Properties

Label 170.2.k.a.161.2
Level $170$
Weight $2$
Character 170.161
Analytic conductor $1.357$
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] = [170,2,Mod(111,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.111");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.k (of order \(8\), degree \(4\), 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: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\Q(\zeta_{16})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 161.2
Root \(0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 170.161
Dual form 170.2.k.a.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.865619 - 2.08979i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(-0.865619 - 2.08979i) q^{6} +(-2.01367 + 0.834089i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.49661 - 1.49661i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.865619 - 2.08979i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(-0.865619 - 2.08979i) q^{6} +(-2.01367 + 0.834089i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.49661 - 1.49661i) q^{9} +(0.923880 - 0.382683i) q^{10} +(1.18524 + 2.86143i) q^{11} +(-2.08979 - 0.865619i) q^{12} +1.91761i q^{13} +(-0.834089 + 2.01367i) q^{14} +(1.59946 - 1.59946i) q^{15} -1.00000 q^{16} +(-3.85403 + 1.46508i) q^{17} -2.11652 q^{18} +(3.27564 - 3.27564i) q^{19} +(0.382683 - 0.923880i) q^{20} +4.93015i q^{21} +(2.86143 + 1.18524i) q^{22} +(-2.44155 - 5.89443i) q^{23} +(-2.08979 + 0.865619i) q^{24} +(0.707107 + 0.707107i) q^{25} +(1.35595 + 1.35595i) q^{26} +(1.84629 - 0.764757i) q^{27} +(0.834089 + 2.01367i) q^{28} +(6.49242 + 2.68925i) q^{29} -2.26197i q^{30} +(-1.66078 + 4.00948i) q^{31} +(-0.707107 + 0.707107i) q^{32} +7.00575 q^{33} +(-1.68925 + 3.76118i) q^{34} -2.17958 q^{35} +(-1.49661 + 1.49661i) q^{36} +(-3.12132 + 7.53553i) q^{37} -4.63246i q^{38} +(4.00740 + 1.65992i) q^{39} +(-0.382683 - 0.923880i) q^{40} +(-0.375285 + 0.155448i) q^{41} +(3.48614 + 3.48614i) q^{42} +(-5.56854 - 5.56854i) q^{43} +(2.86143 - 1.18524i) q^{44} +(-0.809957 - 1.95541i) q^{45} +(-5.89443 - 2.44155i) q^{46} -0.118113i q^{47} +(-0.865619 + 2.08979i) q^{48} +(-1.59059 + 1.59059i) q^{49} +1.00000 q^{50} +(-0.274423 + 9.32231i) q^{51} +1.91761 q^{52} +(2.75378 - 2.75378i) q^{53} +(0.764757 - 1.84629i) q^{54} +3.09719i q^{55} +(2.01367 + 0.834089i) q^{56} +(-4.00995 - 9.68087i) q^{57} +(6.49242 - 2.68925i) q^{58} +(-6.89715 - 6.89715i) q^{59} +(-1.59946 - 1.59946i) q^{60} +(-14.0416 + 5.81623i) q^{61} +(1.66078 + 4.00948i) q^{62} +(4.26197 + 1.76537i) q^{63} +1.00000i q^{64} +(-0.733837 + 1.77164i) q^{65} +(4.95382 - 4.95382i) q^{66} +9.13707 q^{67} +(1.46508 + 3.85403i) q^{68} -14.4316 q^{69} +(-1.54120 + 1.54120i) q^{70} +(2.33489 - 5.63691i) q^{71} +2.11652i q^{72} +(1.53701 + 0.636649i) q^{73} +(3.12132 + 7.53553i) q^{74} +(2.08979 - 0.865619i) q^{75} +(-3.27564 - 3.27564i) q^{76} +(-4.77337 - 4.77337i) q^{77} +(4.00740 - 1.65992i) q^{78} +(3.76904 + 9.09927i) q^{79} +(-0.923880 - 0.382683i) q^{80} -10.8699i q^{81} +(-0.155448 + 0.375285i) q^{82} +(5.90036 - 5.90036i) q^{83} +4.93015 q^{84} +(-4.12132 - 0.121320i) q^{85} -7.87510 q^{86} +(11.2399 - 11.2399i) q^{87} +(1.18524 - 2.86143i) q^{88} -9.71832i q^{89} +(-1.95541 - 0.809957i) q^{90} +(-1.59946 - 3.86143i) q^{91} +(-5.89443 + 2.44155i) q^{92} +(6.94137 + 6.94137i) q^{93} +(-0.0835185 - 0.0835185i) q^{94} +(4.27983 - 1.77276i) q^{95} +(0.865619 + 2.08979i) q^{96} +(1.28598 + 0.532672i) q^{97} +2.24943i q^{98} +(2.50859 - 6.05627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{9} + 16 q^{11} - 8 q^{12} - 8 q^{14} + 8 q^{15} - 8 q^{16} - 16 q^{18} - 16 q^{19} - 8 q^{22} + 24 q^{23} - 8 q^{24} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 16 q^{33} + 8 q^{36} - 8 q^{37} + 32 q^{39} - 8 q^{43} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 8 q^{49} + 8 q^{50} - 40 q^{51} + 24 q^{52} - 8 q^{53} + 40 q^{54} + 16 q^{57} + 8 q^{58} - 40 q^{59} - 8 q^{60} - 24 q^{61} + 16 q^{62} + 8 q^{63} - 8 q^{65} + 16 q^{66} - 16 q^{69} - 8 q^{70} + 24 q^{71} - 16 q^{73} + 8 q^{74} + 8 q^{75} + 16 q^{76} + 8 q^{77} + 32 q^{78} - 8 q^{79} + 8 q^{82} + 8 q^{83} + 16 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{87} + 16 q^{88} - 8 q^{91} - 8 q^{92} - 32 q^{93} - 8 q^{94} + 16 q^{95} - 32 q^{97} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.865619 2.08979i 0.499766 1.20654i −0.449844 0.893107i \(-0.648521\pi\)
0.949610 0.313434i \(-0.101479\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0.923880 + 0.382683i 0.413171 + 0.171141i
\(6\) −0.865619 2.08979i −0.353388 0.853153i
\(7\) −2.01367 + 0.834089i −0.761096 + 0.315256i −0.729260 0.684237i \(-0.760135\pi\)
−0.0318359 + 0.999493i \(0.510135\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.49661 1.49661i −0.498869 0.498869i
\(10\) 0.923880 0.382683i 0.292156 0.121015i
\(11\) 1.18524 + 2.86143i 0.357364 + 0.862753i 0.995669 + 0.0929696i \(0.0296359\pi\)
−0.638305 + 0.769784i \(0.720364\pi\)
\(12\) −2.08979 0.865619i −0.603270 0.249883i
\(13\) 1.91761i 0.531849i 0.963994 + 0.265924i \(0.0856771\pi\)
−0.963994 + 0.265924i \(0.914323\pi\)
\(14\) −0.834089 + 2.01367i −0.222920 + 0.538176i
\(15\) 1.59946 1.59946i 0.412978 0.412978i
\(16\) −1.00000 −0.250000
\(17\) −3.85403 + 1.46508i −0.934740 + 0.355333i
\(18\) −2.11652 −0.498869
\(19\) 3.27564 3.27564i 0.751484 0.751484i −0.223272 0.974756i \(-0.571674\pi\)
0.974756 + 0.223272i \(0.0716739\pi\)
\(20\) 0.382683 0.923880i 0.0855706 0.206586i
\(21\) 4.93015i 1.07585i
\(22\) 2.86143 + 1.18524i 0.610059 + 0.252695i
\(23\) −2.44155 5.89443i −0.509099 1.22907i −0.944403 0.328790i \(-0.893359\pi\)
0.435304 0.900284i \(-0.356641\pi\)
\(24\) −2.08979 + 0.865619i −0.426577 + 0.176694i
\(25\) 0.707107 + 0.707107i 0.141421 + 0.141421i
\(26\) 1.35595 + 1.35595i 0.265924 + 0.265924i
\(27\) 1.84629 0.764757i 0.355318 0.147178i
\(28\) 0.834089 + 2.01367i 0.157628 + 0.380548i
\(29\) 6.49242 + 2.68925i 1.20561 + 0.499381i 0.892808 0.450437i \(-0.148732\pi\)
0.312803 + 0.949818i \(0.398732\pi\)
\(30\) 2.26197i 0.412978i
\(31\) −1.66078 + 4.00948i −0.298285 + 0.720124i 0.701686 + 0.712486i \(0.252431\pi\)
−0.999971 + 0.00763722i \(0.997569\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 7.00575 1.21955
\(34\) −1.68925 + 3.76118i −0.289703 + 0.645036i
