Properties

Label 552.2.b.c.413.1
Level $552$
Weight $2$
Character 552.413
Analytic conductor $4.408$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(413,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.413");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 413.1
Character \(\chi\) \(=\) 552.413
Dual form 552.2.b.c.413.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41196 - 0.0797643i) q^{2} +(-0.807372 - 1.53237i) q^{3} +(1.98728 + 0.225248i) q^{4} -2.83704i q^{5} +(1.01775 + 2.22805i) q^{6} +1.51036i q^{7} +(-2.78799 - 0.476556i) q^{8} +(-1.69630 + 2.47438i) q^{9} +O(q^{10})\) \(q+(-1.41196 - 0.0797643i) q^{2} +(-0.807372 - 1.53237i) q^{3} +(1.98728 + 0.225248i) q^{4} -2.83704i q^{5} +(1.01775 + 2.22805i) q^{6} +1.51036i q^{7} +(-2.78799 - 0.476556i) q^{8} +(-1.69630 + 2.47438i) q^{9} +(-0.226295 + 4.00580i) q^{10} +5.25468i q^{11} +(-1.25931 - 3.22710i) q^{12} +4.42296i q^{13} +(0.120473 - 2.13257i) q^{14} +(-4.34739 + 2.29055i) q^{15} +(3.89853 + 0.895261i) q^{16} -5.44908 q^{17} +(2.59248 - 3.35843i) q^{18} -0.278059 q^{19} +(0.639039 - 5.63799i) q^{20} +(2.31442 - 1.21942i) q^{21} +(0.419136 - 7.41941i) q^{22} +(2.74274 + 3.93413i) q^{23} +(1.52069 + 4.65699i) q^{24} -3.04882 q^{25} +(0.352794 - 6.24505i) q^{26} +(5.16121 + 0.601614i) q^{27} +(-0.340205 + 3.00149i) q^{28} +3.90617 q^{29} +(6.32106 - 2.88740i) q^{30} -0.0236931 q^{31} +(-5.43316 - 1.57504i) q^{32} +(8.05210 - 4.24248i) q^{33} +(7.69390 + 0.434642i) q^{34} +4.28495 q^{35} +(-3.92837 + 4.53519i) q^{36} -10.9457 q^{37} +(0.392609 + 0.0221792i) q^{38} +(6.77760 - 3.57097i) q^{39} +(-1.35201 + 7.90965i) q^{40} -7.21720i q^{41} +(-3.36514 + 1.53717i) q^{42} -7.36445 q^{43} +(-1.18361 + 10.4425i) q^{44} +(7.01993 + 4.81248i) q^{45} +(-3.55884 - 5.77362i) q^{46} +6.38523i q^{47} +(-1.77569 - 6.69678i) q^{48} +4.71882 q^{49} +(4.30481 + 0.243187i) q^{50} +(4.39943 + 8.35000i) q^{51} +(-0.996265 + 8.78964i) q^{52} +9.62419i q^{53} +(-7.23944 - 1.26114i) q^{54} +14.9077 q^{55} +(0.719769 - 4.21086i) q^{56} +(0.224497 + 0.426089i) q^{57} +(-5.51537 - 0.311573i) q^{58} +9.58456 q^{59} +(-9.15541 + 3.57271i) q^{60} -4.91803 q^{61} +(0.0334538 + 0.00188987i) q^{62} +(-3.73720 - 2.56202i) q^{63} +(7.54579 + 2.65727i) q^{64} +12.5481 q^{65} +(-11.7077 + 5.34795i) q^{66} +11.7718 q^{67} +(-10.8288 - 1.22740i) q^{68} +(3.81413 - 7.37919i) q^{69} +(-6.05018 - 0.341786i) q^{70} +5.13535i q^{71} +(5.90846 - 6.09017i) q^{72} -10.4463 q^{73} +(15.4549 + 0.873077i) q^{74} +(2.46153 + 4.67191i) q^{75} +(-0.552580 - 0.0626324i) q^{76} -7.93644 q^{77} +(-9.85456 + 4.50147i) q^{78} +13.3643i q^{79} +(2.53989 - 11.0603i) q^{80} +(-3.24512 - 8.39459i) q^{81} +(-0.575675 + 10.1904i) q^{82} -2.01019i q^{83} +(4.87407 - 1.90200i) q^{84} +15.4593i q^{85} +(10.3983 + 0.587420i) q^{86} +(-3.15373 - 5.98569i) q^{87} +(2.50415 - 14.6500i) q^{88} -13.9059 q^{89} +(-9.52801 - 7.35498i) q^{90} -6.68025 q^{91} +(4.56442 + 8.43600i) q^{92} +(0.0191292 + 0.0363066i) q^{93} +(0.509313 - 9.01570i) q^{94} +0.788866i q^{95} +(1.97304 + 9.59724i) q^{96} -10.1465i q^{97} +(-6.66280 - 0.376394i) q^{98} +(-13.0021 - 8.91352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41196 0.0797643i −0.998408 0.0564019i
\(3\) −0.807372 1.53237i −0.466136 0.884713i
\(4\) 1.98728 + 0.225248i 0.993638 + 0.112624i
\(5\) 2.83704i 1.26876i −0.773020 0.634382i \(-0.781255\pi\)
0.773020 0.634382i \(-0.218745\pi\)
\(6\) 1.01775 + 2.22805i 0.415495 + 0.909596i
\(7\) 1.51036i 0.570861i 0.958399 + 0.285431i \(0.0921366\pi\)
−0.958399 + 0.285431i \(0.907863\pi\)
\(8\) −2.78799 0.476556i −0.985704 0.168488i
\(9\) −1.69630 + 2.47438i −0.565434 + 0.824794i
\(10\) −0.226295 + 4.00580i −0.0715607 + 1.26674i
\(11\) 5.25468i 1.58434i 0.610297 + 0.792172i \(0.291050\pi\)
−0.610297 + 0.792172i \(0.708950\pi\)
\(12\) −1.25931 3.22710i −0.363530 0.931582i
\(13\) 4.42296i 1.22671i 0.789808 + 0.613354i \(0.210180\pi\)
−0.789808 + 0.613354i \(0.789820\pi\)
\(14\) 0.120473 2.13257i 0.0321976 0.569952i
\(15\) −4.34739 + 2.29055i −1.12249 + 0.591417i
\(16\) 3.89853 + 0.895261i 0.974632 + 0.223815i
\(17\) −5.44908 −1.32160 −0.660798 0.750564i \(-0.729782\pi\)
−0.660798 + 0.750564i \(0.729782\pi\)
\(18\) 2.59248 3.35843i 0.611054 0.791589i
\(19\) −0.278059 −0.0637912 −0.0318956 0.999491i \(-0.510154\pi\)
−0.0318956 + 0.999491i \(0.510154\pi\)
\(20\) 0.639039 5.63799i 0.142894 1.26069i
\(21\) 2.31442 1.21942i 0.505048 0.266099i
\(22\) 0.419136 7.41941i 0.0893600 1.58182i
\(23\) 2.74274 + 3.93413i 0.571900 + 0.820323i
\(24\) 1.52069 + 4.65699i 0.310409 + 0.950603i
\(25\) −3.04882 −0.609763
\(26\) 0.352794 6.24505i 0.0691887 1.22476i
\(27\) 5.16121 + 0.601614i 0.993275 + 0.115781i
\(28\) −0.340205 + 3.00149i −0.0642928 + 0.567229i
\(29\) 3.90617 0.725358 0.362679 0.931914i \(-0.381862\pi\)
0.362679 + 0.931914i \(0.381862\pi\)
\(30\) 6.32106 2.88740i 1.15406 0.527165i
\(31\) −0.0236931 −0.00425542 −0.00212771 0.999998i \(-0.500677\pi\)
−0.00212771 + 0.999998i \(0.500677\pi\)
\(32\) −5.43316 1.57504i −0.960457 0.278430i
\(33\) 8.05210 4.24248i 1.40169 0.738521i
\(34\) 7.69390 + 0.434642i 1.31949 + 0.0745405i
\(35\) 4.28495 0.724288
\(36\) −3.92837 + 4.53519i −0.654728 + 0.755864i
\(37\) −10.9457 −1.79946 −0.899732 0.436443i \(-0.856238\pi\)
−0.899732 + 0.436443i \(0.856238\pi\)
\(38\) 0.392609 + 0.0221792i 0.0636896 + 0.00359794i
\(39\) 6.77760 3.57097i 1.08528 0.571813i
\(40\) −1.35201 + 7.90965i −0.213771 + 1.25063i
\(41\) 7.21720i 1.12714i −0.826069 0.563569i \(-0.809428\pi\)
0.826069 0.563569i \(-0.190572\pi\)
\(42\) −3.36514 + 1.53717i −0.519253 + 0.237190i
\(43\) −7.36445 −1.12307 −0.561534 0.827454i \(-0.689789\pi\)
−0.561534 + 0.827454i \(0.689789\pi\)
\(44\) −1.18361 + 10.4425i −0.178436 + 1.57426i
\(45\) 7.01993 + 4.81248i 1.04647 + 0.717403i
\(46\) −3.55884 5.77362i −0.524722 0.851273i
\(47\) 6.38523i 0.931381i 0.884948 + 0.465691i \(0.154194\pi\)
−0.884948 + 0.465691i \(0.845806\pi\)
\(48\) −1.77569 6.69678i −0.256299 0.966598i
\(49\) 4.71882 0.674118
\(50\) 4.30481 + 0.243187i 0.608792 + 0.0343918i
\(51\) 4.39943 + 8.35000i 0.616044 + 1.16923i
\(52\) −0.996265 + 8.78964i −0.138157 + 1.21890i
\(53\) 9.62419i 1.32198i 0.750393 + 0.660992i \(0.229864\pi\)
−0.750393 + 0.660992i \(0.770136\pi\)
\(54\) −7.23944 1.26114i −0.985163 0.171619i
\(55\) 14.9077 2.01016
\(56\) 0.719769 4.21086i 0.0961832 0.562700i
\(57\) 0.224497 + 0.426089i 0.0297354 + 0.0564369i
\(58\) −5.51537 0.311573i −0.724203 0.0409115i
\(59\) 9.58456 1.24780 0.623902 0.781503i \(-0.285547\pi\)
0.623902 + 0.781503i \(0.285547\pi\)
\(60\) −9.15541 + 3.57271i −1.18196 + 0.461235i
\(61\) −4.91803 −0.629690 −0.314845 0.949143i \(-0.601952\pi\)
−0.314845 + 0.949143i \(0.601952\pi\)
\(62\) 0.0334538 + 0.00188987i 0.00424864 + 0.000240013i
\(63\) −3.73720 2.56202i −0.470843 0.322784i
\(64\) 7.54579 + 2.65727i 0.943224 + 0.332158i
\(65\) 12.5481 1.55640
\(66\) −11.7077 + 5.34795i −1.44111 + 0.658287i
\(67\) 11.7718 1.43815 0.719074 0.694933i \(-0.244566\pi\)
0.719074 + 0.694933i \(0.244566\pi\)
\(68\) −10.8288 1.22740i −1.31319 0.148844i
\(69\) 3.81413 7.37919i 0.459167 0.888350i
\(70\) −6.05018 0.341786i −0.723135 0.0408512i
\(71\) 5.13535i 0.609454i 0.952440 + 0.304727i \(0.0985653\pi\)
