32157 0.918578i −0.158118 0.0336090i
\(748\) −34.0114 24.7107i −1.24358 0.903514i
\(749\) 11.5963 + 20.0854i 0.423721 + 0.733906i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 4.19269 1.86671i 0.152993 0.0681170i −0.328811 0.944396i \(-0.606648\pi\)
0.481805 + 0.876279i \(0.339981\pi\)
\(752\) 1.75920 1.27813i 0.0641514 0.0466087i
\(753\) 25.1591 + 11.2015i 0.916848 + 0.408207i
\(754\) 0.0434634 0.00923843i 0.00158284 0.000336444i
\(755\) 1.17991 11.2261i 0.0429415 0.408561i
\(756\) −2.61803 2.90762i −0.0952170 0.105749i
\(757\) −17.1472 + 19.0439i −0.623225 + 0.692162i −0.969254 0.246062i \(-0.920863\pi\)
0.346029 + 0.938224i \(0.387530\pi\)
\(758\) 0.0905693 + 0.861709i 0.00328962 + 0.0312987i
\(759\) 2.70449 + 8.32356i 0.0981667 + 0.302126i
\(760\) −1.74724 5.37745i −0.0633790 0.195060i
\(761\) 1.95630 + 18.6129i 0.0709156 + 0.674717i 0.971013 + 0.239028i \(0.0768287\pi\)
−0.900097 + 0.435689i \(0.856505\pi\)
\(762\) −4.22384 + 4.69105i −0.153014 + 0.169939i
\(763\) 12.4081 + 13.7806i 0.449204 + 0.498891i
\(764\) 1.11718 10.6293i 0.0404182 0.384553i
\(765\) 6.28795 1.33655i 0.227341 0.0483229i
\(766\) −22.6894 10.1020i −0.819803 0.365000i
\(767\) 1.44630 1.05080i 0.0522229 0.0379422i
\(768\) −0.913545 + 0.406737i −0.0329647 + 0.0146768i
\(769\) 5.66036 9.80403i 0.204118 0.353542i −0.745734 0.666244i \(-0.767901\pi\)
0.949851 + 0.312702i \(0.101234\pi\)
\(770\) 12.7937 + 22.1593i 0.461053 + 0.798567i
\(771\) −3.73814 2.71591i −0.134626 0.0978113i
\(772\) 21.9842 + 4.67288i 0.791227 + 0.168181i
\(773\) −12.3607 + 38.0423i −0.444583 + 1.36829i 0.438358 + 0.898800i \(0.355560\pi\)
−0.882941 + 0.469485i \(0.844440\pi\)
\(774\) −6.82518 −0.245326
\(775\) −4.65323 + 3.05736i −0.167149 + 0.109824i
\(776\) −13.7082 −0.492096
\(777\) 0.350489 1.07869i 0.0125737 0.0386979i
\(778\) 17.4666 + 3.71265i 0.626210 + 0.133105i
\(779\) −42.3841 30.7938i −1.51857 1.10330i
\(780\) −0.179813 0.311445i −0.00643833 0.0111515i
\(781\) −28.2251 + 48.8873i −1.00997 + 1.74932i
\(782\) −7.85916 + 3.49912i −0.281043 + 0.125128i
\(783\) −0.0999601 + 0.0726252i −0.00357228 + 0.00259541i
\(784\) 7.59007 + 3.37932i 0.271074 + 0.120690i
\(785\) −6.91131 + 1.46904i −0.246675 + 0.0524325i
\(786\) 0.142319 1.35408i 0.00507636 0.0482983i
\(787\) −18.6712 20.7365i −0.665557 0.739176i 0.311945 0.950100i \(-0.399019\pi\)
−0.977502 + 0.210924i \(0.932353\pi\)
\(788\) −13.1895 + 14.6484i −0.469856 + 0.521828i
\(789\) −1.20061 11.4231i −0.0427429 0.406672i