\(35\) −2.17958 −0.368416
\(36\) −1.49661 + 1.49661i −0.249434 + 0.249434i
\(37\) −3.12132 + 7.53553i −0.513142 + 1.23883i 0.428904 + 0.903350i \(0.358900\pi\)
−0.942046 + 0.335484i \(0.891100\pi\)
\(38\) 4.63246i 0.751484i
\(39\) 4.00740 + 1.65992i 0.641697 + 0.265800i
\(40\) −0.382683 0.923880i −0.0605076 0.146078i
\(41\) −0.375285 + 0.155448i −0.0586097 + 0.0242769i −0.411796 0.911276i \(-0.635098\pi\)
0.353186 + 0.935553i \(0.385098\pi\)
\(42\) 3.48614 + 3.48614i 0.537924 + 0.537924i
\(43\) −5.56854 5.56854i −0.849194 0.849194i 0.140839 0.990033i \(-0.455020\pi\)
−0.990033 + 0.140839i \(0.955020\pi\)
\(44\) 2.86143 1.18524i 0.431377 0.178682i
\(45\) −0.809957 1.95541i −0.120741 0.291495i
\(46\) −5.89443 2.44155i −0.869086 0.359987i
\(47\) 0.118113i 0.0172285i −0.999963 0.00861427i \(-0.997258\pi\)
0.999963 0.00861427i \(-0.00274204\pi\)
\(48\) −0.865619 + 2.08979i −0.124941 + 0.301635i
\(49\) −1.59059 + 1.59059i −0.227227 + 0.227227i
\(50\) 1.00000 0.141421
\(51\) −0.274423 + 9.32231i −0.0384269 + 1.30539i
\(52\) 1.91761 0.265924
\(53\) 2.75378 2.75378i 0.378261 0.378261i −0.492214 0.870474i \(-0.663812\pi\)
0.870474 + 0.492214i \(0.163812\pi\)
\(54\) 0.764757 1.84629i 0.104070 0.251248i
\(55\) 3.09719i 0.417625i
\(56\) 2.01367 + 0.834089i 0.269088 + 0.111460i
\(57\) −4.00995 9.68087i −0.531130 1.28226i
\(58\) 6.49242 2.68925i 0.852496 0.353115i
\(59\) −6.89715 6.89715i −0.897932 0.897932i 0.0973207 0.995253i \(-0.468973\pi\)
−0.995253 + 0.0973207i \(0.968973\pi\)
\(60\) −1.59946 1.59946i −0.206489 0.206489i
\(61\) −14.0416 + 5.81623i −1.79785 + 0.744692i −0.810576 + 0.585634i \(0.800846\pi\)
−0.987269 + 0.159058i \(0.949154\pi\)
\(62\) 1.66078 + 4.00948i 0.210919 + 0.509204i
\(63\) 4.26197 + 1.76537i 0.536958 + 0.222415i
\(64\) 1.00000i 0.125000i
\(65\) −0.733837 + 1.77164i −0.0910212 + 0.219745i
\(66\) 4.95382 4.95382i 0.609773 0.609773i
\(67\) 9.13707 1.11627 0.558135 0.829750i \(-0.311517\pi\)
0.558135 + 0.829750i \(0.311517\pi\)
\(68\) 1.46508 + 3.85403i 0.177667 + 0.467370i
\(69\) −14.4316 −1.73736
\(70\) −1.54120 + 1.54120i −0.184208 + 0.184208i
\(71\) 2.33489 5.63691i 0.277100 0.668978i −0.722653 0.691211i \(-0.757077\pi\)
0.999753 + 0.0222327i \(0.00707746\pi\)
\(72\) 2.11652i 0.249434i
\(73\) 1.53701 + 0.636649i 0.179893 + 0.0745141i 0.470812 0.882234i \(-0.343961\pi\)
−0.290919 + 0.956748i \(0.593961\pi\)
\(74\) 3.12132 + 7.53553i 0.362846 + 0.875988i
\(75\) 2.08979 0.865619i 0.241308 0.0999531i
\(76\) −3.27564 3.27564i −0.375742 0.375742i
\(77\) −4.77337 4.77337i −0.543977 0.543977i
\(78\) 4.00740 1.65992i 0.453748 0.187949i
\(79\) 3.76904 + 9.09927i 0.424050 + 1.02375i 0.981141 + 0.193296i \(0.0619177\pi\)
−0.557090 + 0.830452i \(0.688082\pi\)
\(80\) −0.923880 0.382683i −0.103293 0.0427853i
\(81\) 10.8699i 1.20777i
\(82\) −0.155448 + 0.375285i −0.0171664 + 0.0414433i
\(83\) 5.90036 5.90036i 0.647648 0.647648i −0.304776 0.952424i \(-0.598582\pi\)
0.952424 + 0.304776i \(0.0985815\pi\)
\(84\) 4.93015 0.537924
\(85\) −4.12132 0.121320i −0.447020 0.0131590i
\(86\) −7.87510 −0.849194
\(87\) 11.2399 11.2399i 1.20505 1.20505i
\(88\) 1.18524 2.86143i 0.126347 0.305029i
\(89\) 9.71832i 1.03014i −0.857148 0.515070i \(-0.827766\pi\)
0.857148 0.515070i \(-0.172234\pi\)
\(90\) −1.95541 0.809957i −0.206118 0.0853770i
\(91\) −1.59946 3.86143i −0.167669 0.404788i
\(92\) −5.89443 + 2.44155i −0.614537 + 0.254550i
\(93\) 6.94137 + 6.94137i 0.719786 + 0.719786i
\(94\) −0.0835185 0.0835185i −0.00861427 0.00861427i
\(95\) 4.27983 1.77276i 0.439102 0.181882i
\(96\) 0.865619 + 2.08979i 0.0883469 + 0.213288i
\(97\) 1.28598 + 0.532672i 0.130572 + 0.0540846i 0.447013 0.894528i \(-0.352488\pi\)
−0.316441 + 0.948612i \(0.602488\pi\)
\(98\) 2.24943i 0.227227i
\(99\) 2.50859 6.05627i 0.252123 0.608678i
\(100\) 0.707107 0.707107i 0.0707107 0.0707107i
\(101\) 5.83938 0.581040 0.290520 0.956869i \(-0.406172\pi\)
0.290520 + 0.956869i \(0.406172\pi\)
\(102\) 6.39782 + 6.78592i 0.633479 + 0.671906i
\(103\) −14.9378 −1.47186 −0.735932 0.677056i \(-0.763256\pi\)
−0.735932 + 0.677056i \(0.763256\pi\)
\(104\) 1.35595 1.35595i 0.132962 0.132962i
\(105\) −1.88669 + 4.55487i −0.184122 + 0.444509i
\(106\) 3.89443i 0.378261i
\(107\) −18.6803 7.73765i −1.80590 0.748027i −0.983945 0.178471i \(-0.942885\pi\)
−0.821952 0.569556i \(-0.807115\pi\)
\(108\) −0.764757 1.84629i −0.0735888 0.177659i
\(109\) −10.2687 + 4.25345i −0.983566 + 0.407406i −0.815745 0.578411i \(-0.803673\pi\)
−0.167821 + 0.985818i \(0.553673\pi\)
\(110\) 2.19004 + 2.19004i 0.208812 + 0.208812i
\(111\) 13.0458 + 13.0458i 1.23825 + 1.23825i
\(112\) 2.01367 0.834089i 0.190274 0.0788140i
\(113\) −4.70338 11.3550i −0.442457 1.06819i −0.975084 0.221836i \(-0.928795\pi\)
0.532627 0.846350i \(-0.321205\pi\)
\(114\) −9.68087 4.00995i −0.906696 0.375566i
\(115\) 6.38009i 0.594946i
\(116\) 2.68925 6.49242i 0.249690 0.602806i
\(117\) 2.86990 2.86990i 0.265323 0.265323i
\(118\) −9.75404 −0.897932
\(119\) 6.53874 6.16478i 0.599405 0.565125i
\(120\) −2.26197 −0.206489
\(121\) 0.995200 0.995200i 0.0904727 0.0904727i
\(122\) −5.81623 + 14.0416i −0.526577 + 1.27127i
\(123\) 0.918827i 0.0828478i
\(124\) 4.00948 + 1.66078i 0.360062 + 0.149143i
\(125\) 0.382683 + 0.923880i 0.0342282 + 0.0826343i
\(126\) 4.26197 1.76537i 0.379687 0.157271i
\(127\) 9.87622 + 9.87622i 0.876373 + 0.876373i 0.993157 0.116784i \(-0.0372586\pi\)
−0.116784 + 0.993157i \(0.537259\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −16.4573 + 6.81684i −1.44898 + 0.600189i
\(130\) 0.733837 + 1.77164i 0.0643617 + 0.155383i
\(131\) 11.6230 + 4.81438i 1.01550 + 0.420635i 0.827459 0.561526i \(-0.189786\pi\)
0.188043 + 0.982161i \(0.439786\pi\)
\(132\) 7.00575i 0.609773i
\(133\) −3.86388 + 9.32824i −0.335041 + 0.808861i
\(134\) 6.46088 6.46088i 0.558135 0.558135i
\(135\) 1.99841 0.171996
\(136\) 3.76118 + 1.68925i 0.322518 + 0.144852i
\(137\) 10.0453 0.858230 0.429115 0.903250i \(-0.358826\pi\)
0.429115 + 0.903250i \(0.358826\pi\)
\(138\) −10.2047 + 10.2047i −0.868679 + 0.868679i
\(139\) −0.523852 + 1.26469i −0.0444326 + 0.107270i −0.944538 0.328403i \(-0.893490\pi\)
0.900105 + 0.435673i \(0.143490\pi\)
\(140\) 2.17958i 0.184208i
\(141\) −0.246831 0.102241i −0.0207869 0.00861024i
\(142\) −2.33489 5.63691i −0.195939 0.473039i
\(143\) −5.48710 + 2.27283i −0.458854 + 0.190064i