−0.952440 + 0.304727i \(0.901435\pi\)
\(72\) 5.90846 6.09017i 0.696318 0.717733i
\(73\) −10.4463 −1.22265 −0.611325 0.791380i \(-0.709363\pi\)
−0.611325 + 0.791380i \(0.709363\pi\)
\(74\) 15.4549 + 0.873077i 1.79660 + 0.101493i
\(75\) 2.46153 + 4.67191i 0.284233 + 0.539465i
\(76\) −0.552580 0.0626324i −0.0633853 0.00718443i
\(77\) −7.93644 −0.904441
\(78\) −9.85456 + 4.50147i −1.11581 + 0.509691i
\(79\) 13.3643i 1.50360i 0.659392 + 0.751799i \(0.270814\pi\)
−0.659392 + 0.751799i \(0.729186\pi\)
\(80\) 2.53989 11.0603i 0.283969 1.23658i
\(81\) −3.24512 8.39459i −0.360569 0.932733i
\(82\) −0.575675 + 10.1904i −0.0635726 + 1.12534i
\(83\) 2.01019i 0.220647i −0.993896 0.110323i \(-0.964811\pi\)
0.993896 0.110323i \(-0.0351887\pi\)
\(84\) 4.87407 1.90200i 0.531804 0.207525i
\(85\) 15.4593i 1.67679i
\(86\) 10.3983 + 0.587420i 1.12128 + 0.0633431i
\(87\) −3.15373 5.98569i −0.338115 0.641733i
\(88\) 2.50415 14.6500i 0.266943 1.56169i
\(89\) −13.9059 −1.47402 −0.737012 0.675880i \(-0.763764\pi\)
−0.737012 + 0.675880i \(0.763764\pi\)
\(90\) −9.52801 7.35498i −1.00434 0.775283i
\(91\) −6.68025 −0.700280
\(92\) 4.56442 + 8.43600i 0.475874 + 0.879514i
\(93\) 0.0191292 + 0.0363066i 0.00198360 + 0.00376482i
\(94\) 0.509313 9.01570i 0.0525317 0.929899i
\(95\) 0.788866i 0.0809360i
\(96\) 1.97304 + 9.59724i 0.201373 + 0.979515i
\(97\) 10.1465i 1.03023i −0.857123 0.515113i \(-0.827750\pi\)
0.857123 0.515113i \(-0.172250\pi\)
\(98\) −6.66280 0.376394i −0.673044 0.0380215i
\(99\) −13.0021 8.91352i −1.30676 0.895842i
\(100\) −6.05884 0.686741i −0.605884 0.0686741i
\(101\) 7.70417 0.766594 0.383297 0.923625i \(-0.374789\pi\)
0.383297 + 0.923625i \(0.374789\pi\)
\(102\) −5.54580 12.1408i −0.549116 1.20212i
\(103\) 3.66936i 0.361553i −0.983524 0.180777i \(-0.942139\pi\)
0.983524 0.180777i \(-0.0578611\pi\)
\(104\) 2.10779 12.3312i 0.206686 1.20917i
\(105\) −3.45954 6.56611i −0.337617 0.640787i
\(106\) 0.767667 13.5890i 0.0745624 1.31988i
\(107\) 6.54109i 0.632352i −0.948701 0.316176i \(-0.897601\pi\)
0.948701 0.316176i \(-0.102399\pi\)
\(108\) 10.1212 + 2.35813i 0.973916 + 0.226911i
\(109\) 0.715038 0.0684882 0.0342441 0.999413i \(-0.489098\pi\)
0.0342441 + 0.999413i \(0.489098\pi\)
\(110\) −21.0492 1.18911i −2.00696 0.113377i
\(111\) 8.83725 + 16.7729i 0.838795 + 1.59201i
\(112\) −1.35216 + 5.88816i −0.127767 + 0.556379i
\(113\) −2.54869 −0.239760 −0.119880 0.992788i \(-0.538251\pi\)
−0.119880 + 0.992788i \(0.538251\pi\)
\(114\) −0.282995 0.619529i −0.0265049 0.0580242i
\(115\) 11.1613 7.78127i 1.04080 0.725607i
\(116\) 7.76264 + 0.879858i 0.720743 + 0.0816928i
\(117\) −10.9441 7.50268i −1.01178 0.693623i
\(118\) −13.5330 0.764506i −1.24582 0.0703785i
\(119\) 8.23005i 0.754448i
\(120\) 13.2121 4.31425i 1.20609 0.393836i
\(121\) −16.6116 −1.51015
\(122\) 6.94408 + 0.392283i 0.628687 + 0.0355157i
\(123\) −11.0594 + 5.82696i −0.997193 + 0.525399i
\(124\) −0.0470848 0.00533684i −0.00422834 0.000479263i
\(125\) 5.53560i 0.495119i
\(126\) 5.07242 + 3.91557i 0.451887 + 0.348827i
\(127\) −1.27108 −0.112790 −0.0563950 0.998409i \(-0.517961\pi\)
−0.0563950 + 0.998409i \(0.517961\pi\)
\(128\) −10.4424 4.35385i −0.922988 0.384829i
\(129\) 5.94585 + 11.2850i 0.523503 + 0.993593i
\(130\) −17.7175 1.00089i −1.55393 0.0877841i
\(131\) −10.9007 −0.952399 −0.476199 0.879337i \(-0.657986\pi\)
−0.476199 + 0.879337i \(0.657986\pi\)
\(132\) 16.9573 6.61725i 1.47595 0.575958i
\(133\) 0.419969i 0.0364159i
\(134\) −16.6213 0.938965i −1.43586 0.0811143i
\(135\) 1.70680 14.6426i 0.146898 1.26023i
\(136\) 15.1920 + 2.59679i 1.30270 + 0.222673i
\(137\) 9.56299 0.817021 0.408511 0.912754i \(-0.366048\pi\)
0.408511 + 0.912754i \(0.366048\pi\)
\(138\) −5.97400 + 10.1149i −0.508541 + 0.861038i
\(139\) 19.6353i 1.66545i 0.553690 + 0.832723i \(0.313219\pi\)
−0.553690 + 0.832723i \(0.686781\pi\)
\(140\) 8.51537 + 0.965177i 0.719680 + 0.0815724i
\(141\) 9.78452 5.15525i 0.824005 0.434151i
\(142\) 0.409618 7.25093i 0.0343744 0.608484i
\(143\) −23.2412 −1.94353
\(144\) −8.82829 + 8.12781i −0.735691 + 0.677317i
\(145\) 11.0820i 0.920308i
\(146\) 14.7498 + 0.833243i 1.22070 + 0.0689597i
\(147\) −3.80984 7.23097i −0.314231 0.596401i
\(148\) −21.7521 2.46550i −1.78801 0.202663i
\(149\) 13.2630i 1.08655i 0.839556 + 0.543274i \(0.182815\pi\)
−0.839556 + 0.543274i \(0.817185\pi\)
\(150\) −3.10293 6.79290i −0.253353 0.554638i
\(151\) 0.702221 0.0571460 0.0285730 0.999592i \(-0.490904\pi\)
0.0285730 + 0.999592i \(0.490904\pi\)
\(152\) 0.775227 + 0.132511i 0.0628792 + 0.0107480i
\(153\) 9.24329 13.4831i 0.747275 1.09004i
\(154\) 11.2059 + 0.633044i 0.903001 + 0.0510122i
\(155\) 0.0672185i 0.00539912i
\(156\) 14.2733 5.56986i 1.14278 0.445946i
\(157\) 7.53792 0.601592 0.300796 0.953689i \(-0.402748\pi\)
0.300796 + 0.953689i \(0.402748\pi\)
\(158\) 1.06599 18.8698i 0.0848057 1.50120i
\(159\) 14.7478 7.77030i 1.16958 0.616225i
\(160\) −4.46845 + 15.4141i −0.353262 + 1.21859i
\(161\) −5.94194 + 4.14251i −0.468291 + 0.326476i
\(162\) 3.91240 + 12.1117i 0.307387 + 0.951585i
\(163\) 4.73461i 0.370843i 0.982659 + 0.185421i \(0.0593650\pi\)
−0.982659 + 0.185421i \(0.940635\pi\)
\(164\) 1.62566 14.3426i 0.126943 1.11997i
\(165\) −12.0361 22.8442i −0.937009 1.77841i
\(166\) −0.160341 + 2.83831i −0.0124449 + 0.220296i
\(167\) 12.7163i 0.984019i 0.870590 + 0.492009i \(0.163737\pi\)
−0.870590 + 0.492009i \(0.836263\pi\)
\(168\) −7.03371 + 2.29678i −0.542662 + 0.177200i
\(169\) −6.56258 −0.504814
\(170\) 1.23310 21.8279i 0.0945743 1.67412i
\(171\) 0.471673 0.688025i 0.0360697 0.0526146i
\(172\) −14.6352 1.65883i −1.11592 0.126485i
\(173\) 5.13533 0.390432 0.195216 0.980760i \(-0.437459\pi\)
0.195216 + 0.980760i \(0.437459\pi\)
\(174\) 3.97551 + 8.70312i 0.301382 + 0.659782i
\(175\) 4.60480i 0.348090i
\(176\) −4.70431 + 20.4855i −0.354601 + 1.54415i
\(177\) −7.73830 14.6871i −0.581646 1.10395i
\(178\) 19.6346 + 1.10920i 1.47168 + 0.0831377i
\(179\) −16.0763 −1.20160 −0.600799 0.799400i \(-0.705151\pi\)
−0.600799 + 0.799400i \(0.705151\pi\)
\(180\) 12.8665 + 11.1450i 0.959014 + 0.830696i
\(181\) 17.9778 1.33628 0.668138 0.744037i \(-0.267091\pi\)
0.668138 + 0.744037i \(0.267091\pi\)
\(182\) 9.43226 + 0.532845i 0.699165 + 0.0394971i
\(183\) 3.97068 + 7.53623i 0.293521 + 0.557094i
\(184\) −5.77190 12.2754i −0.425510 0.904954i
\(185\) 31.0535i 2.28310i
\(186\) −0.0241137 0.0527894i −0.00176810 0.00387071i
\(187\) 28.6332i 2.09386i
\(188\) −1.43826 + 12.6892i −0.104896 + 0.925456i
\(189\) −0.908651 + 7.79526i −0.0660946 + 0.567022i
\(190\) 0.0629234 1.11385i 0.00456494 0.0808071i
\(191\) −17.2840 −1.25063 −0.625313 0.780374i \(-0.715029\pi\)
−0.625313 + 0.780374i \(0.715029\pi\)
\(192\) −2.02035 13.7083i −0.145806 0.989313i
\(193\) 6.00676 0.432376 0.216188 0.976352i \(-0.430638\pi\)
0.216188 + 0.976352i \(0.430638\pi\)
\(194\) −0.809332 + 14.3265i −0.0581066 + 1.02859i
\(195\) −10.1310 19.2284i −0.725496 1.37697i
\(196\) 9.37760 + 1.06291i 0.669829 + 0.0759219i
\(197\) −3.33454 −0.237576 −0.118788 0.992920i \(-0.537901\pi\)
−0.118788 + 0.992920i \(0.537901\pi\)
\(198\) 17.6475 + 13.6227i 1.25415 + 0.968120i
\(199\) 5.44215i 0.385784i 0.981220 + 0.192892i \(0.0617867\pi\)
−0.981220 + 0.192892i \(0.938213\pi\)