\(790\) −2.00506 6.17093i −0.0713367 0.219552i
\(791\) −14.3243 44.0857i −0.509314 1.56751i
\(792\) −0.683591 6.50394i −0.0242904 0.231107i
\(793\) 2.66614 2.96104i 0.0946773 0.105150i
\(794\) 25.9631 + 28.8349i 0.921395 + 1.02331i
\(795\) 0.423761 4.03181i 0.0150292 0.142994i
\(796\) −0.946768 + 0.201242i −0.0335573 + 0.00713282i
\(797\) −44.4255 19.7795i −1.57363 0.700625i −0.580138 0.814519i \(-0.697001\pi\)
−0.993493 + 0.113893i \(0.963668\pi\)
\(798\) 17.8975 13.0033i 0.633564 0.460311i
\(799\) −12.7700 + 5.68559i −0.451772 + 0.201142i
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) −3.13834 5.43577i −0.110888 0.192063i
\(802\) −15.6356 11.3599i −0.552111 0.401132i
\(803\) 99.0192 + 21.0472i 3.49431 + 0.742739i
\(804\) −3.70479 + 11.4022i −0.130658 + 0.402124i
\(805\) 5.23607 0.184547
\(806\) −0.115491 1.99898i −0.00406800 0.0704109i
\(807\) −9.84443 −0.346540
\(808\) 2.66680 8.20755i 0.0938175 0.288741i
\(809\) 14.5660 + 3.09611i 0.512115 + 0.108853i 0.456719 0.889611i \(-0.349025\pi\)
0.0553960 + 0.998464i \(0.482358\pi\)
\(810\) 0.809017 + 0.587785i 0.0284260 + 0.0206527i
\(811\) 6.65503 + 11.5269i 0.233690 + 0.404763i 0.958891 0.283774i \(-0.0915867\pi\)
−0.725201 + 0.688537i \(0.758253\pi\)
\(812\) 0.241715 0.418662i 0.00848253 0.0146922i
\(813\) 7.93048 3.53088i 0.278134 0.123833i
\(814\) 1.53372 1.11431i 0.0537569 0.0390567i
\(815\) −3.75930 1.67375i −0.131683 0.0586289i
\(816\) 6.28795 1.33655i 0.220122 0.0467885i
\(817\) 4.03384 38.3794i 0.141126 1.34273i
\(818\) −18.8735 20.9612i −0.659897 0.732890i
\(819\) 0.941512 1.04565i 0.0328991 0.0365381i
\(820\) 0.968523 + 9.21488i 0.0338223 + 0.321797i
\(821\) −3.30083 10.1589i −0.115200 0.354548i 0.876789 0.480876i \(-0.159681\pi\)
−0.991989 + 0.126327i \(0.959681\pi\)
\(822\) 1.44289 + 4.44076i 0.0503266 + 0.154889i
\(823\) 2.33070 + 22.1752i 0.0812432 + 0.772978i 0.956973 + 0.290176i \(0.0937140\pi\)
−0.875730 + 0.482801i \(0.839619\pi\)
\(824\) 11.6375 12.9247i 0.405411 0.450255i
\(825\) −4.37595 4.85999i −0.152351 0.169203i
\(826\) 2.03306 19.3432i 0.0707391 0.673038i
\(827\) 1.55272 0.330040i 0.0539933 0.0114766i −0.180836 0.983513i \(-0.557880\pi\)
0.234829 + 0.972037i \(0.424547\pi\)
\(828\) −1.22256 0.544320i −0.0424870 0.0189164i
\(829\) −21.0181 + 15.2706i −0.729990 + 0.530369i −0.889560 0.456818i \(-0.848989\pi\)
0.159570 + 0.987187i \(0.448989\pi\)
\(830\) −4.03615 + 1.79701i −0.140097 + 0.0623751i