\(144\) 1.49661 + 1.49661i 0.124717 + 0.124717i
\(145\) 4.96908 + 4.96908i 0.412660 + 0.412660i
\(146\) 1.53701 0.636649i 0.127203 0.0526894i
\(147\) 1.94715 + 4.70084i 0.160598 + 0.387718i
\(148\) 7.53553 + 3.12132i 0.619417 + 0.256571i
\(149\) 14.4592i 1.18454i 0.805739 + 0.592270i \(0.201768\pi\)
−0.805739 + 0.592270i \(0.798232\pi\)
\(150\) 0.865619 2.08979i 0.0706775 0.170631i
\(151\) 6.14161 6.14161i 0.499797 0.499797i −0.411578 0.911375i \(-0.635022\pi\)
0.911375 + 0.411578i \(0.135022\pi\)
\(152\) −4.63246 −0.375742
\(153\) 7.96061 + 3.57532i 0.643577 + 0.289048i
\(154\) −6.75057 −0.543977
\(155\) −3.06872 + 3.06872i −0.246486 + 0.246486i
\(156\) 1.65992 4.00740i 0.132900 0.320849i
\(157\) 16.3611i 1.30576i −0.757463 0.652878i \(-0.773562\pi\)
0.757463 0.652878i \(-0.226438\pi\)
\(158\) 9.09927 + 3.76904i 0.723899 + 0.299849i
\(159\) −3.37109 8.13854i −0.267345 0.645428i
\(160\) −0.923880 + 0.382683i −0.0730391 + 0.0302538i
\(161\) 9.83296 + 9.83296i 0.774946 + 0.774946i
\(162\) −7.68618 7.68618i −0.603883 0.603883i
\(163\) −10.7843 + 4.46701i −0.844694 + 0.349884i −0.762702 0.646750i \(-0.776128\pi\)
−0.0819911 + 0.996633i \(0.526128\pi\)
\(164\) 0.155448 + 0.375285i 0.0121385 + 0.0293049i
\(165\) 6.47247 + 2.68099i 0.503881 + 0.208715i
\(166\) 8.34436i 0.647648i
\(167\) −5.40808 + 13.0563i −0.418490 + 1.01032i 0.564295 + 0.825573i \(0.309148\pi\)
−0.982785 + 0.184751i \(0.940852\pi\)
\(168\) 3.48614 3.48614i 0.268962 0.268962i
\(169\) 9.32278 0.717137
\(170\) −3.00000 + 2.82843i −0.230089 + 0.216930i
\(171\) −9.80469 −0.749783
\(172\) −5.56854 + 5.56854i −0.424597 + 0.424597i
\(173\) −0.893211 + 2.15640i −0.0679096 + 0.163948i −0.954190 0.299200i \(-0.903280\pi\)
0.886281 + 0.463148i \(0.153280\pi\)
\(174\) 15.8956i 1.20505i
\(175\) −2.01367 0.834089i −0.152219 0.0630512i
\(176\) −1.18524 2.86143i −0.0893410 0.215688i
\(177\) −20.3839 + 8.44329i −1.53215 + 0.634636i
\(178\) −6.87189 6.87189i −0.515070 0.515070i
\(179\) 7.20533 + 7.20533i 0.538551 + 0.538551i 0.923103 0.384552i \(-0.125644\pi\)
−0.384552 + 0.923103i \(0.625644\pi\)
\(180\) −1.95541 + 0.809957i −0.145748 + 0.0603706i
\(181\) 0.857002 + 2.06899i 0.0637005 + 0.153787i 0.952524 0.304462i \(-0.0984768\pi\)
−0.888824 + 0.458249i \(0.848477\pi\)
\(182\) −3.86143 1.59946i −0.286228 0.118560i
\(183\) 34.3787i 2.54135i
\(184\) −2.44155 + 5.89443i −0.179994 + 0.434543i
\(185\) −5.76745 + 5.76745i −0.424031 + 0.424031i
\(186\) 9.81657 0.719786
\(187\) −8.76017 9.29156i −0.640607 0.679467i
\(188\) −0.118113 −0.00861427
\(189\) −3.07994 + 3.07994i −0.224032 + 0.224032i
\(190\) 1.77276 4.27983i 0.128610 0.310492i
\(191\) 12.2384i 0.885541i −0.896635 0.442771i \(-0.853996\pi\)
0.896635 0.442771i \(-0.146004\pi\)
\(192\) 2.08979 + 0.865619i 0.150818 + 0.0624707i
\(193\) 9.00555 + 21.7413i 0.648234 + 1.56498i 0.815306 + 0.579030i \(0.196569\pi\)
−0.167072 + 0.985945i \(0.553431\pi\)
\(194\) 1.28598 0.532672i 0.0923282 0.0382436i
\(195\) 3.06713 + 3.06713i 0.219642 + 0.219642i
\(196\) 1.59059 + 1.59059i 0.113613 + 0.113613i
\(197\) 24.9703 10.3430i 1.77906 0.736911i 0.786151 0.618034i \(-0.212071\pi\)
0.992909 0.118876i \(-0.0379292\pi\)
\(198\) −2.50859 6.05627i −0.178278 0.430400i
\(199\) 16.1659 + 6.69613i 1.14597 + 0.474676i 0.873180 0.487398i \(-0.162054\pi\)
0.272789 + 0.962074i \(0.412054\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 7.90923 19.0946i 0.557874 1.34683i
\(202\) 4.12906 4.12906i 0.290520 0.290520i
\(203\) −15.3167 −1.07502
\(204\) 9.32231 + 0.274423i 0.652693 + 0.0192135i
\(205\) −0.406206 −0.0283707
\(206\) −10.5626 + 10.5626i −0.735932 + 0.735932i
\(207\) −5.16760 + 12.4757i −0.359173 + 0.867120i
\(208\) 1.91761i 0.132962i
\(209\) 13.2554 + 5.49059i 0.916899 + 0.379792i
\(210\) 1.88669 + 4.55487i 0.130194 + 0.314316i
\(211\) −11.5668 + 4.79111i −0.796289 + 0.329834i −0.743469 0.668770i \(-0.766821\pi\)
−0.0528202 + 0.998604i \(0.516821\pi\)
\(212\) −2.75378 2.75378i −0.189130 0.189130i
\(213\) −9.75884 9.75884i −0.668665 0.668665i
\(214\) −18.6803 + 7.73765i −1.27696 + 0.528935i
\(215\) −3.01367 7.27564i −0.205531 0.496195i
\(216\) −1.84629 0.764757i −0.125624 0.0520351i
\(217\) 9.45901i 0.642119i
\(218\) −4.25345 + 10.2687i −0.288080 + 0.695486i
\(219\) 2.66092 2.66092i 0.179809 0.179809i
\(220\) 3.09719 0.208812
\(221\) −2.80944 7.39052i −0.188983 0.497140i
\(222\) 18.4496 1.23825
\(223\) 0.416933 0.416933i 0.0279199 0.0279199i −0.693009 0.720929i \(-0.743715\pi\)
0.720929 + 0.693009i \(0.243715\pi\)
\(224\) 0.834089 2.01367i 0.0557299 0.134544i
\(225\) 2.11652i 0.141101i
\(226\) −11.3550 4.70338i −0.755321 0.312864i
\(227\) −6.70725 16.1927i −0.445176 1.07475i −0.974108 0.226085i \(-0.927407\pi\)
0.528932 0.848664i \(-0.322593\pi\)
\(228\) −9.68087 + 4.00995i −0.641131 + 0.265565i
\(229\) −11.6753 11.6753i −0.771527 0.771527i 0.206846 0.978373i \(-0.433680\pi\)
−0.978373 + 0.206846i \(0.933680\pi\)
\(230\) −4.51140 4.51140i −0.297473 0.297473i
\(231\) −14.1073 + 5.84343i −0.928191 + 0.384469i
\(232\) −2.68925 6.49242i −0.176558 0.426248i
\(233\) 19.1475 + 7.93116i 1.25439 + 0.519587i 0.908185 0.418570i \(-0.137468\pi\)
0.346210 + 0.938157i \(0.387468\pi\)
\(234\) 4.05866i 0.265323i
\(235\) 0.0451999 0.109122i 0.00294851 0.00711834i
\(236\) −6.89715 + 6.89715i −0.448966 + 0.448966i
\(237\) 22.2781 1.44712
\(238\) 0.264427 8.98275i 0.0171403 0.582265i
\(239\) 17.3225 1.12050 0.560251 0.828323i \(-0.310705\pi\)
0.560251 + 0.828323i \(0.310705\pi\)
\(240\) −1.59946 + 1.59946i −0.103244 + 0.103244i
\(241\) 10.5789 25.5397i 0.681446 1.64516i −0.0798937 0.996803i \(-0.525458\pi\)
0.761340 0.648353i \(-0.224542\pi\)
\(242\) 1.40743i 0.0904727i
\(243\) −17.1770 7.11493i −1.10190 0.456423i
\(244\) 5.81623 + 14.0416i 0.372346 + 0.898923i
\(245\) −2.07820 + 0.860819i −0.132771 + 0.0549957i
\(246\) 0.649709 + 0.649709i 0.0414239 + 0.0414239i
\(247\) 6.28140 + 6.28140i 0.399676 + 0.399676i
\(248\) 4.00948 1.66078i 0.254602 0.105460i
\(249\) −7.22304 17.4380i −0.457742 1.10509i
\(250\) 0.923880 + 0.382683i 0.0584313 + 0.0242030i
\(251\) 15.5217i 0.979719i −0.871802 0.489859i \(-0.837048\pi\)
0.871802 0.489859i \(-0.162952\pi\)
\(252\) 1.76537 4.26197i 0.111208 0.268479i
\(253\) 13.9727 13.9727i 0.878454 0.878454i
\(254\) 13.9671 0.876373
\(255\) −3.82103 + 8.50768i −0.239282 + 0.532771i
\(256\) 1.00000 0.0625000