\(200\) 8.50007 + 1.45293i 0.601046 + 0.102738i
\(201\) −9.50418 18.0387i −0.670373 1.27235i
\(202\) −10.8780 0.614518i −0.765373 0.0432373i
\(203\) 5.89971i 0.414078i
\(204\) 6.86206 + 17.5847i 0.480440 + 1.23118i
\(205\) −20.4755 −1.43007
\(206\) −0.292684 + 5.18100i −0.0203923 + 0.360978i
\(207\) −14.3871 + 0.113103i −0.999969 + 0.00786119i
\(208\) −3.95970 + 17.2430i −0.274556 + 1.19559i
\(209\) 1.46111i 0.101067i
\(210\) 4.36101 + 9.54706i 0.300938 + 0.658809i
\(211\) 6.98441i 0.480826i −0.970671 0.240413i \(-0.922717\pi\)
0.970671 0.240413i \(-0.0772829\pi\)
\(212\) −2.16783 + 19.1259i −0.148887 + 1.31357i
\(213\) 7.86925 4.14614i 0.539192 0.284089i
\(214\) −0.521746 + 9.23578i −0.0356658 + 0.631345i
\(215\) 20.8933i 1.42491i
\(216\) −14.1027 4.13690i −0.959567 0.281480i
\(217\) 0.0357851i 0.00242925i
\(218\) −1.00961 0.0570345i −0.0683792 0.00386286i
\(219\) 8.43406 + 16.0076i 0.569921 + 1.08169i
\(220\) 29.6258 + 3.35795i 1.99737 + 0.226393i
\(221\) 24.1011i 1.62121i
\(222\) −11.1400 24.3875i −0.747668 1.63678i
\(223\) 3.51479 0.235368 0.117684 0.993051i \(-0.462453\pi\)
0.117684 + 0.993051i \(0.462453\pi\)
\(224\) 2.37887 8.20601i 0.158945 0.548287i
\(225\) 5.17171 7.54393i 0.344781 0.502929i
\(226\) 3.59865 + 0.203294i 0.239379 + 0.0135229i
\(227\) 3.95674i 0.262618i −0.991341 0.131309i \(-0.958082\pi\)
0.991341 0.131309i \(-0.0419180\pi\)
\(228\) 0.350162 + 0.897324i 0.0231900 + 0.0594267i
\(229\) 14.4693 0.956161 0.478081 0.878316i \(-0.341333\pi\)
0.478081 + 0.878316i \(0.341333\pi\)
\(230\) −16.3800 + 10.0966i −1.08007 + 0.665749i
\(231\) 6.40765 + 12.1615i 0.421593 + 0.800171i
\(232\) −10.8904 1.86151i −0.714988 0.122214i
\(233\) 6.38619i 0.418373i −0.977876 0.209186i \(-0.932918\pi\)
0.977876 0.209186i \(-0.0670816\pi\)
\(234\) 14.8542 + 11.4664i 0.971049 + 0.749585i
\(235\) 18.1152 1.18170
\(236\) 19.0472 + 2.15891i 1.23986 + 0.140533i
\(237\) 20.4790 10.7899i 1.33025 0.700882i
\(238\) −0.656465 + 11.6205i −0.0425523 + 0.753247i
\(239\) 3.65421i 0.236371i 0.992992 + 0.118185i \(0.0377077\pi\)
−0.992992 + 0.118185i \(0.962292\pi\)
\(240\) −18.9991 + 5.03771i −1.22638 + 0.325183i
\(241\) 14.5478i 0.937107i 0.883435 + 0.468553i \(0.155225\pi\)
−0.883435 + 0.468553i \(0.844775\pi\)
\(242\) 23.4550 + 1.32502i 1.50774 + 0.0851752i
\(243\) −10.2436 + 11.7503i −0.657126 + 0.753780i
\(244\) −9.77348 1.10778i −0.625683 0.0709183i
\(245\) 13.3875i 0.855296i
\(246\) 16.0802 7.34531i 1.02524 0.468320i
\(247\) 1.22985i 0.0782532i
\(248\) 0.0660563 + 0.0112911i 0.00419458 + 0.000716986i
\(249\) −3.08035 + 1.62297i −0.195209 + 0.102851i
\(250\) −0.441543 + 7.81605i −0.0279256 + 0.494331i
\(251\) 5.58993i 0.352833i 0.984316 + 0.176417i \(0.0564506\pi\)
−0.984316 + 0.176417i \(0.943549\pi\)
\(252\) −6.84975 5.93324i −0.431494 0.373759i
\(253\) −20.6726 + 14.4122i −1.29967 + 0.906087i
\(254\) 1.79471 + 0.101387i 0.112610 + 0.00636156i
\(255\) 23.6893 12.4814i 1.48348 0.781615i
\(256\) 14.3970 + 6.98040i 0.899813 + 0.436275i
\(257\) 3.98354i 0.248486i −0.992252 0.124243i \(-0.960350\pi\)
0.992252 0.124243i \(-0.0396503\pi\)
\(258\) −7.49517 16.4083i −0.466629 1.02154i
\(259\) 16.5319i 1.02724i
\(260\) 24.9366 + 2.82645i 1.54650 + 0.175289i
\(261\) −6.62604 + 9.66535i −0.410142 + 0.598270i
\(262\) 15.3914 + 0.869487i 0.950883 + 0.0537171i
\(263\) 8.31685 0.512839 0.256419 0.966566i \(-0.417457\pi\)
0.256419 + 0.966566i \(0.417457\pi\)
\(264\) −24.4710 + 7.99072i −1.50608 + 0.491795i
\(265\) 27.3042 1.67729
\(266\) −0.0334985 + 0.592980i −0.00205393 + 0.0363579i
\(267\) 11.2272 + 21.3090i 0.687096 + 1.30409i
\(268\) 23.3937 + 2.65157i 1.42900 + 0.161970i
\(269\) 6.72690 0.410146 0.205073 0.978747i \(-0.434257\pi\)
0.205073 + 0.978747i \(0.434257\pi\)
\(270\) −3.57790 + 20.5386i −0.217744 + 1.24994i
\(271\) −11.4000 −0.692500 −0.346250 0.938142i \(-0.612545\pi\)
−0.346250 + 0.938142i \(0.612545\pi\)
\(272\) −21.2434 4.87835i −1.28807 0.295793i
\(273\) 5.39344 + 10.2366i 0.326426 + 0.619547i
\(274\) −13.5026 0.762785i −0.815721 0.0460815i
\(275\) 16.0205i 0.966075i
\(276\) 9.24187 13.8054i 0.556295 0.830985i
\(277\) 24.3492i 1.46300i 0.681842 + 0.731500i \(0.261179\pi\)
−0.681842 + 0.731500i \(0.738821\pi\)
\(278\) 1.56620 27.7243i 0.0939343 1.66279i
\(279\) 0.0401907 0.0586259i 0.00240616 0.00350984i
\(280\) −11.9464 2.04202i −0.713934 0.122034i
\(281\) 3.27622 0.195443 0.0977215 0.995214i \(-0.468845\pi\)
0.0977215 + 0.995214i \(0.468845\pi\)
\(282\) −14.2266 + 6.49857i −0.847180 + 0.386984i
\(283\) −20.5517 −1.22167 −0.610836 0.791757i \(-0.709167\pi\)
−0.610836 + 0.791757i \(0.709167\pi\)
\(284\) −1.15673 + 10.2054i −0.0686393 + 0.605577i
\(285\) 1.20883 0.636908i 0.0716051 0.0377272i
\(286\) 32.8157 + 1.85382i 1.94044 + 0.109619i
\(287\) 10.9005 0.643439
\(288\) 13.1135 10.7720i 0.772722 0.634745i
\(289\) 12.6925 0.746616
\(290\) −0.883946 + 15.6473i −0.0519071 + 0.918843i
\(291\) −15.5482 + 8.19203i −0.911453 + 0.480225i
\(292\) −20.7597 2.35302i −1.21487 0.137700i
\(293\) 2.96154i 0.173015i 0.996251 + 0.0865076i \(0.0275707\pi\)
−0.996251 + 0.0865076i \(0.972429\pi\)
\(294\) 4.80258 + 10.5138i 0.280092 + 0.613174i
\(295\) 27.1918i 1.58317i
\(296\) 30.5165 + 5.21624i 1.77374 + 0.303188i
\(297\) −3.16129 + 27.1205i −0.183436 + 1.57369i
\(298\) 1.05791 18.7269i 0.0612833 1.08482i
\(299\) −17.4005 + 12.1310i −1.00630 + 0.701555i
\(300\) 3.83939 + 9.83882i 0.221667 + 0.568045i
\(301\) 11.1229i 0.641116i
\(302\) −0.991510 0.0560122i −0.0570550 0.00322314i
\(303\) −6.22013 11.8056i −0.357337 0.678215i
\(304\) −1.08402 0.248936i −0.0621729 0.0142774i
\(305\) 13.9527i 0.798928i
\(306\) −14.1266 + 18.3003i −0.807566 + 1.04616i
\(307\) 16.2366i 0.926672i −0.886183 0.463336i \(-0.846652\pi\)
0.886183 0.463336i \(-0.153348\pi\)
\(308\) −15.7719 1.78767i −0.898687 0.101862i
\(309\) −5.62282 + 2.96254i −0.319871 + 0.168533i
\(310\) 0.00536164 0.0949100i 0.000304520 0.00539052i
\(311\) 5.86765i 0.332724i 0.986065 + 0.166362i \(0.0532020\pi\)
−0.986065 + 0.166362i \(0.946798\pi\)
\(312\) −20.5977 + 6.72594i −1.16611 + 0.380781i
\(313\) 11.2752i 0.637313i −0.947870 0.318656i \(-0.896768\pi\)
0.947870 0.318656i \(-0.103232\pi\)
\(314\) −10.6433 0.601257i −0.600634 0.0339309i
\(315\) −7.26856 + 10.6026i −0.409537 + 0.597388i
\(316\) −3.01028 + 26.5585i −0.169341 + 1.49403i
\(317\) −29.8569 −1.67693 −0.838466 0.544954i \(-0.816547\pi\)
−0.838466 + 0.544954i \(0.816547\pi\)
\(318\) −21.4431 + 9.79502i −1.20247 + 0.549277i
\(319\) 20.5257i 1.14922i
\(320\) 7.53878 21.4077i 0.421431 1.19673i
\(321\) −10.0234 + 5.28109i −0.559450 + 0.294762i
\(322\) 8.72022 5.37512i 0.485959 0.299544i
\(323\) 1.51517 0.0843062
\(324\) −4.55808 17.4133i −0.253226 0.967407i
\(325\) 13.4848i 0.748002i
\(326\) 0.377653 6.68509i 0.0209162 0.370253i
\(327\) −0.577301 1.09570i −0.0319248 0.0605924i
\(328\) −3.43940 + 20.1215i −0.189909 + 1.11102i
\(329\) −9.64397 −0.531689
\(330\) 15.1724 + 33.2151i 0.835211 + 1.82843i
\(331\) 29.3591i 1.61372i −0.590740 0.806862i \(-0.701164\pi\)
0.590740 0.806862i \(-0.298836\pi\)
\(332\) 0.452792 3.99480i 0.0248502 0.219243i
\(333\) 18.5672 27.0838i 1.01748 1.48419i
\(334\) 1.01431 17.9550i 0.0555005 0.982452i
\(335\) 33.3970i 1.82467i