\(831\) −0.777904 + 1.34737i −0.0269852 + 0.0467397i
\(832\) −0.179813 0.311445i −0.00623388 0.0107974i
\(833\) −43.2094 31.3935i −1.49712 1.08772i
\(834\) 4.20341 + 0.893462i 0.145552 + 0.0309381i
\(835\) 0.563159 1.73322i 0.0194889 0.0599807i
\(836\) 36.9770 1.27888
\(837\) 2.55422 + 4.94732i 0.0882868 + 0.171004i
\(838\) −34.6736 −1.19778
\(839\) −3.49390 + 10.7531i −0.120623 + 0.371239i −0.993078 0.117455i \(-0.962526\pi\)
0.872455 + 0.488694i \(0.162526\pi\)
\(840\) −3.82709 0.813473i −0.132047 0.0280675i
\(841\) 23.4491 + 17.0368i 0.808591 + 0.587476i
\(842\) −19.0619 33.0161i −0.656915 1.13781i
\(843\) 10.2147 17.6924i 0.351813 0.609358i
\(844\) −20.1335 + 8.96403i −0.693025 + 0.308555i
\(845\) −10.4126 + 7.56519i −0.358204 + 0.260250i
\(846\) −1.98649 0.884444i −0.0682971 0.0304078i
\(847\) −121.581 + 25.8428i −4.17757 + 0.887969i
\(848\) 0.423761 4.03181i 0.0145520 0.138453i
\(849\) 6.50507 + 7.22462i 0.223254 + 0.247948i
\(850\) 4.30146 4.77726i 0.147539 0.163859i
\(851\) −0.0405511 0.385818i −0.00139007 0.0132257i
\(852\) −2.66739 8.20937i −0.0913831 0.281248i
\(853\) −6.85942 21.1111i −0.234862 0.722831i −0.997140 0.0755810i \(-0.975919\pi\)
0.762278 0.647250i \(-0.224081\pi\)
\(854\) −4.53127 43.1122i −0.155057 1.47527i
\(855\) −3.78339 + 4.20188i −0.129389 + 0.143701i
\(856\) −3.96641 4.40514i −0.135569 0.150565i
\(857\) −2.11263 + 20.1003i −0.0721660 + 0.686614i 0.897306 + 0.441410i \(0.145522\pi\)
−0.969472 + 0.245204i \(0.921145\pi\)
\(858\) 2.30047 0.488980i 0.0785368 0.0166935i
\(859\) 10.4549 + 4.65481i 0.356715 + 0.158820i 0.577267 0.816555i \(-0.304119\pi\)
−0.220552 + 0.975375i \(0.570786\pi\)
\(860\) −5.52169 + 4.01174i −0.188288 + 0.136799i
\(861\) −33.1184 + 14.7453i −1.12867 + 0.502518i
\(862\) 18.0417 31.2491i 0.614502 1.06435i
\(863\) 5.75021 + 9.95965i 0.195739 + 0.339030i 0.947143 0.320813i \(-0.103956\pi\)
−0.751403 + 0.659843i \(0.770623\pi\)
\(864\) 0.809017 + 0.587785i 0.0275233 + 0.0199969i
\(865\) −17.1792 3.65154i −0.584109 0.124156i
\(866\) 4.04684 12.4549i 0.137517 0.423234i
\(867\) −24.3247 −0.826111
\(868\) −17.0028 13.6186i −0.577111 0.462244i
\(869\) 42.4332 1.43945
\(870\) −0.0381813 + 0.117510i −0.00129447 + 0.00398397i
\(871\) −4.21731 0.896418i −0.142898 0.0303740i
\(872\) −3.83432 2.78579i −0.129846 0.0943389i
\(873\) 6.85410 + 11.8717i 0.231976 + 0.401795i
\(874\) 3.78339 6.55302i 0.127975 0.221659i
\(875\) −3.57433 + 1.59139i −0.120834 + 0.0537989i