\(257\) −18.5530 + 18.5530i −1.15730 + 1.15730i −0.172251 + 0.985053i \(0.555104\pi\)
−0.985053 + 0.172251i \(0.944896\pi\)
\(258\) −6.81684 + 16.4573i −0.424398 + 1.02459i
\(259\) 17.7775i 1.10464i
\(260\) 1.77164 + 0.733837i 0.109872 + 0.0455106i
\(261\) −5.69184 13.7413i −0.352316 0.850567i
\(262\) 11.6230 4.81438i 0.718068 0.297434i
\(263\) −1.78704 1.78704i −0.110194 0.110194i 0.649860 0.760054i \(-0.274827\pi\)
−0.760054 + 0.649860i \(0.774827\pi\)
\(264\) −4.95382 4.95382i −0.304886 0.304886i
\(265\) 3.59798 1.49033i 0.221022 0.0915505i
\(266\) 3.86388 + 9.32824i 0.236910 + 0.571951i
\(267\) −20.3093 8.41237i −1.24291 0.514829i
\(268\) 9.13707i 0.558135i
\(269\) 5.84337 14.1071i 0.356276 0.860127i −0.639541 0.768757i \(-0.720875\pi\)
0.995817 0.0913699i \(-0.0291246\pi\)
\(270\) 1.41309 1.41309i 0.0859978 0.0859978i
\(271\) −15.7334 −0.955738 −0.477869 0.878431i \(-0.658591\pi\)
−0.477869 + 0.878431i \(0.658591\pi\)
\(272\) 3.85403 1.46508i 0.233685 0.0888333i
\(273\) −9.45410 −0.572188
\(274\) 7.10311 7.10311i 0.429115 0.429115i
\(275\) −1.18524 + 2.86143i −0.0714728 + 0.172551i
\(276\) 14.4316i 0.868679i
\(277\) 24.4537 + 10.1291i 1.46928 + 0.608596i 0.966695 0.255930i \(-0.0823818\pi\)
0.502587 + 0.864527i \(0.332382\pi\)
\(278\) 0.523852 + 1.26469i 0.0314186 + 0.0758512i
\(279\) 8.48614 3.51508i 0.508052 0.210442i
\(280\) 1.54120 + 1.54120i 0.0921041 + 0.0921041i
\(281\) 7.32983 + 7.32983i 0.437261 + 0.437261i 0.891089 0.453828i \(-0.149942\pi\)
−0.453828 + 0.891089i \(0.649942\pi\)
\(282\) −0.246831 + 0.102241i −0.0146986 + 0.00608836i
\(283\) 1.92831 + 4.65534i 0.114626 + 0.276731i 0.970772 0.240002i \(-0.0771480\pi\)
−0.856147 + 0.516733i \(0.827148\pi\)
\(284\) −5.63691 2.33489i −0.334489 0.138550i
\(285\) 10.4785i 0.620692i
\(286\) −2.27283 + 5.48710i −0.134395 + 0.324459i
\(287\) 0.626043 0.626043i 0.0369542 0.0369542i
\(288\) 2.11652 0.124717
\(289\) 12.7071 11.2929i 0.747477 0.664288i
\(290\) 7.02734 0.412660
\(291\) 2.22634 2.22634i 0.130511 0.130511i
\(292\) 0.636649 1.53701i 0.0372570 0.0899464i
\(293\) 14.3469i 0.838157i −0.907950 0.419078i \(-0.862353\pi\)
0.907950 0.419078i \(-0.137647\pi\)
\(294\) 4.70084 + 1.94715i 0.274158 + 0.113560i
\(295\) −3.73271 9.01156i −0.217327 0.524673i
\(296\) 7.53553 3.12132i 0.437994 0.181423i
\(297\) 4.37660 + 4.37660i 0.253956 + 0.253956i
\(298\) 10.2242 + 10.2242i 0.592270 + 0.592270i
\(299\) 11.3032 4.68194i 0.653681 0.270764i
\(300\) −0.865619 2.08979i −0.0499766 0.120654i
\(301\) 15.8578 + 6.56854i 0.914031 + 0.378604i
\(302\) 8.68554i 0.499797i
\(303\) 5.05468 12.2031i 0.290384 0.701048i
\(304\) −3.27564 + 3.27564i −0.187871 + 0.187871i
\(305\) −15.1985 −0.870266
\(306\) 8.15713 3.10086i 0.466312 0.177264i
\(307\) 23.7650 1.35634 0.678170 0.734905i \(-0.262773\pi\)
0.678170 + 0.734905i \(0.262773\pi\)
\(308\) −4.77337 + 4.77337i −0.271988 + 0.271988i
\(309\) −12.9304 + 31.2168i −0.735587 + 1.77586i
\(310\) 4.33983i 0.246486i
\(311\) −26.2186 10.8601i −1.48672 0.615820i −0.516120 0.856516i \(-0.672624\pi\)
−0.970600 + 0.240696i \(0.922624\pi\)
\(312\) −1.65992 4.00740i −0.0939744 0.226874i
\(313\) −7.95541 + 3.29524i −0.449666 + 0.186258i −0.596012 0.802976i \(-0.703249\pi\)
0.146346 + 0.989234i \(0.453249\pi\)
\(314\) −11.5690 11.5690i −0.652878 0.652878i
\(315\) 3.26197 + 3.26197i 0.183791 + 0.183791i
\(316\) 9.09927 3.76904i 0.511874 0.212025i
\(317\) 3.46436 + 8.36370i 0.194578 + 0.469752i 0.990814 0.135234i \(-0.0431787\pi\)
−0.796236 + 0.604986i \(0.793179\pi\)
\(318\) −8.13854 3.37109i −0.456387 0.189042i
\(319\) 21.7650i 1.21861i
\(320\) −0.382683 + 0.923880i −0.0213927 + 0.0516464i
\(321\) −32.3401 + 32.3401i −1.80505 + 1.80505i
\(322\) 13.9059 0.774946
\(323\) −7.82536 + 17.4235i −0.435415 + 0.969469i
\(324\) −10.8699 −0.603883
\(325\) −1.35595 + 1.35595i −0.0752148 + 0.0752148i
\(326\) −4.46701 + 10.7843i −0.247405 + 0.597289i
\(327\) 25.1414i 1.39032i
\(328\) 0.375285 + 0.155448i 0.0207217 + 0.00858320i
\(329\) 0.0985168 + 0.237841i 0.00543141 + 0.0131126i
\(330\) 6.47247 2.68099i 0.356298 0.147583i
\(331\) 2.06713 + 2.06713i 0.113620 + 0.113620i 0.761631 0.648011i \(-0.224399\pi\)
−0.648011 + 0.761631i \(0.724399\pi\)
\(332\) −5.90036 5.90036i −0.323824 0.323824i
\(333\) 15.9491 6.60634i 0.874006 0.362025i
\(334\) 5.40808 + 13.0563i 0.295917 + 0.714407i
\(335\) 8.44155 + 3.49661i 0.461211 + 0.191040i
\(336\) 4.93015i 0.268962i
\(337\) −5.10693 + 12.3292i −0.278192 + 0.671616i −0.999786 0.0207015i \(-0.993410\pi\)
0.721593 + 0.692317i \(0.243410\pi\)
\(338\) 6.59220 6.59220i 0.358568 0.358568i
\(339\) −27.8008 −1.50993
\(340\) −0.121320 + 4.12132i −0.00657952 + 0.223510i
\(341\) −13.4413 −0.727885
\(342\) −6.93296 + 6.93296i −0.374892 + 0.374892i
\(343\) 7.71485 18.6253i 0.416563 1.00567i
\(344\) 7.87510i 0.424597i
\(345\) −13.3330 5.52273i −0.717827 0.297334i
\(346\) 0.893211 + 2.15640i 0.0480193 + 0.115929i
\(347\) −33.0738 + 13.6996i −1.77549 + 0.735433i −0.781769 + 0.623568i \(0.785682\pi\)
−0.993723 + 0.111865i \(0.964318\pi\)
\(348\) −11.2399 11.2399i −0.602523 0.602523i
\(349\) −10.0303 10.0303i −0.536909 0.536909i 0.385711 0.922620i \(-0.373956\pi\)
−0.922620 + 0.385711i \(0.873956\pi\)
\(350\) −2.01367 + 0.834089i −0.107635 + 0.0445839i
\(351\) 1.46650 + 3.54046i 0.0782762 + 0.188976i
\(352\) −2.86143 1.18524i −0.152515 0.0631736i
\(353\) 17.5181i 0.932396i −0.884680 0.466198i \(-0.845623\pi\)
0.884680 0.466198i \(-0.154377\pi\)
\(354\) −8.44329 + 20.3839i −0.448756 + 1.08339i
\(355\) 4.31431 4.31431i 0.228980 0.228980i
\(356\) −9.71832 −0.515070
\(357\) −7.22304 19.0010i −0.382284 1.00564i
\(358\) 10.1899 0.538551
\(359\) −19.5067 + 19.5067i −1.02952 + 1.02952i −0.0299733 + 0.999551i \(0.509542\pi\)
−0.999551 + 0.0299733i \(0.990458\pi\)
\(360\) −0.809957 + 1.95541i −0.0426885 + 0.103059i
\(361\) 2.45967i 0.129456i
\(362\) 2.06899 + 0.857002i 0.108744 + 0.0450430i
\(363\) −1.21829 2.94122i −0.0639439 0.154374i
\(364\) −3.86143 + 1.59946i −0.202394 + 0.0838343i
\(365\) 1.17637 + 1.17637i 0.0615742 + 0.0615742i
\(366\) 24.3094 + 24.3094i 1.27067 + 1.27067i
\(367\) 4.87216 2.01811i 0.254324 0.105345i −0.251879 0.967759i \(-0.581048\pi\)
0.506203 + 0.862414i \(0.331048\pi\)
\(368\) 2.44155 + 5.89443i 0.127275 + 0.307268i
\(369\) 0.794299 + 0.329009i 0.0413496 + 0.0171275i