\(336\) 10.1145 2.68193i 0.551793 0.146311i
\(337\) 35.2740i 1.92150i 0.277417 + 0.960750i \(0.410522\pi\)
−0.277417 + 0.960750i \(0.589478\pi\)
\(338\) 9.26612 + 0.523460i 0.504010 + 0.0284724i
\(339\) 2.05774 + 3.90553i 0.111761 + 0.212119i
\(340\) −3.48218 + 30.7218i −0.188848 + 1.66613i
\(341\) 0.124500i 0.00674205i
\(342\) −0.720864 + 0.933842i −0.0389798 + 0.0504964i
\(343\) 17.6996i 0.955689i
\(344\) 20.5320 + 3.50957i 1.10701 + 0.189223i
\(345\) −20.9351 10.8208i −1.12711 0.582575i
\(346\) −7.25090 0.409616i −0.389811 0.0220211i
\(347\) 13.5906 0.729581 0.364790 0.931090i \(-0.381141\pi\)
0.364790 + 0.931090i \(0.381141\pi\)
\(348\) −4.91907 12.6056i −0.263690 0.675730i
\(349\) 22.5138i 1.20514i −0.798067 0.602568i \(-0.794144\pi\)
0.798067 0.602568i \(-0.205856\pi\)
\(350\) −0.367299 + 6.50180i −0.0196329 + 0.347536i
\(351\) −2.66091 + 22.8278i −0.142029 + 1.21846i
\(352\) 8.27632 28.5495i 0.441129 1.52169i
\(353\) 12.0054i 0.638984i −0.947589 0.319492i \(-0.896488\pi\)
0.947589 0.319492i \(-0.103512\pi\)
\(354\) 9.75469 + 21.3548i 0.518456 + 1.13500i
\(355\) 14.5692 0.773254
\(356\) −27.6349 3.13228i −1.46465 0.166011i
\(357\) −12.6115 + 6.64471i −0.667470 + 0.351675i
\(358\) 22.6991 + 1.28231i 1.19969 + 0.0677724i
\(359\) −12.3407 −0.651317 −0.325658 0.945488i \(-0.605586\pi\)
−0.325658 + 0.945488i \(0.605586\pi\)
\(360\) −17.2781 16.7625i −0.910634 0.883464i
\(361\) −18.9227 −0.995931
\(362\) −25.3839 1.43398i −1.33415 0.0753685i
\(363\) 13.4118 + 25.4551i 0.703935 + 1.33605i
\(364\) −13.2755 1.50471i −0.695825 0.0788685i
\(365\) 29.6367i 1.55125i
\(366\) −5.00533 10.9576i −0.261633 0.572763i
\(367\) 10.4677i 0.546408i −0.961956 0.273204i \(-0.911917\pi\)
0.961956 0.273204i \(-0.0880834\pi\)
\(368\) 7.17056 + 17.7928i 0.373791 + 0.927513i
\(369\) 17.8581 + 12.2425i 0.929655 + 0.637322i
\(370\) 2.47696 43.8463i 0.128771 2.27946i
\(371\) −14.5360 −0.754669
\(372\) 0.0298369 + 0.0764601i 0.00154697 + 0.00396427i
\(373\) −19.0982 −0.988867 −0.494433 0.869216i \(-0.664624\pi\)
−0.494433 + 0.869216i \(0.664624\pi\)
\(374\) −2.28390 + 40.4289i −0.118098 + 2.09053i
\(375\) −8.48257 + 4.46928i −0.438038 + 0.230793i
\(376\) 3.04292 17.8020i 0.156927 0.918066i
\(377\) 17.2768i 0.889802i
\(378\) 1.90476 10.9341i 0.0979705 0.562391i
\(379\) 27.6320 1.41936 0.709680 0.704524i \(-0.248839\pi\)
0.709680 + 0.704524i \(0.248839\pi\)
\(380\) −0.177691 + 1.56769i −0.00911535 + 0.0804210i
\(381\) 1.02623 + 1.94776i 0.0525755 + 0.0997867i
\(382\) 24.4044 + 1.37865i 1.24864 + 0.0705377i
\(383\) 24.5172 1.25277 0.626384 0.779514i \(-0.284534\pi\)
0.626384 + 0.779514i \(0.284534\pi\)
\(384\) 1.75922 + 19.5168i 0.0897747 + 0.995962i
\(385\) 22.5160i 1.14752i
\(386\) −8.48132 0.479125i −0.431688 0.0243868i
\(387\) 12.4923 18.2224i 0.635021 0.926299i
\(388\) 2.28549 20.1640i 0.116028 1.02367i
\(389\) 17.6113i 0.892929i −0.894801 0.446465i \(-0.852683\pi\)
0.894801 0.446465i \(-0.147317\pi\)
\(390\) 12.7709 + 27.9578i 0.646678 + 1.41570i
\(391\) −14.9454 21.4374i −0.755821 1.08414i
\(392\) −13.1560 2.24878i −0.664480 0.113581i
\(393\) 8.80092 + 16.7039i 0.443948 + 0.842600i
\(394\) 4.70824 + 0.265977i 0.237198 + 0.0133997i
\(395\) 37.9150 1.90771
\(396\) −23.8309 20.6423i −1.19755 1.03732i
\(397\) 26.0926i 1.30955i −0.755825 0.654774i \(-0.772764\pi\)
0.755825 0.654774i \(-0.227236\pi\)
\(398\) 0.434090 7.68412i 0.0217589 0.385170i
\(399\) −0.643547 + 0.339071i −0.0322176 + 0.0169748i
\(400\) −11.8859 2.72949i −0.594294 0.136474i
\(401\) −5.82998 −0.291135 −0.145568 0.989348i \(-0.546501\pi\)
−0.145568 + 0.989348i \(0.546501\pi\)
\(402\) 11.9807 + 26.2280i 0.597543 + 1.30813i
\(403\) 0.104794i 0.00522015i
\(404\) 15.3103 + 1.73535i 0.761716 + 0.0863370i
\(405\) −23.8158 + 9.20654i −1.18342 + 0.457477i
\(406\) 0.470586 8.33017i 0.0233548 0.413419i
\(407\) 57.5162i 2.85097i
\(408\) −8.28634 25.3763i −0.410235 1.25631i
\(409\) 33.6916 1.66594 0.832971 0.553317i \(-0.186638\pi\)
0.832971 + 0.553317i \(0.186638\pi\)
\(410\) 28.9106 + 1.63321i 1.42779 + 0.0806587i
\(411\) −7.72089 14.6540i −0.380843 0.722829i
\(412\) 0.826518 7.29204i 0.0407196 0.359253i
\(413\) 14.4761i 0.712323i
\(414\) 20.3230 + 0.987876i 0.998821 + 0.0485515i
\(415\) −5.70299 −0.279949
\(416\) 6.96633 24.0307i 0.341552 1.17820i
\(417\) 30.0885 15.8530i 1.47344 0.776325i
\(418\) −0.116545 + 2.06304i −0.00570038 + 0.100906i
\(419\) 17.4910i 0.854490i −0.904136 0.427245i \(-0.859484\pi\)
0.904136 0.427245i \(-0.140516\pi\)
\(420\) −5.39606 13.8279i −0.263301 0.674734i
\(421\) 18.6829 0.910550 0.455275 0.890351i \(-0.349541\pi\)
0.455275 + 0.890351i \(0.349541\pi\)
\(422\) −0.557106 + 9.86172i −0.0271195 + 0.480061i
\(423\) −15.7995 10.8313i −0.768197 0.526635i
\(424\) 4.58646 26.8322i 0.222738 1.30308i
\(425\) 16.6132 0.805861
\(426\) −11.4418 + 5.22651i −0.554357 + 0.253225i
\(427\) 7.42798i 0.359465i
\(428\) 1.47337 12.9990i 0.0712181 0.628328i
\(429\) 18.7643 + 35.6141i 0.905950 + 1.71947i
\(430\) 1.66654 29.5005i 0.0803675 1.42264i
\(431\) 3.99271 0.192322 0.0961610 0.995366i \(-0.469344\pi\)
0.0961610 + 0.995366i \(0.469344\pi\)
\(432\) 19.5825 + 6.96603i 0.942164 + 0.335153i
\(433\) 20.4619i 0.983336i 0.870783 + 0.491668i \(0.163613\pi\)
−0.870783 + 0.491668i \(0.836387\pi\)
\(434\) −0.00285437 + 0.0505272i −0.000137014 + 0.00242538i
\(435\) −16.9817 + 8.94727i −0.814208 + 0.428989i
\(436\) 1.42098 + 0.161061i 0.0680525 + 0.00771343i
\(437\) −0.762644 1.09392i −0.0364822 0.0523294i
\(438\) −10.6317 23.2749i −0.508004 1.11212i
\(439\) 13.4074 0.639900 0.319950 0.947434i \(-0.396334\pi\)
0.319950 + 0.947434i \(0.396334\pi\)
\(440\) −41.5627 7.10437i −1.98142 0.338688i
\(441\) −8.00455 + 11.6762i −0.381169 + 0.556008i
\(442\) −1.92240 + 34.0298i −0.0914395 + 1.61863i
\(443\) 35.7620 1.69910 0.849552 0.527505i \(-0.176873\pi\)
0.849552 + 0.527505i \(0.176873\pi\)
\(444\) 13.7840 + 35.3229i 0.654160 + 1.67635i
\(445\) 39.4517i 1.87019i
\(446\) −4.96275 0.280355i −0.234993 0.0132752i
\(447\) 20.3238 10.7082i 0.961283 0.506479i
\(448\) −4.01342 + 11.3968i −0.189616 + 0.538450i
\(449\) 12.9815i 0.612636i 0.951929 + 0.306318i \(0.0990971\pi\)
−0.951929 + 0.306318i \(0.900903\pi\)
\(450\) −7.90400 + 10.2392i −0.372598 + 0.482682i
\(451\) 37.9241 1.78577
\(452\) −5.06494 0.574088i −0.238235 0.0270028i
\(453\) −0.566954 1.07606i −0.0266378 0.0505578i
\(454\) −0.315607 + 5.58677i −0.0148122 + 0.262200i
\(455\) 18.9522i 0.888491i
\(456\) −0.422841 1.29492i −0.0198013 0.0606401i
\(457\) 23.2473i 1.08746i −0.839259 0.543732i \(-0.817011\pi\)
0.839259 0.543732i \(-0.182989\pi\)
\(458\) −20.4302 1.15414i −0.954639 0.0539293i
\(459\) −28.1238 3.27824i −1.31271 0.153015i
\(460\) 23.9333 12.9495i 1.11590 0.603771i
\(461\) −26.5945 −1.23863 −0.619314 0.785143i \(-0.712589\pi\)
−0.619314 + 0.785143i \(0.712589\pi\)
\(462\) −8.07731 17.6827i −0.375790 0.822675i
\(463\) −22.2831 −1.03558 −0.517791 0.855507i \(-0.673246\pi\)
−0.517791 + 0.855507i \(0.673246\pi\)
\(464\) 15.2283 + 3.49704i 0.706956 + 0.162346i
\(465\) 0.103003 0.0542703i 0.00477667 0.00251673i
\(466\) −0.509390 + 9.01705i −0.0235970 + 0.417707i
\(467\) 9.03811i 0.418234i −0.977891 0.209117i \(-0.932941\pi\)
0.977891 0.209117i \(-0.0670589\pi\)