\(876\) −12.5231 + 9.09854i −0.423115 + 0.307411i
\(877\) −46.7038 20.7939i −1.57708 0.702160i −0.583166 0.812353i \(-0.698186\pi\)
−0.993910 + 0.110193i \(0.964853\pi\)
\(878\) −0.0778405 + 0.0165455i −0.00262699 + 0.000558384i
\(879\) −0.109750 + 1.04420i −0.00370178 + 0.0352201i
\(880\) −4.37595 4.85999i −0.147513 0.163830i
\(881\) 15.3111 17.0047i 0.515845 0.572904i −0.427796 0.903875i \(-0.640710\pi\)
0.943641 + 0.330972i \(0.107376\pi\)
\(882\) −0.868460 8.26285i −0.0292426 0.278225i
\(883\) −6.28848 19.3540i −0.211624 0.651312i −0.999376 0.0353197i \(-0.988755\pi\)
0.787752 0.615993i \(-0.211245\pi\)
\(884\) 0.714394 + 2.19868i 0.0240277 + 0.0739496i
\(885\) 0.519619 + 4.94385i 0.0174668 + 0.166186i
\(886\) 2.56835 2.85244i 0.0862855 0.0958297i
\(887\) 7.21397 + 8.01192i 0.242221 + 0.269014i 0.851981 0.523572i \(-0.175401\pi\)
−0.609760 + 0.792586i \(0.708734\pi\)
\(888\) −0.0303013 + 0.288298i −0.00101685 + 0.00967465i
\(889\) −24.1582 + 5.13499i −0.810242 + 0.172222i
\(890\) −5.73403 2.55296i −0.192205 0.0855753i
\(891\) −5.29078 + 3.84398i −0.177248 + 0.128778i
\(892\) −23.3920 + 10.4148i −0.783221 + 0.348712i
\(893\) 6.14748 10.6477i 0.205718 0.356313i
\(894\) 8.75414 + 15.1626i 0.292782 + 0.507114i
\(895\) −18.0982 13.1491i −0.604956 0.439526i
\(896\) −3.82709 0.813473i −0.127854 0.0271762i
\(897\) 0.148721 0.457718i 0.00496566 0.0152827i
\(898\) 35.7433 1.19277
\(899\) −0.483836 + 0.489042i −0.0161368 + 0.0163105i
\(900\) 1.00000 0.0333333
\(901\) −8.05329 + 24.7855i −0.268294 + 0.825724i
\(902\) −59.2709 12.5984i −1.97350 0.419481i
\(903\) −21.6041 15.6963i −0.718939 0.522340i
\(904\) 5.92376 + 10.2603i 0.197021 + 0.341251i
\(905\) −3.28444 + 5.68882i −0.109179 + 0.189103i
\(906\) −10.3121 + 4.59123i −0.342596 + 0.152534i
\(907\) 35.8956 26.0797i 1.19190 0.865963i 0.198432 0.980115i \(-0.436415\pi\)
0.993463 + 0.114152i \(0.0364151\pi\)
\(908\) −6.08550 2.70944i −0.201954 0.0899159i
\(909\) −8.44135 + 1.79426i −0.279982 + 0.0595120i
\(910\) 0.147079 1.39936i 0.00487561 0.0463883i
\(911\) −9.07283 10.0764i −0.300596 0.333846i 0.573857 0.818955i \(-0.305446\pi\)
−0.874453 + 0.485109i \(0.838780\pi\)
\(912\) −3.78339 + 4.20188i −0.125280 + 0.139138i
\(913\) −3.02018 28.7351i −0.0999535 0.950994i
\(914\) 3.53720 + 10.8864i 0.117000 + 0.360090i
\(915\) 3.42376 + 10.5373i 0.113186 + 0.348351i
\(916\) 1.66390 + 15.8309i 0.0549767 + 0.523068i
\(917\) 3.56455 3.95883i 0.117712 0.130732i
\(918\) −4.30146 4.77726i −0.141969 0.157673i