\(370\) 8.15640i 0.424031i
\(371\) −3.24830 + 7.84210i −0.168643 + 0.407141i
\(372\) 6.94137 6.94137i 0.359893 0.359893i
\(373\) −2.25490 −0.116754 −0.0583771 0.998295i \(-0.518593\pi\)
−0.0583771 + 0.998295i \(0.518593\pi\)
\(374\) −12.7645 0.375752i −0.660037 0.0194297i
\(375\) 2.26197 0.116808
\(376\) −0.0835185 + 0.0835185i −0.00430714 + 0.00430714i
\(377\) −5.15692 + 12.4499i −0.265595 + 0.641203i
\(378\) 4.35569i 0.224032i
\(379\) 5.79430 + 2.40008i 0.297633 + 0.123284i 0.526503 0.850173i \(-0.323503\pi\)
−0.228870 + 0.973457i \(0.573503\pi\)
\(380\) −1.77276 4.27983i −0.0909409 0.219551i
\(381\) 29.1883 12.0902i 1.49536 0.619399i
\(382\) −8.65387 8.65387i −0.442771 0.442771i
\(383\) 9.29235 + 9.29235i 0.474817 + 0.474817i 0.903469 0.428653i \(-0.141012\pi\)
−0.428653 + 0.903469i \(0.641012\pi\)
\(384\) 2.08979 0.865619i 0.106644 0.0441735i
\(385\) −2.58333 6.23671i −0.131659 0.317852i
\(386\) 21.7413 + 9.00555i 1.10660 + 0.458371i
\(387\) 16.6678i 0.847272i
\(388\) 0.532672 1.28598i 0.0270423 0.0652859i
\(389\) −15.5600 + 15.5600i −0.788922 + 0.788922i −0.981318 0.192395i \(-0.938374\pi\)
0.192395 + 0.981318i \(0.438374\pi\)
\(390\) 4.33758 0.219642
\(391\) 18.0456 + 19.1403i 0.912606 + 0.967964i
\(392\) 2.24943 0.113613
\(393\) 20.1221 20.1221i 1.01503 1.01503i
\(394\) 10.3430 24.9703i 0.521075 1.25799i
\(395\) 9.84898i 0.495556i
\(396\) −6.05627 2.50859i −0.304339 0.126061i
\(397\) 0.990400 + 2.39104i 0.0497067 + 0.120003i 0.946782 0.321874i \(-0.104313\pi\)
−0.897076 + 0.441877i \(0.854313\pi\)
\(398\) 16.1659 6.69613i 0.810322 0.335647i
\(399\) 16.1494 + 16.1494i 0.808482 + 0.808482i
\(400\) −0.707107 0.707107i −0.0353553 0.0353553i
\(401\) 11.2964 4.67913i 0.564116 0.233665i −0.0823549 0.996603i \(-0.526244\pi\)
0.646471 + 0.762938i \(0.276244\pi\)
\(402\) −7.90923 19.0946i −0.394476 0.952350i
\(403\) −7.68861 3.18473i −0.382997 0.158642i
\(404\) 5.83938i 0.290520i
\(405\) 4.15973 10.0425i 0.206699 0.499015i
\(406\) −10.8305 + 10.8305i −0.537509 + 0.537509i
\(407\) −25.2619 −1.25219
\(408\) 6.78592 6.39782i 0.335953 0.316740i
\(409\) −15.1513 −0.749181 −0.374591 0.927190i \(-0.622217\pi\)
−0.374591 + 0.927190i \(0.622217\pi\)
\(410\) −0.287231 + 0.287231i −0.0141853 + 0.0141853i
\(411\) 8.69543 20.9926i 0.428914 1.03549i
\(412\) 14.9378i 0.735932i
\(413\) 19.6414 + 8.13574i 0.966491 + 0.400334i
\(414\) 5.16760 + 12.4757i 0.253974 + 0.613146i
\(415\) 7.70919 3.19325i 0.378429 0.156750i
\(416\) −1.35595 1.35595i −0.0664811 0.0664811i
\(417\) 2.18948 + 2.18948i 0.107219 + 0.107219i
\(418\) 13.2554 5.49059i 0.648345 0.268553i
\(419\) −0.882820 2.13132i −0.0431286 0.104122i 0.900847 0.434136i \(-0.142946\pi\)
−0.943976 + 0.330015i \(0.892946\pi\)
\(420\) 4.55487 + 1.88669i 0.222255 + 0.0920609i
\(421\) 4.11496i 0.200551i 0.994960 + 0.100275i \(0.0319724\pi\)
−0.994960 + 0.100275i \(0.968028\pi\)
\(422\) −4.79111 + 11.5668i −0.233228 + 0.563062i
\(423\) −0.176769 + 0.176769i −0.00859478 + 0.00859478i
\(424\) −3.89443 −0.189130
\(425\) −3.76118 1.68925i −0.182444 0.0819405i
\(426\) −13.8011 −0.668665
\(427\) 23.4239 23.4239i 1.13356 1.13356i
\(428\) −7.73765 + 18.6803i −0.374014 + 0.902949i
\(429\) 13.4343i 0.648614i
\(430\) −7.27564 3.01367i −0.350863 0.145332i
\(431\) 2.37887 + 5.74309i 0.114586 + 0.276635i 0.970760 0.240053i \(-0.0771648\pi\)
−0.856174 + 0.516688i \(0.827165\pi\)
\(432\) −1.84629 + 0.764757i −0.0888295 + 0.0367944i
\(433\) −1.52706 1.52706i −0.0733858 0.0733858i 0.669461 0.742847i \(-0.266525\pi\)
−0.742847 + 0.669461i \(0.766525\pi\)
\(434\) −6.68853 6.68853i −0.321060 0.321060i
\(435\) 14.6857 6.08300i 0.704124 0.291658i
\(436\) 4.25345 + 10.2687i 0.203703 + 0.491783i
\(437\) −27.3057 11.3104i −1.30621 0.541049i
\(438\) 3.76311i 0.179809i
\(439\) 12.8375 30.9925i 0.612700 1.47919i −0.247322 0.968933i \(-0.579551\pi\)
0.860022 0.510256i \(-0.170449\pi\)
\(440\) 2.19004 2.19004i 0.104406 0.104406i
\(441\) 4.76096 0.226712
\(442\) −7.21246 3.23931i −0.343062 0.154078i
\(443\) 17.8435 0.847772 0.423886 0.905716i \(-0.360666\pi\)
0.423886 + 0.905716i \(0.360666\pi\)
\(444\) 13.0458 13.0458i 0.619127 0.619127i
\(445\) 3.71904 8.97856i 0.176299 0.425624i
\(446\) 0.589632i 0.0279199i
\(447\) 30.2166 + 12.5161i 1.42920 + 0.591993i
\(448\) −0.834089 2.01367i −0.0394070 0.0951370i
\(449\) 31.4026 13.0074i 1.48198 0.613856i 0.512425 0.858732i \(-0.328747\pi\)
0.969554 + 0.244877i \(0.0787474\pi\)
\(450\) −1.49661 1.49661i −0.0705507 0.0705507i
\(451\) −0.889609 0.889609i −0.0418900 0.0418900i
\(452\) −11.3550 + 4.70338i −0.534093 + 0.221229i
\(453\) −7.51838 18.1510i −0.353244 0.852807i
\(454\) −16.1927 6.70725i −0.759963 0.314787i
\(455\) 4.17958i 0.195942i
\(456\) −4.00995 + 9.68087i −0.187783 + 0.453348i
\(457\) −13.4932 + 13.4932i −0.631188 + 0.631188i −0.948366 0.317178i \(-0.897265\pi\)
0.317178 + 0.948366i \(0.397265\pi\)
\(458\) −16.5114 −0.771527
\(459\) −5.99522 + 5.65235i −0.279833 + 0.263829i
\(460\) −6.38009 −0.297473
\(461\) 18.6471 18.6471i 0.868483 0.868483i −0.123821 0.992305i \(-0.539515\pi\)
0.992305 + 0.123821i \(0.0395150\pi\)
\(462\) −5.84343 + 14.1073i −0.271861 + 0.656330i
\(463\) 11.5661i 0.537521i 0.963207 + 0.268761i \(0.0866141\pi\)
−0.963207 + 0.268761i \(0.913386\pi\)
\(464\) −6.49242 2.68925i −0.301403 0.124845i
\(465\) 3.75664 + 9.06933i 0.174210 + 0.420580i
\(466\) 19.1475 7.93116i 0.886991 0.367404i
\(467\) 0.546261 + 0.546261i 0.0252779 + 0.0252779i 0.719633 0.694355i \(-0.244310\pi\)
−0.694355 + 0.719633i \(0.744310\pi\)
\(468\) −2.86990 2.86990i −0.132661 0.132661i
\(469\) −18.3990 + 7.62113i −0.849589 + 0.351911i
\(470\) −0.0451999 0.109122i −0.00208491 0.00503343i
\(471\) −34.1912 14.1625i −1.57545 0.652572i
\(472\) 9.75404i 0.448966i
\(473\) 9.33390 22.5340i 0.429173 1.03612i
\(474\) 15.7530 15.7530i 0.723560 0.723560i
\(475\) 4.63246 0.212552
\(476\) −6.16478 6.53874i −0.282562 0.299703i
\(477\) −8.24264 −0.377405
\(478\) 12.2489 12.2489i 0.560251 0.560251i
\(479\) −2.38229 + 5.75135i −0.108850 + 0.262786i −0.968913 0.247401i \(-0.920424\pi\)
0.860064 + 0.510187i \(0.170424\pi\)
\(480\) 2.26197i 0.103244i
\(481\) −14.4502 5.98547i −0.658872 0.272914i
\(482\) −10.5789 25.5397i −0.481855 1.16330i
\(483\) 29.0604 12.0372i 1.32230 0.547713i
\(484\) −0.995200 0.995200i −0.0452364 0.0452364i