\(468\) −20.0590 17.3750i −0.927225 0.803161i
\(469\) 17.7795i 0.820983i
\(470\) −25.5779 1.44494i −1.17982 0.0666503i
\(471\) −6.08590 11.5509i −0.280424 0.532236i
\(472\) −26.7217 4.56758i −1.22996 0.210240i
\(473\) 38.6978i 1.77933i
\(474\) −29.7762 + 13.6015i −1.36767 + 0.624737i
\(475\) 0.847752 0.0388975
\(476\) 1.85381 16.3554i 0.0849691 0.749648i
\(477\) −23.8139 16.3255i −1.09036 0.747495i
\(478\) 0.291475 5.15960i 0.0133318 0.235995i
\(479\) 9.04841 0.413432 0.206716 0.978401i \(-0.433722\pi\)
0.206716 + 0.978401i \(0.433722\pi\)
\(480\) 27.2278 5.59761i 1.24277 0.255495i
\(481\) 48.4124i 2.20742i
\(482\) 1.16040 20.5410i 0.0528546 0.935615i
\(483\) 11.1452 + 5.76069i 0.507124 + 0.262121i
\(484\) −33.0119 3.74174i −1.50054 0.170079i
\(485\) −28.7862 −1.30711
\(486\) 15.4008 15.7739i 0.698595 0.715517i
\(487\) −12.0729 −0.547076 −0.273538 0.961861i \(-0.588194\pi\)
−0.273538 + 0.961861i \(0.588194\pi\)
\(488\) 13.7114 + 2.34372i 0.620687 + 0.106095i
\(489\) 7.25516 3.82259i 0.328090 0.172863i
\(490\) −1.06785 + 18.9027i −0.0482403 + 0.853935i
\(491\) −1.06548 −0.0480844 −0.0240422 0.999711i \(-0.507654\pi\)
−0.0240422 + 0.999711i \(0.507654\pi\)
\(492\) −23.2906 + 9.08867i −1.05002 + 0.409749i
\(493\) −21.2850 −0.958630
\(494\) −0.0980978 + 1.73650i −0.00441363 + 0.0781286i
\(495\) −25.2880 + 36.8874i −1.13661 + 1.65797i
\(496\) −0.0923684 0.0212116i −0.00414746 0.000952427i
\(497\) −7.75622 −0.347914
\(498\) 4.47879 2.04587i 0.200699 0.0916776i
\(499\) 15.7374i 0.704501i 0.935906 + 0.352250i \(0.114583\pi\)
−0.935906 + 0.352250i \(0.885417\pi\)
\(500\) 1.24688 11.0008i 0.0557623 0.491969i
\(501\) 19.4861 10.2668i 0.870574 0.458687i
\(502\) 0.445877 7.89277i 0.0199004 0.352271i
\(503\) 0.610236 0.0272091 0.0136045 0.999907i \(-0.495669\pi\)
0.0136045 + 0.999907i \(0.495669\pi\)
\(504\) 9.19833 + 8.92387i 0.409726 + 0.397501i
\(505\) 21.8571i 0.972627i
\(506\) 30.3385 18.7006i 1.34871 0.831341i
\(507\) 5.29844 + 10.0563i 0.235312 + 0.446615i
\(508\) −2.52598 0.286308i −0.112072 0.0127029i
\(509\) 34.2520 1.51819 0.759095 0.650979i \(-0.225642\pi\)
0.759095 + 0.650979i \(0.225642\pi\)
\(510\) −34.4440 + 15.7337i −1.52520 + 0.696699i
\(511\) 15.7777i 0.697963i
\(512\) −19.7713 11.0044i −0.873774 0.486332i
\(513\) −1.43512 0.167284i −0.0633622 0.00738578i
\(514\) −0.317744 + 5.62461i −0.0140151 + 0.248091i
\(515\) −10.4101 −0.458726
\(516\) 9.27410 + 23.7658i 0.408269 + 1.04623i
\(517\) −33.5523 −1.47563
\(518\) −1.31866 + 23.3425i −0.0579385 + 1.02561i
\(519\) −4.14612 7.86922i −0.181995 0.345420i
\(520\) −34.9841 5.97989i −1.53415 0.262235i
\(521\) 12.3295 0.540165 0.270083 0.962837i \(-0.412949\pi\)
0.270083 + 0.962837i \(0.412949\pi\)
\(522\) 10.1267 13.1186i 0.443233 0.574185i
\(523\) −0.786343 −0.0343844 −0.0171922 0.999852i \(-0.505473\pi\)
−0.0171922 + 0.999852i \(0.505473\pi\)
\(524\) −21.6627 2.45537i −0.946339 0.107263i
\(525\) −7.05624 + 3.71778i −0.307960 + 0.162257i
\(526\) −11.7431 0.663387i −0.512022 0.0289251i
\(527\) 0.129106 0.00562394
\(528\) 35.1894 9.33068i 1.53142 0.406066i
\(529\) −7.95478 + 21.5806i −0.345860 + 0.938286i
\(530\) −38.5526 2.17790i −1.67462 0.0946021i
\(531\) −16.2583 + 23.7159i −0.705551 + 1.02918i
\(532\) 0.0945973 0.834593i 0.00410131 0.0361842i
\(533\) 31.9214 1.38267
\(534\) −14.1527 30.9830i −0.612449 1.34077i
\(535\) −18.5574 −0.802305
\(536\) −32.8195 5.60990i −1.41759 0.242311i
\(537\) 12.9795 + 24.6348i 0.560109 + 1.06307i
\(538\) −9.49813 0.536566i −0.409493 0.0231330i
\(539\) 24.7959i 1.06803i
\(540\) 6.69010 28.7144i 0.287896 1.23567i
\(541\) 14.9417i 0.642394i 0.947012 + 0.321197i \(0.104085\pi\)
−0.947012 + 0.321197i \(0.895915\pi\)
\(542\) 16.0964 + 0.909313i 0.691398 + 0.0390583i
\(543\) −14.5147 27.5485i −0.622887 1.18222i
\(544\) 29.6057 + 8.58251i 1.26934 + 0.367972i
\(545\) 2.02859i 0.0868954i
\(546\) −6.79882 14.8839i −0.290963 0.636972i
\(547\) 26.1652i 1.11874i 0.828917 + 0.559371i \(0.188957\pi\)
−0.828917 + 0.559371i \(0.811043\pi\)
\(548\) 19.0043 + 2.15405i 0.811823 + 0.0920164i
\(549\) 8.34247 12.1691i 0.356048 0.519364i
\(550\) −1.27787 + 22.6204i −0.0544884 + 0.964537i
\(551\) −1.08615 −0.0462714
\(552\) −14.1503 + 18.7555i −0.602279 + 0.798286i
\(553\) −20.1848 −0.858346
\(554\) 1.94219 34.3801i 0.0825159 1.46067i
\(555\) 47.5853 25.0717i 2.01988 1.06423i
\(556\) −4.42282 + 39.0208i −0.187569 + 1.65485i
\(557\) 31.3190i 1.32703i −0.748164 0.663513i \(-0.769065\pi\)
0.748164 0.663513i \(-0.230935\pi\)
\(558\) −0.0614241 + 0.0795717i −0.00260029 + 0.00336854i
\(559\) 32.5727i 1.37768i
\(560\) 16.7050 + 3.83615i 0.705914 + 0.162107i
\(561\) −43.8765 + 23.1176i −1.85247 + 0.976026i
\(562\) −4.62590 0.261325i −0.195132 0.0110233i
\(563\) 43.2187i 1.82145i 0.413014 + 0.910725i \(0.364476\pi\)
−0.413014 + 0.910725i \(0.635524\pi\)
\(564\) 20.6057 8.04096i 0.867658 0.338585i
\(565\) 7.23074i 0.304199i
\(566\) 29.0182 + 1.63929i 1.21973 + 0.0689046i
\(567\) 12.6788 4.90129i 0.532461 0.205835i
\(568\) 2.44728 14.3173i 0.102686 0.600741i
\(569\) 9.00515 0.377515 0.188758 0.982024i \(-0.439554\pi\)
0.188758 + 0.982024i \(0.439554\pi\)
\(570\) −1.75763 + 0.802869i −0.0736190 + 0.0336285i
\(571\) −39.7928 −1.66528 −0.832639 0.553816i \(-0.813171\pi\)
−0.832639 + 0.553816i \(0.813171\pi\)
\(572\) −46.1867 5.23505i −1.93116 0.218888i
\(573\) 13.9546 + 26.4855i 0.582963 + 1.10645i
\(574\) −15.3912 0.869474i −0.642414 0.0362912i
\(575\) −8.36210 11.9944i −0.348724 0.500203i
\(576\) −19.3750 + 14.1636i −0.807293 + 0.590151i
\(577\) 26.7652 1.11425 0.557126 0.830428i \(-0.311904\pi\)
0.557126 + 0.830428i \(0.311904\pi\)
\(578\) −17.9213 1.01241i −0.745428 0.0421106i
\(579\) −4.84969 9.20456i −0.201546 0.382529i
\(580\) 2.49620 22.0229i 0.103649 0.914453i
\(581\) 3.03610 0.125959
\(582\) 22.6069 10.3266i 0.937088 0.428053i
\(583\) −50.5720 −2.09448
\(584\) 29.1242 + 4.97825i 1.20517 + 0.206002i
\(585\) −21.2854 + 31.0489i −0.880044 + 1.28371i
\(586\) 0.236225 4.18159i 0.00975838 0.172740i
\(587\) −31.7614 −1.31094 −0.655468 0.755223i \(-0.727528\pi\)
−0.655468 + 0.755223i \(0.727528\pi\)
\(588\) −5.94244 15.2281i −0.245062 0.627996i
\(589\) 0.00658810 0.000271458
\(590\) −2.16894 + 38.3938i −0.0892937 + 1.58065i
\(591\) 2.69221 + 5.10974i 0.110743 + 0.210187i
\(592\) −42.6721 9.79927i −1.75381 0.402747i
\(593\) 22.6400i 0.929712i −0.885386 0.464856i \(-0.846106\pi\)
0.885386 0.464856i \(-0.153894\pi\)
\(594\) 6.62686 38.0409i 0.271903 1.56084i
\(595\) −23.3490 −0.957217
\(596\) −2.98747 + 26.3572i −0.122372 + 1.07963i
\(597\) 8.33938 4.39384i 0.341308 0.179828i
\(598\) 25.5365 15.7406i 1.04426 0.643681i
\(599\) 14.8241i 0.605697i −0.953039 0.302848i \(-0.902062\pi\)
0.953039 0.302848i \(-0.0979376\pi\)
\(600\) −4.63629 14.1983i −0.189276 0.579643i
\(601\) 4.48110 0.182788 0.0913939 0.995815i \(-0.470868\pi\)
0.0913939 + 0.995815i \(0.470868\pi\)
\(602\) −0.887214 + 15.7052i −0.0361601 + 0.640095i
\(603\) −19.9684 + 29.1278i −0.813178 + 1.18618i
\(604\) 1.39551 + 0.158174i 0.0567824 + 0.00643602i
\(605\) 47.1279i 1.91602i
\(606\) 7.84092 + 17.1652i 0.318516 + 0.697290i
\(607\) 38.8731 1.57781 0.788905 0.614516i \(-0.210648\pi\)
0.788905 + 0.614516i \(0.210648\pi\)