\(919\) 5.34183 50.8241i 0.176211 1.67653i −0.447043 0.894512i \(-0.647523\pi\)
0.623254 0.782020i \(-0.285810\pi\)
\(920\) −1.30902 + 0.278240i −0.0431570 + 0.00917331i
\(921\) −19.7129 8.77675i −0.649562 0.289204i
\(922\) 21.1526 15.3683i 0.696624 0.506127i
\(923\) 2.83585 1.26260i 0.0933433 0.0415591i
\(924\) 12.7937 22.1593i 0.420882 0.728989i
\(925\) 0.144943 + 0.251049i 0.00476570 + 0.00825443i
\(926\) −4.68375 3.40294i −0.153918 0.111828i
\(927\) −17.0119 3.61599i −0.558744 0.118765i
\(928\) −0.0381813 + 0.117510i −0.00125336 + 0.00385746i
\(929\) 50.2709 1.64934 0.824668 0.565618i \(-0.191362\pi\)
0.824668 + 0.565618i \(0.191362\pi\)
\(930\) 4.97437 + 2.50113i 0.163116 + 0.0820153i
\(931\) 46.9770 1.53961
\(932\) 4.22723 13.0101i 0.138468 0.426160i
\(933\) 6.51958 + 1.38578i 0.213441 + 0.0453684i
\(934\) −19.3529 14.0607i −0.633247 0.460081i
\(935\) 21.0202 + 36.4081i 0.687434 + 1.19067i
\(936\) −0.179813 + 0.311445i −0.00587736 + 0.0101799i
\(937\) 40.5578 18.0575i 1.32496 0.589912i 0.382419 0.923989i \(-0.375091\pi\)
0.942546 + 0.334077i \(0.108424\pi\)
\(938\) −37.9493 + 27.5717i −1.23909 + 0.900250i
\(939\) 20.6735 + 9.20444i 0.674654 + 0.300376i
\(940\) −2.12697 + 0.452102i −0.0693741 + 0.0147459i
\(941\) −1.40288 + 13.3475i −0.0457327 + 0.435118i 0.947568 + 0.319556i \(0.103534\pi\)
−0.993300 + 0.115562i \(0.963133\pi\)
\(942\) 4.72789 + 5.25085i 0.154043 + 0.171082i
\(943\) −8.29711 + 9.21488i −0.270191 + 0.300078i
\(944\) 0.519619 + 4.94385i 0.0169122 + 0.160909i
\(945\) 1.20906 + 3.72109i 0.0393306 + 0.121047i
\(946\) −13.7930 42.4505i −0.448449 1.38018i
\(947\) −4.79408 45.6126i −0.155787 1.48221i −0.741095 0.671400i \(-0.765693\pi\)
0.585309 0.810810i \(-0.300973\pi\)
\(948\) −4.34165 + 4.82189i −0.141010 + 0.156608i
\(949\) −3.72490 4.13692i −0.120915 0.134290i
\(950\) −0.591023 + 5.62321i −0.0191753 + 0.182441i
\(951\) 19.7013 4.18764i 0.638858 0.135794i
\(952\) 22.9773 + 10.2302i 0.744700 + 0.331562i
\(953\) −35.3665 + 25.6953i −1.14563 + 0.832352i −0.987894 0.155129i \(-0.950421\pi\)
−0.157740 + 0.987481i \(0.550421\pi\)
\(954\) −3.70353 + 1.64892i −0.119906 + 0.0533857i
\(955\) −5.34391 + 9.25592i −0.172925 + 0.299515i
\(956\) 11.4766 + 19.8781i 0.371180 + 0.642902i
\(957\) −0.653715 0.474952i −0.0211316 0.0153530i
\(958\) −7.98640 1.69756i −0.258029 0.0548457i
\(959\) −5.64544 + 17.3749i −0.182301 + 0.561064i
\(960\) 1.00000 0.0322749
\(961\) 18.4887 + 24.8831i 0.596410 + 0.802680i