\(485\) 0.984249 + 0.984249i 0.0446925 + 0.0446925i
\(486\) −17.1770 + 7.11493i −0.779162 + 0.322740i
\(487\) −2.70956 6.54146i −0.122782 0.296422i 0.850523 0.525938i \(-0.176286\pi\)
−0.973305 + 0.229516i \(0.926286\pi\)
\(488\) 14.0416 + 5.81623i 0.635634 + 0.263288i
\(489\) 26.4037i 1.19402i
\(490\) −0.860819 + 2.07820i −0.0388879 + 0.0938836i
\(491\) −29.8236 + 29.8236i −1.34592 + 1.34592i −0.455879 + 0.890042i \(0.650675\pi\)
−0.890042 + 0.455879i \(0.849325\pi\)
\(492\) 0.918827 0.0414239
\(493\) −28.9619 0.852559i −1.30438 0.0383973i
\(494\) 8.88324 0.399676
\(495\) 4.63527 4.63527i 0.208340 0.208340i
\(496\) 1.66078 4.00948i 0.0745713 0.180031i
\(497\) 13.2984i 0.596514i
\(498\) −17.4380 7.22304i −0.781414 0.323672i
\(499\) −12.6995 30.6592i −0.568506 1.37249i −0.902814 0.430031i \(-0.858503\pi\)
0.334309 0.942464i \(-0.391497\pi\)
\(500\) 0.923880 0.382683i 0.0413171 0.0171141i
\(501\) 22.6035 + 22.6035i 1.00985 + 1.00985i
\(502\) −10.9755 10.9755i −0.489859 0.489859i
\(503\) −7.36754 + 3.05174i −0.328502 + 0.136070i −0.540838 0.841127i \(-0.681893\pi\)
0.212336 + 0.977197i \(0.431893\pi\)
\(504\) −1.76537 4.26197i −0.0786357 0.189843i
\(505\) 5.39488 + 2.23463i 0.240069 + 0.0994399i
\(506\) 19.7603i 0.878454i
\(507\) 8.06998 19.4827i 0.358400 0.865255i
\(508\) 9.87622 9.87622i 0.438187 0.438187i
\(509\) −16.4093 −0.727331 −0.363665 0.931530i \(-0.618475\pi\)
−0.363665 + 0.931530i \(0.618475\pi\)
\(510\) 3.31396 + 8.71771i 0.146745 + 0.386027i
\(511\) −3.62604 −0.160407
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 3.54271 8.55285i 0.156414 0.377618i
\(514\) 26.2379i 1.15730i
\(515\) −13.8007 5.71644i −0.608132 0.251897i
\(516\) 6.81684 + 16.4573i 0.300095 + 0.724492i
\(517\) 0.337972 0.139993i 0.0148640 0.00615686i
\(518\) −12.5706 12.5706i −0.552321 0.552321i
\(519\) 3.73325 + 3.73325i 0.163871 + 0.163871i
\(520\) 1.77164 0.733837i 0.0776915 0.0321809i
\(521\) 4.54033 + 10.9613i 0.198916 + 0.480225i 0.991590 0.129421i \(-0.0413118\pi\)
−0.792674 + 0.609646i \(0.791312\pi\)
\(522\) −13.7413 5.69184i −0.601442 0.249125i
\(523\) 37.8846i 1.65658i 0.560300 + 0.828290i \(0.310686\pi\)
−0.560300 + 0.828290i \(0.689314\pi\)
\(524\) 4.81438 11.6230i 0.210317 0.507751i
\(525\) −3.48614 + 3.48614i −0.152148 + 0.152148i
\(526\) −2.52726 −0.110194
\(527\) 0.526510 17.8858i 0.0229351 0.779119i
\(528\) −7.00575 −0.304886
\(529\) −12.5197 + 12.5197i −0.544334 + 0.544334i
\(530\) 1.49033 3.59798i 0.0647360 0.156286i
\(531\) 20.6446i 0.895901i
\(532\) 9.32824 + 3.86388i 0.404431 + 0.167521i
\(533\) −0.298089 0.719650i −0.0129117 0.0311715i
\(534\) −20.3093 + 8.41237i −0.878867 + 0.364039i
\(535\) −14.2973 14.2973i −0.618127 0.618127i
\(536\) −6.46088 6.46088i −0.279068 0.279068i
\(537\) 21.2947 8.82055i 0.918934 0.380635i
\(538\) −5.84337 14.1071i −0.251925 0.608202i
\(539\) −6.43658 2.66612i −0.277243 0.114838i
\(540\) 1.99841i 0.0859978i
\(541\) 0.993942 2.39959i 0.0427329 0.103166i −0.901072 0.433670i \(-0.857218\pi\)
0.943805 + 0.330503i \(0.107218\pi\)
\(542\) −11.1252 + 11.1252i −0.477869 + 0.477869i
\(543\) 5.06559 0.217385
\(544\) 1.68925 3.76118i 0.0724258 0.161259i
\(545\) −11.1148 −0.476106
\(546\) −6.68506 + 6.68506i −0.286094 + 0.286094i
\(547\) −3.27444 + 7.90519i −0.140005 + 0.338001i −0.978293 0.207226i \(-0.933557\pi\)
0.838288 + 0.545227i \(0.183557\pi\)
\(548\) 10.0453i 0.429115i
\(549\) 29.7194 + 12.3102i 1.26839 + 0.525385i
\(550\) 1.18524 + 2.86143i 0.0505389 + 0.122012i
\(551\) 30.0758 12.4578i 1.28127 0.530721i
\(552\) 10.2047 + 10.2047i 0.434339 + 0.434339i
\(553\) −15.1792 15.1792i −0.645486 0.645486i
\(554\) 24.4537 10.1291i 1.03894 0.430343i
\(555\) 7.06034 + 17.0452i 0.299695 + 0.723527i
\(556\) 1.26469 + 0.523852i 0.0536349 + 0.0222163i
\(557\) 17.8744i 0.757364i 0.925527 + 0.378682i \(0.123623\pi\)
−0.925527 + 0.378682i \(0.876377\pi\)
\(558\) 3.51508 8.48614i 0.148805 0.359247i
\(559\) 10.6783 10.6783i 0.451643 0.451643i
\(560\) 2.17958 0.0921041
\(561\) −27.0004 + 10.2640i −1.13996 + 0.433345i
\(562\) 10.3659 0.437261
\(563\) −6.76659 + 6.76659i −0.285178 + 0.285178i −0.835170 0.549992i \(-0.814631\pi\)
0.549992 + 0.835170i \(0.314631\pi\)
\(564\) −0.102241 + 0.246831i −0.00430512 + 0.0103935i
\(565\) 12.2905i 0.517067i
\(566\) 4.65534 + 1.92831i 0.195679 + 0.0810527i
\(567\) 9.06647 + 21.8884i 0.380756 + 0.919226i
\(568\) −5.63691 + 2.33489i −0.236520 + 0.0979696i
\(569\) −13.4709 13.4709i −0.564729 0.564729i 0.365918 0.930647i \(-0.380755\pi\)
−0.930647 + 0.365918i \(0.880755\pi\)
\(570\) −7.40941 7.40941i −0.310346 0.310346i
\(571\) −9.84467 + 4.07779i −0.411986 + 0.170650i −0.579043 0.815297i \(-0.696574\pi\)
0.167057 + 0.985947i \(0.446574\pi\)
\(572\) 2.27283 + 5.48710i 0.0950318 + 0.229427i
\(573\) −25.5757 10.5938i −1.06844 0.442563i
\(574\) 0.885359i 0.0369542i
\(575\) 2.44155 5.89443i 0.101820 0.245815i
\(576\) 1.49661 1.49661i 0.0623586 0.0623586i
\(577\) 3.43248 0.142896 0.0714480 0.997444i \(-0.477238\pi\)
0.0714480 + 0.997444i \(0.477238\pi\)
\(578\) 1.00000 16.9706i 0.0415945 0.705882i
\(579\) 53.2302 2.21217
\(580\) 4.96908 4.96908i 0.206330 0.206330i
\(581\) −6.95995 + 16.8028i −0.288747 + 0.697097i
\(582\) 3.14853i 0.130511i
\(583\) 11.1436 + 4.61585i 0.461522 + 0.191169i
\(584\) −0.636649 1.53701i −0.0263447 0.0636017i
\(585\) 3.74971 1.55318i 0.155031 0.0642161i
\(586\) −10.1448 10.1448i −0.419078 0.419078i
\(587\) 4.19531 + 4.19531i 0.173159 + 0.173159i 0.788366 0.615207i \(-0.210927\pi\)
−0.615207 + 0.788366i \(0.710927\pi\)
\(588\) 4.70084 1.94715i 0.193859 0.0802991i
\(589\) 7.69350 + 18.5737i 0.317005 + 0.765318i
\(590\) −9.01156 3.73271i −0.371000 0.153673i
\(591\) 61.1358i 2.51479i
\(592\) 3.12132 7.53553i 0.128285 0.309709i
\(593\) −8.23946 + 8.23946i −0.338354 + 0.338354i −0.855748 0.517394i \(-0.826902\pi\)
0.517394 + 0.855748i \(0.326902\pi\)
\(594\) 6.18944 0.253956
\(595\) 8.40017 3.19325i 0.344373 0.130910i
\(596\) 14.4592 0.592270
\(597\) 27.9870 27.9870i 1.14543 1.14543i
\(598\) 4.68194 11.3032i 0.191459 0.462222i
\(599\) 7.52264i 0.307367i 0.988120 + 0.153683i \(0.0491136\pi\)
−0.988120 + 0.153683i \(0.950886\pi\)
\(600\) −2.08979 0.865619i −0.0853153 0.0353388i
\(601\) 8.72192 + 21.0566i 0.355775 + 0.858916i 0.995884 + 0.0906326i \(0.0288889\pi\)
−0.640110 + 0.768284i \(0.721111\pi\)
\(602\) 15.8578 6.56854i 0.646318 0.267714i