\(608\) 1.51074 + 0.437954i 0.0612687 + 0.0177614i
\(609\) 9.04052 4.76326i 0.366341 0.193017i
\(610\) 1.11293 19.7006i 0.0450610 0.797656i
\(611\) −28.2416 −1.14253
\(612\) 21.4060 24.7126i 0.865286 0.998947i
\(613\) 47.3280 1.91156 0.955780 0.294084i \(-0.0950144\pi\)
0.955780 + 0.294084i \(0.0950144\pi\)
\(614\) −1.29510 + 22.9255i −0.0522661 + 0.925197i
\(615\) 16.5313 + 31.3760i 0.666608 + 1.26520i
\(616\) 22.1267 + 3.78216i 0.891511 + 0.152387i
\(617\) −18.2646 −0.735307 −0.367653 0.929963i \(-0.619839\pi\)
−0.367653 + 0.929963i \(0.619839\pi\)
\(618\) 8.17551 3.73450i 0.328867 0.150223i
\(619\) −5.94337 −0.238884 −0.119442 0.992841i \(-0.538111\pi\)
−0.119442 + 0.992841i \(0.538111\pi\)
\(620\) −0.0151409 + 0.133582i −0.000608071 + 0.00536477i
\(621\) 11.7890 + 21.9549i 0.473077 + 0.881021i
\(622\) 0.468029 8.28490i 0.0187663 0.332194i
\(623\) 21.0029i 0.841463i
\(624\) 29.6196 7.85381i 1.18573 0.314404i
\(625\) −30.9488 −1.23795
\(626\) −0.899359 + 15.9202i −0.0359456 + 0.636298i
\(627\) −2.23896 + 1.17966i −0.0894155 + 0.0471111i
\(628\) 14.9799 + 1.69790i 0.597764 + 0.0677538i
\(629\) 59.6440 2.37816
\(630\) 11.1086 14.3907i 0.442579 0.573339i
\(631\) 12.8561i 0.511794i −0.966704 0.255897i \(-0.917629\pi\)
0.966704 0.255897i \(-0.0823709\pi\)
\(632\) 6.36882 37.2595i 0.253338 1.48210i
\(633\) −10.7027 + 5.63901i −0.425393 + 0.224131i
\(634\) 42.1569 + 2.38152i 1.67426 + 0.0945821i
\(635\) 3.60610i 0.143104i
\(636\) 31.0582 12.1198i 1.23154 0.480581i
\(637\) 20.8712i 0.826946i
\(638\) 1.63722 28.9815i 0.0648180 1.14739i
\(639\) −12.7068 8.71111i −0.502674 0.344606i
\(640\) −12.3520 + 29.6256i −0.488258 + 1.17105i
\(641\) 37.2339 1.47065 0.735326 0.677714i \(-0.237029\pi\)
0.735326 + 0.677714i \(0.237029\pi\)
\(642\) 14.5739 6.65720i 0.575184 0.262739i
\(643\) −4.26786 −0.168308 −0.0841541 0.996453i \(-0.526819\pi\)
−0.0841541 + 0.996453i \(0.526819\pi\)
\(644\) −12.7414 + 6.89390i −0.502080 + 0.271658i
\(645\) 32.0162 16.8686i 1.26064 0.664202i
\(646\) −2.13936 0.120856i −0.0841720 0.00475503i
\(647\) 1.13278i 0.0445340i −0.999752 0.0222670i \(-0.992912\pi\)
0.999752 0.0222670i \(-0.00708839\pi\)
\(648\) 5.04687 + 24.9505i 0.198260 + 0.980150i
\(649\) 50.3638i 1.97695i
\(650\) −1.07560 + 19.0400i −0.0421887 + 0.746811i
\(651\) −0.0548359 + 0.0288919i −0.00214919 + 0.00113236i
\(652\) −1.06646 + 9.40897i −0.0417659 + 0.368484i
\(653\) 27.5832 1.07941 0.539707 0.841853i \(-0.318535\pi\)
0.539707 + 0.841853i \(0.318535\pi\)
\(654\) 0.727730 + 1.59314i 0.0284565 + 0.0622966i
\(655\) 30.9258i 1.20837i
\(656\) 6.46128 28.1364i 0.252270 1.09854i
\(657\) 17.7201 25.8482i 0.691327 1.00843i
\(658\) 13.6169 + 0.769245i 0.530843 + 0.0299883i
\(659\) 27.3110i 1.06388i −0.846781 0.531942i \(-0.821462\pi\)
0.846781 0.531942i \(-0.178538\pi\)
\(660\) −18.7734 48.1087i −0.730755 1.87263i
\(661\) −8.45225 −0.328754 −0.164377 0.986398i \(-0.552561\pi\)
−0.164377 + 0.986398i \(0.552561\pi\)
\(662\) −2.34181 + 41.4540i −0.0910171 + 1.61116i
\(663\) −36.9317 + 19.4585i −1.43431 + 0.755706i
\(664\) −0.957967 + 5.60439i −0.0371763 + 0.217492i
\(665\) −1.19147 −0.0462032
\(666\) −28.3765 + 36.7604i −1.09957 + 1.42444i
\(667\) 10.7136 + 15.3674i 0.414832 + 0.595028i
\(668\) −2.86433 + 25.2708i −0.110824 + 0.977758i
\(669\) −2.83774 5.38595i −0.109713 0.208233i
\(670\) −2.66389 + 47.1553i −0.102915 + 1.82177i
\(671\) 25.8427i 0.997645i
\(672\) −14.4953 + 2.98000i −0.559167 + 0.114956i
\(673\) 28.7225 1.10717 0.553585 0.832793i \(-0.313260\pi\)
0.553585 + 0.832793i \(0.313260\pi\)
\(674\) 2.81361 49.8056i 0.108376 1.91844i
\(675\) −15.7356 1.83421i −0.605662 0.0705987i
\(676\) −13.0417 1.47821i −0.501602 0.0568542i
\(677\) 7.23891i 0.278214i −0.990277 0.139107i \(-0.955577\pi\)
0.990277 0.139107i \(-0.0444232\pi\)
\(678\) −2.59393 5.67859i −0.0996191 0.218085i
\(679\) 15.3249 0.588115
\(680\) 7.36721 43.1003i 0.282520 1.65282i
\(681\) −6.06318 + 3.19456i −0.232342 + 0.122416i
\(682\) −0.00993064 + 0.175789i −0.000380264 + 0.00673131i
\(683\) 11.1797 0.427778 0.213889 0.976858i \(-0.431387\pi\)
0.213889 + 0.976858i \(0.431387\pi\)
\(684\) 1.09232 1.26105i 0.0417659 0.0482175i
\(685\) 27.1306i 1.03661i
\(686\) 1.41180 24.9912i 0.0539026 0.954167i
\(687\) −11.6821 22.1724i −0.445701 0.845928i
\(688\) −28.7105 6.59310i −1.09458 0.251360i
\(689\) −42.5674 −1.62169
\(690\) 28.6964 + 16.9485i 1.09245 + 0.645218i
\(691\) 9.57423i 0.364221i −0.983278 0.182110i \(-0.941707\pi\)
0.983278 0.182110i \(-0.0582928\pi\)
\(692\) 10.2053 + 1.15673i 0.387948 + 0.0439721i
\(693\) 13.4626 19.6378i 0.511402 0.745977i
\(694\) −19.1894 1.08404i −0.728419 0.0411497i
\(695\) 55.7062 2.11306
\(696\) 5.94006 + 18.1910i 0.225157 + 0.689527i
\(697\) 39.3271i 1.48962i
\(698\) −1.79580 + 31.7886i −0.0679719 + 1.20322i
\(699\) −9.78599 + 5.15603i −0.370140 + 0.195019i
\(700\) 1.03722 9.15100i 0.0392034 0.345875i
\(701\) 12.8330i 0.484697i −0.970189 0.242349i \(-0.922082\pi\)
0.970189 0.242349i \(-0.0779178\pi\)
\(702\) 5.57795 32.0198i 0.210526 1.20851i
\(703\) 3.04356 0.114790
\(704\) −13.9631 + 39.6507i −0.526253 + 1.49439i
\(705\) −14.6257 27.7591i −0.550835 1.04547i
\(706\) −0.957603 + 16.9512i −0.0360399 + 0.637966i
\(707\) 11.6360i 0.437618i
\(708\) −12.0699 30.9303i −0.453615 1.16243i
\(709\) −2.20392 −0.0827701 −0.0413850 0.999143i \(-0.513177\pi\)
−0.0413850 + 0.999143i \(0.513177\pi\)
\(710\) −20.5712 1.16210i −0.772023 0.0436130i
\(711\) −33.0683 22.6698i −1.24016 0.850185i
\(712\) 38.7696 + 6.62694i 1.45295 + 0.248355i
\(713\) −0.0649841 0.0932120i −0.00243367 0.00349082i
\(714\) 18.3369 8.37614i 0.686242 0.313469i
\(715\) 65.9364i 2.46588i
\(716\) −31.9480 3.62116i −1.19395 0.135329i
\(717\) 5.59959 2.95030i 0.209120 0.110181i
\(718\) 17.4246 + 0.984346i 0.650280 + 0.0367355i
\(719\) 45.9821i 1.71484i 0.514616 + 0.857421i \(0.327935\pi\)
−0.514616 + 0.857421i \(0.672065\pi\)
\(720\) 23.0589 + 25.0463i 0.859356 + 0.933419i
\(721\) 5.54205 0.206397
\(722\) 26.7181 + 1.50935i 0.994345 + 0.0561724i
\(723\) 22.2926 11.7455i 0.829071 0.436820i
\(724\) 35.7268 + 4.04946i 1.32778 + 0.150497i
\(725\) −11.9092 −0.442296
\(726\) −16.9065 37.0115i −0.627459 1.37362i
\(727\) 40.8296i 1.51428i 0.653250 + 0.757142i \(0.273405\pi\)
−0.653250 + 0.757142i \(0.726595\pi\)
\(728\) 18.6245 + 3.18351i 0.690269 + 0.117989i
\(729\) 26.2761 + 6.21011i 0.973190 + 0.230004i
\(730\) 2.36395 41.8459i 0.0874936 1.54878i
\(731\) 40.1295 1.48424
\(732\) 6.19331 + 15.8710i 0.228911 + 0.586608i
\(733\) 10.9115 0.403024 0.201512 0.979486i \(-0.435414\pi\)
0.201512 + 0.979486i \(0.435414\pi\)
\(734\) −0.834946 + 14.7800i −0.0308184 + 0.545538i
\(735\) −20.5146 + 10.8087i −0.756692 + 0.398685i
\(736\) −8.70533 25.6947i −0.320883 0.947119i
\(737\) 61.8568i 2.27852i
\(738\) −24.2384 18.7105i −0.892229 0.688741i
\(739\) 39.1912i 1.44167i −0.693105 0.720836i \(-0.743758\pi\)
0.693105 0.720836i \(-0.256242\pi\)
\(740\) −6.99474 + 61.7118i −0.257132 + 2.26857i
\(741\) −1.88458 + 0.992942i −0.0692316 + 0.0364766i
\(742\) 20.5242 + 1.15945i 0.753468 + 0.0425648i
\(743\) 53.5532 1.96468 0.982338 0.187113i \(-0.0599132\pi\)
0.982338 + 0.187113i \(0.0599132\pi\)
\(744\) −0.0360298 0.110339i −0.00132092 0.00404521i
\(745\) 37.6277 1.37857