\(962\) −0.104250 −0.00336117
\(963\) −1.83176 + 5.63758i −0.0590277 + 0.181669i
\(964\) 19.6324 + 4.17299i 0.632317 + 0.134403i
\(965\) −18.1829 13.2106i −0.585328 0.425266i
\(966\) −2.61803 4.53457i −0.0842339 0.145897i
\(967\) −28.2831 + 48.9878i −0.909524 + 1.57534i −0.0947982 + 0.995497i \(0.530221\pi\)
−0.814726 + 0.579846i \(0.803113\pi\)
\(968\) 29.0219 12.9214i 0.932801 0.415310i
\(969\) 29.4058 21.3645i 0.944649 0.686328i
\(970\) 12.5231 + 5.57563i 0.402091 + 0.179023i
\(971\) 15.1365 3.21737i 0.485754 0.103250i 0.0414768 0.999139i \(-0.486794\pi\)
0.444278 + 0.895889i \(0.353460\pi\)
\(972\) 0.104528 0.994522i 0.00335275 0.0318993i
\(973\) 11.2505 + 12.4950i 0.360675 + 0.400570i
\(974\) 4.20019 4.66479i 0.134583 0.149469i
\(975\) 0.0375911 + 0.357655i 0.00120388 + 0.0114541i
\(976\) 3.42376 + 10.5373i 0.109592 + 0.337289i
\(977\) 17.1651 + 52.8288i 0.549160 + 1.69014i 0.710887 + 0.703306i \(0.248294\pi\)
−0.161727 + 0.986836i \(0.551706\pi\)
\(978\) 0.430142 + 4.09252i 0.0137544 + 0.130864i
\(979\) 27.4665 30.5046i 0.877832 0.974932i
\(980\) −5.55938 6.17432i −0.177588 0.197231i
\(981\) −0.495410 + 4.71351i −0.0158172 + 0.150491i
\(982\) −12.1581 + 2.58429i −0.387981 + 0.0824679i
\(983\) 36.1515 + 16.0957i 1.15305 + 0.513372i 0.892037 0.451963i \(-0.149276\pi\)
0.261015 + 0.965335i \(0.415943\pi\)
\(984\) 7.49606 5.44620i 0.238966 0.173619i
\(985\) 18.0072 8.01733i 0.573758 0.255453i
\(986\) 0.397140 0.687867i 0.0126475 0.0219062i
\(987\) −4.25394 7.36804i −0.135404 0.234527i
\(988\) −1.64505 1.19520i −0.0523359 0.0380242i
\(989\) −8.93428 1.89904i −0.284094 0.0603859i
\(990\) −2.02090 + 6.21968i −0.0642283 + 0.197674i
\(991\) 15.9409 0.506378 0.253189 0.967417i \(-0.418521\pi\)
0.253189 + 0.967417i \(0.418521\pi\)
\(992\) 4.97437 + 2.50113i 0.157936 + 0.0794110i
\(993\) 10.3513 0.328490
\(994\) 10.4364 32.1199i 0.331022 1.01878i
\(995\) 0.946768 + 0.201242i 0.0300146 + 0.00637979i
\(996\) 3.57433 + 2.59690i 0.113257 + 0.0822860i
\(997\) 20.5797 + 35.6450i 0.651764 + 1.12889i 0.982695 + 0.185233i \(0.0593041\pi\)
−0.330930 + 0.943655i \(0.607363\pi\)
\(998\) 9.69598 16.7939i 0.306921 0.531602i
\(999\) 0.264824 0.117907i 0.00837866 0.00373042i
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 930.2.bg.a.691.1 8
31.7 even 15 inner 930.2.bg.a.751.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.a.691.1 8 1.1 even 1 trivial
930.2.bg.a.751.1 yes 8 31.7 even 15 inner