\(603\) −13.6746 13.6746i −0.556872 0.556872i
\(604\) −6.14161 6.14161i −0.249898 0.249898i
\(605\) 1.30029 0.538598i 0.0528644 0.0218971i
\(606\) −5.05468 12.2031i −0.205332 0.495716i
\(607\) 2.47909 + 1.02687i 0.100623 + 0.0416795i 0.432427 0.901669i \(-0.357657\pi\)
−0.331804 + 0.943348i \(0.607657\pi\)
\(608\) 4.63246i 0.187871i
\(609\) −13.2584 + 32.0086i −0.537257 + 1.29705i
\(610\) −10.7470 + 10.7470i −0.435133 + 0.435133i
\(611\) 0.226494 0.00916298
\(612\) 3.57532 7.96061i 0.144524 0.321788i
\(613\) 24.0425 0.971066 0.485533 0.874218i \(-0.338626\pi\)
0.485533 + 0.874218i \(0.338626\pi\)
\(614\) 16.8044 16.8044i 0.678170 0.678170i
\(615\) −0.351620 + 0.848885i −0.0141787 + 0.0342304i
\(616\) 6.75057i 0.271988i
\(617\) 30.0134 + 12.4320i 1.20829 + 0.500492i 0.893670 0.448724i \(-0.148121\pi\)
0.314624 + 0.949216i \(0.398121\pi\)
\(618\) 12.9304 + 31.2168i 0.520138 + 1.25573i
\(619\) −20.9655 + 8.68419i −0.842675 + 0.349047i −0.761908 0.647686i \(-0.775737\pi\)
−0.0807670 + 0.996733i \(0.525737\pi\)
\(620\) 3.06872 + 3.06872i 0.123243 + 0.123243i
\(621\) −9.01562 9.01562i −0.361784 0.361784i
\(622\) −26.2186 + 10.8601i −1.05127 + 0.435450i
\(623\) 8.10595 + 19.5695i 0.324758 + 0.784035i
\(624\) −4.00740 1.65992i −0.160424 0.0664499i
\(625\) 1.00000i 0.0400000i
\(626\) −3.29524 + 7.95541i −0.131704 + 0.317962i
\(627\) 22.9483 22.9483i 0.916469 0.916469i
\(628\) −16.3611 −0.652878
\(629\) 0.989538 33.6152i 0.0394554 1.34032i
\(630\) 4.61313 0.183791
\(631\) −11.6556 + 11.6556i −0.464004 + 0.464004i −0.899965 0.435962i \(-0.856408\pi\)
0.435962 + 0.899965i \(0.356408\pi\)
\(632\) 3.76904 9.09927i 0.149924 0.361949i
\(633\) 28.3194i 1.12560i
\(634\) 8.36370 + 3.46436i 0.332165 + 0.137587i
\(635\) 5.34497 + 12.9039i 0.212109 + 0.512076i
\(636\) −8.13854 + 3.37109i −0.322714 + 0.133673i
\(637\) −3.05012 3.05012i −0.120850 0.120850i
\(638\) 15.3902 + 15.3902i 0.609303 + 0.609303i
\(639\) −11.9306 + 4.94183i −0.471969 + 0.195496i
\(640\) 0.382683 + 0.923880i 0.0151269 + 0.0365195i
\(641\) 22.8119 + 9.44900i 0.901016 + 0.373213i 0.784611 0.619989i \(-0.212863\pi\)
0.116405 + 0.993202i \(0.462863\pi\)
\(642\) 45.7359i 1.80505i
\(643\) −2.25830 + 5.45202i −0.0890586 + 0.215006i −0.962133 0.272581i \(-0.912123\pi\)
0.873074 + 0.487587i \(0.162123\pi\)
\(644\) 9.83296 9.83296i 0.387473 0.387473i
\(645\) −17.8133 −0.701396
\(646\) 6.78690 + 17.8536i 0.267027 + 0.702442i
\(647\) 6.56743 0.258192 0.129096 0.991632i \(-0.458792\pi\)
0.129096 + 0.991632i \(0.458792\pi\)
\(648\) −7.68618 + 7.68618i −0.301942 + 0.301942i
\(649\) 11.5609 27.9105i 0.453805 1.09558i
\(650\) 1.91761i 0.0752148i
\(651\) −19.7673 8.18790i −0.774743 0.320909i
\(652\) 4.46701 + 10.7843i 0.174942 + 0.422347i
\(653\) 0.744178 0.308249i 0.0291219 0.0120627i −0.368075 0.929796i \(-0.619983\pi\)
0.397197 + 0.917733i \(0.369983\pi\)
\(654\) 17.7776 + 17.7776i 0.695160 + 0.695160i
\(655\) 8.89582 + 8.89582i 0.347588 + 0.347588i
\(656\) 0.375285 0.155448i 0.0146524 0.00606924i
\(657\) −1.34748 3.25310i −0.0525702 0.126916i
\(658\) 0.237841 + 0.0985168i 0.00927199 + 0.00384058i
\(659\) 5.39957i 0.210337i 0.994454 + 0.105169i \(0.0335383\pi\)
−0.994454 + 0.105169i \(0.966462\pi\)
\(660\) 2.68099 6.47247i 0.104357 0.251941i
\(661\) −27.6342 + 27.6342i −1.07485 + 1.07485i −0.0778836 + 0.996962i \(0.524816\pi\)
−0.996962 + 0.0778836i \(0.975184\pi\)
\(662\) 2.92336 0.113620
\(663\) −17.8765 0.526236i −0.694267 0.0204373i
\(664\) −8.34436 −0.323824
\(665\) −7.13953 + 7.13953i −0.276859 + 0.276859i
\(666\) 6.60634 15.9491i 0.255990 0.618015i
\(667\) 44.8350i 1.73602i
\(668\) 13.0563 + 5.40808i 0.505162 + 0.209245i
\(669\) −0.510397 1.23221i −0.0197331 0.0476399i
\(670\) 8.44155 3.49661i 0.326126 0.135086i
\(671\) −33.2855 33.2855i −1.28497 1.28497i
\(672\) −3.48614 3.48614i −0.134481 0.134481i
\(673\) −15.1202 + 6.26298i −0.582840 + 0.241420i −0.654567 0.756004i \(-0.727149\pi\)
0.0717272 + 0.997424i \(0.477149\pi\)
\(674\) 5.10693 + 12.3292i 0.196712 + 0.474904i
\(675\) 1.84629 + 0.764757i 0.0710636 + 0.0294355i
\(676\) 9.32278i 0.358568i
\(677\) −12.4451 + 30.0452i −0.478305 + 1.15473i 0.482098 + 0.876117i \(0.339875\pi\)
−0.960403 + 0.278614i \(0.910125\pi\)
\(678\) −19.6582 + 19.6582i −0.754967 + 0.754967i
\(679\) −3.03384 −0.116428
\(680\) 2.82843 + 3.00000i 0.108465 + 0.115045i
\(681\) −39.6453 −1.51921
\(682\) −9.50441 + 9.50441i −0.363943 + 0.363943i
\(683\) 0.600330 1.44932i 0.0229710 0.0554569i −0.911978 0.410239i \(-0.865445\pi\)
0.934949 + 0.354783i \(0.115445\pi\)
\(684\) 9.80469i 0.374892i
\(685\) 9.28067 + 3.84418i 0.354596 + 0.146878i
\(686\) −7.71485 18.6253i −0.294554 0.711117i
\(687\) −34.5054 + 14.2926i −1.31646 + 0.545296i
\(688\) 5.56854 + 5.56854i 0.212298 + 0.212298i
\(689\) 5.28067 + 5.28067i 0.201177 + 0.201177i
\(690\) −13.3330 + 5.52273i −0.507580 + 0.210247i
\(691\) 0.492008 + 1.18781i 0.0187169 + 0.0451865i 0.932962 0.359976i \(-0.117215\pi\)
−0.914245 + 0.405162i \(0.867215\pi\)
\(692\) 2.15640 + 0.893211i 0.0819741 + 0.0339548i
\(693\) 14.2877i 0.542746i
\(694\) −13.6996 + 33.0738i −0.520030 + 1.25546i
\(695\) −0.967953 + 0.967953i −0.0367166 + 0.0367166i
\(696\) −15.8956 −0.602523
\(697\) 1.21862 1.14892i 0.0461584 0.0435186i
\(698\) −14.1850 −0.536909
\(699\) 33.1489 33.1489i 1.25381 1.25381i
\(700\) −0.834089 + 2.01367i −0.0315256 + 0.0761096i
\(701\) 2.21212i 0.0835505i 0.999127 + 0.0417752i \(0.0133013\pi\)
−0.999127 + 0.0417752i \(0.986699\pi\)
\(702\) 3.54046 + 1.46650i 0.133626 + 0.0553496i
\(703\) 14.4594 + 34.9080i 0.545346 + 1.31658i
\(704\) −2.86143 + 1.18524i −0.107844 + 0.0446705i
\(705\) −0.188917 0.188917i −0.00711501 0.00711501i
\(706\) −12.3872 12.3872i −0.466198 0.466198i
\(707\) −11.7586 + 4.87056i −0.442227 + 0.183176i
\(708\) 8.44329 + 20.3839i 0.317318 + 0.766074i
\(709\) −25.3245 10.4898i −0.951082 0.393951i −0.147445 0.989070i \(-0.547105\pi\)
−0.803637 + 0.595119i \(0.797105\pi\)
\(710\) 6.10135i 0.228980i
\(711\) 7.97725 19.2588i 0.299170 0.722261i
\(712\) −6.87189 + 6.87189i −0.257535 + 0.257535i
\(713\) 27.6885 1.03694
\(714\) −18.5432 8.32824i −0.693961 0.311677i
\(715\) −5.93919 −0.222113
\(716\) 7.20533 7.20533i 0.269276 0.269276i
\(717\) 14.9947 36.2005i 0.559988 1.35193i
\(718\) 27.5866i 1.02952i
\(719\) −13.5359 5.60674i −0.504803 0.209096i 0.115724 0.993281i \(-0.463081\pi\)