\(746\) 26.9659 + 1.52335i 0.987293 + 0.0557739i
\(747\) 4.97397 + 3.40989i 0.181988 + 0.124761i
\(748\) 6.44957 56.9020i 0.235820 2.08054i
\(749\) 9.87939 0.360985
\(750\) 12.3336 5.63385i 0.450358 0.205719i
\(751\) 13.1585i 0.480161i −0.970753 0.240081i \(-0.922826\pi\)
0.970753 0.240081i \(-0.0771739\pi\)
\(752\) −5.71645 + 24.8930i −0.208457 + 0.907754i
\(753\) 8.56582 4.51315i 0.312156 0.164468i
\(754\) 1.37807 24.3942i 0.0501865 0.888386i
\(755\) 1.99223i 0.0725048i
\(756\) −3.56161 + 15.2867i −0.129535 + 0.555971i
\(757\) 16.8295 0.611680 0.305840 0.952083i \(-0.401063\pi\)
0.305840 + 0.952083i \(0.401063\pi\)
\(758\) −39.0153 2.20405i −1.41710 0.0800546i
\(759\) 38.7753 + 20.0420i 1.40745 + 0.727479i
\(760\) 0.375939 2.19935i 0.0136367 0.0797789i
\(761\) 49.7398i 1.80307i −0.432708 0.901534i \(-0.642442\pi\)
0.432708 0.901534i \(-0.357558\pi\)
\(762\) −1.29364 2.83202i −0.0468636 0.102593i
\(763\) 1.07996i 0.0390973i
\(764\) −34.3481 3.89319i −1.24267 0.140851i
\(765\) −38.2521 26.2236i −1.38301 0.948116i
\(766\) −34.6173 1.95559i −1.25077 0.0706585i
\(767\) 42.3921i 1.53069i
\(768\) −0.927206 27.6973i −0.0334577 0.999440i
\(769\) 13.3506i 0.481434i −0.970595 0.240717i \(-0.922617\pi\)
0.970595 0.240717i \(-0.0773825\pi\)
\(770\) 1.79597 31.7918i 0.0647224 1.14570i
\(771\) −6.10425 + 3.21620i −0.219839 + 0.115829i
\(772\) 11.9371 + 1.35301i 0.429625 + 0.0486960i
\(773\) 27.4662i 0.987890i 0.869493 + 0.493945i \(0.164446\pi\)
−0.869493 + 0.493945i \(0.835554\pi\)
\(774\) −19.0922 + 24.7330i −0.686255 + 0.889008i
\(775\) 0.0722360 0.00259480
\(776\) −4.83539 + 28.2885i −0.173580 + 1.01550i
\(777\) −25.3330 + 13.3474i −0.908816 + 0.478836i
\(778\) −1.40475 + 24.8665i −0.0503629 + 0.891508i
\(779\) 2.00681i 0.0719014i
\(780\) −15.8019 40.4940i −0.565800 1.44992i
\(781\) −26.9846 −0.965586
\(782\) 19.3924 + 31.4609i 0.693471 + 1.12504i
\(783\) 20.1606 + 2.35001i 0.720479 + 0.0839823i
\(784\) 18.3965 + 4.22458i 0.657016 + 0.150878i
\(785\) 21.3854i 0.763278i
\(786\) −11.0942 24.2873i −0.395717 0.866298i
\(787\) −41.9113 −1.49398 −0.746988 0.664837i \(-0.768501\pi\)
−0.746988 + 0.664837i \(0.768501\pi\)
\(788\) −6.62665 0.751100i −0.236065 0.0267568i
\(789\) −6.71479 12.7445i −0.239053 0.453715i
\(790\) −53.5346 3.02426i −1.90467 0.107599i
\(791\) 3.84943i 0.136870i
\(792\) 32.0019 + 31.0470i 1.13714 + 1.10321i
\(793\) 21.7523i 0.772446i
\(794\) −2.08125 + 36.8417i −0.0738610 + 1.30746i
\(795\) −22.0447 41.8401i −0.781844 1.48392i
\(796\) −1.22584 + 10.8151i −0.0434486 + 0.383330i
\(797\) 1.43260i 0.0507454i 0.999678 + 0.0253727i \(0.00807725\pi\)
−0.999678 + 0.0253727i \(0.991923\pi\)
\(798\) 0.935709 0.427423i 0.0331237 0.0151306i
\(799\) 34.7936i 1.23091i
\(800\) 16.5647 + 4.80200i 0.585651 + 0.169776i
\(801\) 23.5886 34.4085i 0.833463 1.21577i
\(802\) 8.23171 + 0.465024i 0.290672 + 0.0164206i
\(803\) 54.8920i 1.93710i
\(804\) −14.8242 37.9886i −0.522811 1.33975i
\(805\) 11.7525 + 16.8575i 0.414221 + 0.594150i
\(806\) −0.00835881 + 0.147965i −0.000294426 + 0.00521184i
\(807\) −5.43111 10.3081i −0.191184 0.362862i
\(808\) −21.4792 3.67147i −0.755634 0.129162i
\(809\) 41.7684i 1.46850i 0.678881 + 0.734248i \(0.262465\pi\)
−0.678881 + 0.734248i \(0.737535\pi\)
\(810\) 34.3614 11.0996i 1.20734 0.390002i
\(811\) 10.2543i 0.360078i 0.983659 + 0.180039i \(0.0576223\pi\)
−0.983659 + 0.180039i \(0.942378\pi\)
\(812\) −1.32890 + 11.7243i −0.0466352 + 0.411444i
\(813\) 9.20403 + 17.4690i 0.322800 + 0.612664i
\(814\) −4.58774 + 81.2107i −0.160800 + 2.84643i
\(815\) 13.4323 0.470512
\(816\) 9.67588 + 36.4913i 0.338724 + 1.27745i
\(817\) 2.04775 0.0716418
\(818\) −47.5712 2.68739i −1.66329 0.0939622i
\(819\) 11.3317 16.5295i 0.395962 0.577587i
\(820\) −40.6905 4.61207i −1.42097 0.161061i
\(821\) −35.9779 −1.25564 −0.627819 0.778359i \(-0.716052\pi\)
−0.627819 + 0.778359i \(0.716052\pi\)
\(822\) 9.73274 + 21.3068i 0.339468 + 0.743159i
\(823\) 31.1038 1.08421 0.542106 0.840310i \(-0.317627\pi\)
0.542106 + 0.840310i \(0.317627\pi\)
\(824\) −1.74866 + 10.2302i −0.0609173 + 0.356384i
\(825\) −24.5494 + 12.9345i −0.854699 + 0.450323i
\(826\) 1.15468 20.4397i 0.0401763 0.711189i
\(827\) 44.8962i 1.56119i 0.625036 + 0.780596i \(0.285084\pi\)
−0.625036 + 0.780596i \(0.714916\pi\)
\(828\) −28.6165 3.01589i −0.994492 0.104810i
\(829\) 24.4025i 0.847535i −0.905771 0.423768i \(-0.860707\pi\)
0.905771 0.423768i \(-0.139293\pi\)
\(830\) 8.05241 + 0.454895i 0.279503 + 0.0157896i
\(831\) 37.3119 19.6588i 1.29433 0.681957i
\(832\) −11.7530 + 33.3747i −0.407461 + 1.15706i
\(833\) −25.7132 −0.890911
\(834\) −43.7484 + 19.9838i −1.51488 + 0.691984i
\(835\) 36.0768 1.24849
\(836\) 0.329113 2.90363i 0.0113826 0.100424i
\(837\) −0.122285 0.0142541i −0.00422680 0.000492695i
\(838\) −1.39516 + 24.6966i −0.0481949 + 0.853130i
\(839\) −42.3798 −1.46311 −0.731557 0.681780i \(-0.761206\pi\)
−0.731557 + 0.681780i \(0.761206\pi\)
\(840\) 6.51606 + 19.9549i 0.224825 + 0.688511i
\(841\) −13.7418 −0.473856
\(842\) −26.3796 1.49023i −0.909100 0.0513567i
\(843\) −2.64513 5.02038i −0.0911030 0.172911i
\(844\) 1.57323 13.8799i 0.0541527 0.477767i
\(845\) 18.6183i 0.640490i
\(846\) 21.4443 + 16.5536i 0.737271 + 0.569124i
\(847\) 25.0895i 0.862085i
\(848\) −8.61616 + 37.5202i −0.295880 + 1.28845i
\(849\) 16.5929 + 31.4928i 0.569466 + 1.08083i
\(850\) −23.4573 1.32514i −0.804578 0.0454520i
\(851\) −30.0212 43.0619i −1.02911 1.47614i
\(852\) 16.5723 6.46698i 0.567757 0.221555i
\(853\) 39.5979i 1.35581i 0.735151 + 0.677903i \(0.237111\pi\)
−0.735151 + 0.677903i \(0.762889\pi\)
\(854\) −0.592488 + 10.4880i −0.0202745 + 0.358893i
\(855\) −1.95196 1.33816i −0.0667555 0.0457640i
\(856\) −3.11720 + 18.2365i −0.106544 + 0.623311i
\(857\) 45.3290i 1.54841i −0.632935 0.774205i \(-0.718150\pi\)
0.632935 0.774205i \(-0.281850\pi\)
\(858\) −23.6538 51.7825i −0.807526 1.76783i
\(859\) 24.6318i 0.840426i 0.907426 + 0.420213i \(0.138045\pi\)
−0.907426 + 0.420213i \(0.861955\pi\)
\(860\) −4.70617 + 41.5207i −0.160479 + 1.41584i
\(861\) −8.80079 16.7036i −0.299930 0.569259i
\(862\) −5.63755 0.318475i −0.192016 0.0108473i
\(863\) 21.3840i 0.727921i 0.931414 + 0.363960i \(0.118576\pi\)
−0.931414 + 0.363960i \(0.881424\pi\)
\(864\) −27.0941 11.3978i −0.921760 0.387760i
\(865\) 14.5692i 0.495366i
\(866\) 1.63213 28.8914i 0.0554620 0.981770i
\(867\) −10.2475 19.4495i −0.348025 0.660541i
\(868\) 0.00806054 0.0711149i 0.000273592 0.00241380i
\(869\) −70.2249 −2.38222
\(870\) 24.6911 11.2787i 0.837108 0.382383i
\(871\) 52.0660i 1.76419i
\(872\) −1.99352 0.340755i −0.0675091 0.0115394i
\(873\) 25.1064 + 17.2116i 0.849723 + 0.582524i
\(874\) 0.989568 + 1.60541i 0.0334727 + 0.0543037i
\(875\) 8.36072 0.282644
\(876\) 13.1551 + 33.7113i 0.444470 + 1.13900i
\(877\) 7.10030i 0.239760i −0.992788 0.119880i \(-0.961749\pi\)
0.992788 0.119880i \(-0.0382510\pi\)
\(878\) −18.9307 1.06943i −0.638881 0.0360915i
\(879\) 4.53817 2.39107i 0.153069 0.0806487i
\(880\) 58.1183 + 13.3463i 1.95917 + 0.449905i
\(881\) 21.8256 0.735323 0.367661 0.929960i \(-0.380159\pi\)
0.367661 + 0.929960i \(0.380159\pi\)
\(882\) 12.2335 15.8478i 0.411922 0.533624i
\(883\) 34.5350i 1.16220i −0.813834 0.581098i \(-0.802623\pi\)
0.813834 0.581098i \(-0.197377\pi\)
\(884\) 5.42873 47.8955i 0.182588 1.61090i
\(885\) −41.6679 + 21.9539i −1.40065 + 0.737972i
\(886\) −50.4946 2.85253i −1.69640 0.0958326i
\(887\) 23.9052i 0.802660i −0.915934 0.401330i \(-0.868548\pi\)
0.915934 0.401330i \(-0.131452\pi\)
\(888\) −16.6450 50.9740i −0.558569 1.71058i
\(889\) 1.91978i 0.0643874i
\(890\) 3.14684 55.7043i 0.105482 1.86721i
\(891\) 44.1109 17.0521i 1.47777 0.571265i
\(892\) 6.98485 + 0.791700i 0.233870 + 0.0265081i
\(893\) 1.77547i 0.0594139i
\(894\) −29.5506 + 13.4984i −0.988319 + 0.451455i
\(895\) 45.6091i 1.52455i
\(896\) 6.57586 15.7718i 0.219684 0.526898i
\(897\) 32.6379 + 16.8697i 1.08975 + 0.563264i
\(898\) 1.03546 18.3294i 0.0345538 0.611661i
\(899\) −0.0925495 −0.00308670
\(900\) 11.9769 13.8269i 0.399229 0.460898i
\(901\) 52.4430i 1.74713i
\(902\) −53.5473 3.02499i −1.78293 0.100721i
\(903\) −17.0444 + 8.98035i −0.567203 + 0.298847i
\(904\) 7.10572 + 1.21459i 0.236333 + 0.0403967i
\(905\) 51.0037i 1.69542i
\(906\) 0.714686 + 1.56458i 0.0237438 + 0.0519797i
\(907\) 20.9902 0.696967 0.348484 0.937315i \(-0.386697\pi\)
0.348484 + 0.937315i \(0.386697\pi\)
\(908\) 0.891249 7.86313i 0.0295771 0.260947i
\(909\) −13.0686 + 19.0630i −0.433458 + 0.632281i
\(910\) 1.51171 26.7597i 0.0501125 0.887076i
\(911\) 19.5906 0.649064 0.324532 0.945875i \(-0.394793\pi\)
0.324532 + 0.945875i \(0.394793\pi\)
\(912\) 0.493747 + 1.86210i 0.0163496 + 0.0616604i
\(913\) 10.5629 0.349581
\(914\) −1.85431 + 32.8243i −0.0613350 + 1.08573i
\(915\) 21.3806 11.2650i 0.706822 0.372409i
\(916\) 28.7546 + 3.25920i 0.950078 + 0.107687i
\(917\) 16.4639i 0.543688i
\(918\) 39.4483 + 6.87203i 1.30199 + 0.226811i
\(919\) 5.56361i 0.183527i 0.995781 + 0.0917633i \(0.0292503\pi\)
−0.995781 + 0.0917633i \(0.970750\pi\)
\(920\) −34.8258 + 16.3751i −1.14817 + 0.539872i
\(921\) −24.8805 + 13.1090i −0.819839 + 0.431956i
\(922\) 37.5504 + 2.12129i 1.23666 + 0.0698610i
\(923\) −22.7135 −0.747623
\(924\) 9.99441 + 25.6116i 0.328792 + 0.842561i
\(925\) 33.3714 1.09725
\(926\) 31.4629 + 1.77739i 1.03393 + 0.0584088i
\(927\) 9.07940 + 6.22435i 0.298207 + 0.204434i
\(928\) −21.2229 6.15237i −0.696674 0.201961i
\(929\) 15.4930i 0.508309i 0.967164 + 0.254155i \(0.0817972\pi\)
−0.967164 + 0.254155i \(0.918203\pi\)
\(930\) −0.149766 + 0.0684116i −0.00491101 + 0.00224331i
\(931\) −1.31211 −0.0430028
\(932\) 1.43848 12.6911i 0.0471189 0.415711i
\(933\) 8.99140 4.73738i 0.294365 0.155095i
\(934\) −0.720918 + 12.7615i −0.0235892 + 0.417568i
\(935\) −81.2335 −2.65662
\(936\) 26.9366 + 26.1329i 0.880450 + 0.854179i
\(937\) 3.40862i 0.111355i −0.998449 0.0556774i \(-0.982268\pi\)
0.998449 0.0556774i \(-0.0177318\pi\)
\(938\) 1.41817 25.1040i 0.0463050 0.819676i
\(939\) −17.2778 + 9.10329i −0.563839 + 0.297075i
\(940\) 35.9998 + 4.08041i 1.17419 + 0.133088i
\(941\) 14.3553i 0.467969i −0.972240 0.233985i \(-0.924823\pi\)
0.972240 0.233985i \(-0.0751765\pi\)
\(942\) 7.67172 + 16.7948i 0.249958 + 0.547205i
\(943\) 28.3934 19.7949i 0.924617 0.644610i
\(944\) 37.3657 + 8.58068i 1.21615 + 0.279277i
\(945\) 22.1155 + 2.57788i 0.719417 + 0.0838585i
\(946\) −3.08670 + 54.6398i −0.100357 + 1.77649i
\(947\) −10.2010 −0.331490 −0.165745 0.986169i \(-0.553003\pi\)
−0.165745 + 0.986169i \(0.553003\pi\)
\(948\) 43.1278 16.8297i 1.40073 0.546604i
\(949\) 46.2037i 1.49983i
\(950\) −1.19699 0.0676203i −0.0388356 0.00219389i
\(951\) 24.1056 + 45.7518i 0.781679 + 1.48360i
\(952\) −3.92208 + 22.9453i −0.127115 + 0.743662i
\(953\) 10.7012 0.346645 0.173323 0.984865i \(-0.444550\pi\)
0.173323 + 0.984865i \(0.444550\pi\)
\(954\) 32.3221 + 24.9505i 1.04647 + 0.807803i
\(955\) 49.0355i 1.58675i
\(956\) −0.823104 + 7.26191i −0.0266211 + 0.234867i
\(957\) 31.4529 16.5718i 1.01673 0.535692i
\(958\) −12.7760 0.721740i −0.412774 0.0233184i
\(959\) 14.4435i 0.466406i
\(960\) −38.8911 + 5.73181i −1.25521 + 0.184993i
\(961\) −30.9994 −0.999982
\(962\) −3.86158 + 68.3565i −0.124502 + 2.20390i
\(963\) 16.1852 + 11.0957i 0.521559 + 0.357553i
\(964\) −3.27687 + 28.9105i −0.105541 + 0.931145i
\(965\) 17.0414i 0.548583i
\(966\) −15.2771 9.02287i −0.491533 0.290306i
\(967\) 6.66228 0.214244 0.107122 0.994246i \(-0.465836\pi\)
0.107122 + 0.994246i \(0.465836\pi\)
\(968\) 46.3131 + 7.91637i 1.48856 + 0.254442i
\(969\) −1.22330 2.32179i −0.0392982 0.0745868i
\(970\) 40.6450 + 2.29611i 1.30503 + 0.0737236i
\(971\) 46.2279i 1.48352i −0.670663 0.741762i \(-0.733990\pi\)
0.670663 0.741762i \(-0.266010\pi\)
\(972\) −23.0036 + 21.0437i −0.737839 + 0.674976i
\(973\) −29.6563 −0.950738
\(974\) 17.0465 + 0.962987i 0.546205 + 0.0308561i
\(975\) −20.6637 + 10.8872i −0.661767 + 0.348671i
\(976\) −19.1731 4.40292i −0.613715 0.140934i
\(977\) 3.77134 0.120656 0.0603280 0.998179i \(-0.480785\pi\)
0.0603280 + 0.998179i \(0.480785\pi\)
\(978\) −10.5489 + 4.81865i −0.337317 + 0.154083i
\(979\) 73.0711i 2.33536i
\(980\) 3.01551 26.6047i 0.0963271 0.849855i
\(981\) −1.21292 + 1.76928i −0.0387256 + 0.0564886i
\(982\) 1.50442 + 0.0849872i 0.0480079 + 0.00271205i
\(983\) 10.4725 0.334021 0.167010 0.985955i \(-0.446589\pi\)
0.167010 + 0.985955i \(0.446589\pi\)
\(984\) 33.6104 10.9751i 1.07146 0.349873i
\(985\) 9.46023i 0.301428i
\(986\) 30.0537 + 1.69779i 0.957104 + 0.0540685i
\(987\) 7.78627 + 14.7781i 0.247840 + 0.470392i
\(988\) 0.277021 2.44404i 0.00881320 0.0777553i
\(989\) −20.1988 28.9727i −0.642283 0.921279i
\(990\) 38.6481 50.0666i 1.22832 1.59122i
\(991\) 15.3490 0.487576 0.243788 0.969829i \(-0.421610\pi\)
0.243788 + 0.969829i \(0.421610\pi\)
\(992\) 0.128729 + 0.0373176i 0.00408714 + 0.00118484i
\(993\) −44.9890 + 23.7037i −1.42768 + 0.752215i
\(994\) 10.9515 + 0.618669i 0.347360 + 0.0196230i
\(995\) 15.4396 0.489469
\(996\) −6.48707 + 2.53144i −0.205551 + 0.0802118i
\(997\) 49.8784i 1.57967i 0.613323 + 0.789833i \(0.289833\pi\)
−0.613323 + 0.789833i \(0.710167\pi\)
\(998\) 1.25528 22.2206i 0.0397352 0.703379i
\(999\) −56.4931 6.58509i −1.78736 0.208343i
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 552.2.b.c.413.1 80
3.2 odd 2 inner 552.2.b.c.413.80 yes 80
4.3 odd 2 2208.2.b.c.689.55 80
8.3 odd 2 2208.2.b.c.689.26 80
8.5 even 2 inner 552.2.b.c.413.78 yes 80
12.11 even 2 2208.2.b.c.689.28 80
23.22 odd 2 inner 552.2.b.c.413.2 yes 80
24.5 odd 2 inner 552.2.b.c.413.3 yes 80
24.11 even 2 2208.2.b.c.689.53 80
69.68 even 2 inner 552.2.b.c.413.79 yes 80
92.91 even 2 2208.2.b.c.689.56 80
184.45 odd 2 inner 552.2.b.c.413.77 yes 80
184.91 even 2 2208.2.b.c.689.25 80
276.275 odd 2 2208.2.b.c.689.27 80
552.275 odd 2 2208.2.b.c.689.54 80
552.413 even 2 inner 552.2.b.c.413.4 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.b.c.413.1 80 1.1 even 1 trivial
552.2.b.c.413.2 yes 80 23.22 odd 2 inner
552.2.b.c.413.3 yes 80 24.5 odd 2 inner
552.2.b.c.413.4 yes 80 552.413 even 2 inner
552.2.b.c.413.77 yes 80 184.45 odd 2 inner
552.2.b.c.413.78 yes 80 8.5 even 2 inner
552.2.b.c.413.79 yes 80 69.68 even 2 inner
552.2.b.c.413.80 yes 80 3.2 odd 2 inner
2208.2.b.c.689.25 80 184.91 even 2
2208.2.b.c.689.26 80 8.3 odd 2
2208.2.b.c.689.27 80 276.275 odd 2
2208.2.b.c.689.28 80 12.11 even 2
2208.2.b.c.689.53 80 24.11 even 2
2208.2.b.c.689.54 80 552.275 odd 2
2208.2.b.c.689.55 80 4.3 odd 2
2208.2.b.c.689.56 80 92.91 even 2