−0.620527 + 0.784185i \(0.713081\pi\)
\(720\) 0.809957 + 1.95541i 0.0301853 + 0.0728738i
\(721\) 30.0798 12.4594i 1.12023 0.464014i
\(722\) −1.73925 1.73925i −0.0647281 0.0647281i
\(723\) −44.2153 44.2153i −1.64439 1.64439i
\(724\) 2.06899 0.857002i 0.0768933 0.0318502i
\(725\) 2.68925 + 6.49242i 0.0998761 + 0.241122i
\(726\) −2.94122 1.21829i −0.109159 0.0452152i
\(727\) 35.9003i 1.33147i 0.746188 + 0.665735i \(0.231882\pi\)
−0.746188 + 0.665735i \(0.768118\pi\)
\(728\) −1.59946 + 3.86143i −0.0592798 + 0.143114i
\(729\) −6.67887 + 6.67887i −0.247365 + 0.247365i
\(730\) 1.66364 0.0615742
\(731\) 29.6196 + 13.3030i 1.09552 + 0.492029i
\(732\) 34.3787 1.27067
\(733\) −28.7070 + 28.7070i −1.06032 + 1.06032i −0.0622582 + 0.998060i \(0.519830\pi\)
−0.998060 + 0.0622582i \(0.980170\pi\)
\(734\) 2.01811 4.87216i 0.0744899 0.179835i
\(735\) 5.08815i 0.187679i
\(736\) 5.89443 + 2.44155i 0.217272 + 0.0899968i
\(737\) 10.8296 + 26.1451i 0.398915 + 0.963066i
\(738\) 0.794299 0.329009i 0.0292386 0.0121110i
\(739\) 15.1436 + 15.1436i 0.557068 + 0.557068i 0.928471 0.371404i \(-0.121123\pi\)
−0.371404 + 0.928471i \(0.621123\pi\)
\(740\) 5.76745 + 5.76745i 0.212016 + 0.212016i
\(741\) 18.5641 7.68950i 0.681969 0.282481i
\(742\) 3.24830 + 7.84210i 0.119249 + 0.287892i
\(743\) −16.2739 6.74088i −0.597032 0.247299i 0.0636406 0.997973i \(-0.479729\pi\)
−0.660673 + 0.750674i \(0.729729\pi\)
\(744\) 9.81657i 0.359893i
\(745\) −5.53328 + 13.3585i −0.202724 + 0.489418i
\(746\) −1.59445 + 1.59445i −0.0583771 + 0.0583771i
\(747\) −17.6610 −0.646183
\(748\) −9.29156 + 8.76017i −0.339733 + 0.320304i
\(749\) 44.0699 1.61028
\(750\) 1.59946 1.59946i 0.0584039 0.0584039i
\(751\) 14.2763 34.4661i 0.520951 1.25769i −0.416362 0.909199i \(-0.636695\pi\)
0.937313 0.348488i \(-0.113305\pi\)
\(752\) 0.118113i 0.00430714i
\(753\) −32.4370 13.4359i −1.18207 0.489630i
\(754\) 5.15692 + 12.4499i 0.187804 + 0.453399i
\(755\) 8.02440 3.32381i 0.292038 0.120966i
\(756\) 3.07994 + 3.07994i 0.112016 + 0.112016i
\(757\) −25.3671 25.3671i −0.921983 0.921983i 0.0751869 0.997169i \(-0.476045\pi\)
−0.997169 + 0.0751869i \(0.976045\pi\)
\(758\) 5.79430 2.40008i 0.210458 0.0871747i
\(759\) −17.1049 41.2949i −0.620869 1.49891i
\(760\) −4.27983 1.77276i −0.155246 0.0643049i
\(761\) 11.3236i 0.410479i −0.978712 0.205240i \(-0.934203\pi\)
0.978712 0.205240i \(-0.0657974\pi\)
\(762\) 12.0902 29.1883i 0.437981 1.05738i
\(763\) 17.1301 17.1301i 0.620151 0.620151i
\(764\) −12.2384 −0.442771
\(765\) 5.98642 + 6.34956i 0.216440 + 0.229569i
\(766\) 13.1414 0.474817
\(767\) 13.2260 13.2260i 0.477564 0.477564i
\(768\) 0.865619 2.08979i 0.0312354 0.0754088i
\(769\) 2.65802i 0.0958505i −0.998851 0.0479253i \(-0.984739\pi\)
0.998851 0.0479253i \(-0.0152609\pi\)
\(770\) −6.23671 2.58333i −0.224756 0.0930968i
\(771\) 22.7120 + 54.8317i 0.817954 + 1.97472i
\(772\) 21.7413 9.00555i 0.782488 0.324117i
\(773\) 30.9014 + 30.9014i 1.11145 + 1.11145i 0.992955 + 0.118491i \(0.0378057\pi\)
0.118491 + 0.992955i \(0.462194\pi\)
\(774\) 11.7859 + 11.7859i 0.423636 + 0.423636i
\(775\) −4.00948 + 1.66078i −0.144025 + 0.0596570i
\(776\) −0.532672 1.28598i −0.0191218 0.0461641i
\(777\) −37.1513 15.3886i −1.33280 0.552062i
\(778\) 22.0051i 0.788922i
\(779\) −0.720108 + 1.73849i −0.0258005 + 0.0622880i
\(780\) 3.06713 3.06713i 0.109821 0.109821i
\(781\) 18.8970 0.676189
\(782\) 26.2944 + 0.774034i 0.940285 + 0.0276794i
\(783\) 14.0435 0.501873
\(784\) 1.59059 1.59059i 0.0568067 0.0568067i
\(785\) 6.26111 15.1157i 0.223469 0.539501i
\(786\) 28.4570i 1.01503i
\(787\) −33.5552 13.8990i −1.19611 0.495446i −0.306371 0.951912i \(-0.599115\pi\)
−0.889741 + 0.456466i \(0.849115\pi\)
\(788\) −10.3430 24.9703i −0.368455 0.889530i
\(789\) −5.28145 + 2.18765i −0.188025 + 0.0778823i
\(790\) 6.96428 + 6.96428i 0.247778 + 0.247778i
\(791\) 18.9421 + 18.9421i 0.673504 + 0.673504i
\(792\) −6.05627 + 2.50859i −0.215200 + 0.0891389i
\(793\) −11.1532 26.9263i −0.396063 0.956182i
\(794\) 2.39104 + 0.990400i 0.0848547 + 0.0351480i
\(795\) 8.80910i 0.312426i
\(796\) 6.69613 16.1659i 0.237338 0.572985i
\(797\) 11.9755 11.9755i 0.424193 0.424193i −0.462452 0.886645i \(-0.653030\pi\)
0.886645 + 0.462452i \(0.153030\pi\)
\(798\) 22.8387 0.808482
\(799\) 0.173044 + 0.455211i 0.00612187 + 0.0161042i
\(800\) −1.00000 −0.0353553
\(801\) −14.5445 + 14.5445i −0.513905 + 0.513905i
\(802\) 4.67913 11.2964i 0.165226 0.398890i
\(803\) 5.15261i 0.181832i
\(804\) −19.0946 7.90923i −0.673413 0.278937i
\(805\) 5.32156 + 12.8474i 0.187560 + 0.452811i
\(806\) −7.68861 + 3.18473i −0.270820 + 0.112177i
\(807\) −24.4228 24.4228i −0.859724 0.859724i
\(808\) −4.12906 4.12906i −0.145260 0.145260i
\(809\) 21.2912 8.81909i 0.748558 0.310063i 0.0244047 0.999702i \(-0.492231\pi\)
0.724153 + 0.689639i \(0.242231\pi\)
\(810\) −4.15973 10.0425i −0.146158 0.352857i
\(811\) 9.13563 + 3.78410i 0.320795 + 0.132878i 0.537270 0.843411i \(-0.319456\pi\)
−0.216474 + 0.976288i \(0.569456\pi\)
\(812\) 15.3167i 0.537509i
\(813\) −13.6192 + 32.8796i −0.477645 + 1.15314i
\(814\) −17.8629 + 17.8629i −0.626093 + 0.626093i
\(815\) −11.6729 −0.408883
\(816\) 0.274423 9.32231i 0.00960674 0.326346i
\(817\) −36.4811 −1.27631
\(818\) −10.7136 + 10.7136i −0.374591 + 0.374591i
\(819\) −3.38528 + 8.17279i −0.118291 + 0.285580i
\(820\) 0.406206i 0.0141853i
\(821\) −25.0560 10.3786i −0.874462 0.362214i −0.100115 0.994976i \(-0.531921\pi\)
−0.774346 + 0.632762i \(0.781921\pi\)
\(822\) −8.69543 20.9926i −0.303288 0.732201i
\(823\) −29.3578 + 12.1604i −1.02335 + 0.423884i −0.830307 0.557307i \(-0.811835\pi\)
−0.193040 + 0.981191i \(0.561835\pi\)
\(824\) 10.5626 + 10.5626i 0.367966 + 0.367966i
\(825\) 4.95382 + 4.95382i 0.172470 + 0.172470i
\(826\) 19.6414 8.13574i 0.683412 0.283079i
\(827\) −10.6086 25.6115i −0.368898 0.890598i −0.993932 0.110000i \(-0.964915\pi\)
0.625034 0.780598i \(-0.285085\pi\)
\(828\) 12.4757 + 5.16760i 0.433560 + 0.179586i
\(829\) 34.9929i 1.21535i −0.794185 0.607676i \(-0.792102\pi\)
0.794185 0.607676i \(-0.207898\pi\)
\(830\) 3.19325 7.70919i 0.110839 0.267590i
\(831\) 42.3352 42.3352i 1.46859 1.46859i
\(832\) −1.91761 −0.0664811
\(833\) 3.79984 8.46050i 0.131657 0.293139i
\(834\) 3.09640 0.107219
\(835\) −9.99284 + 9.99284i −0.345816 + 0.345816i
\(836\) 5.49059 13.2554i 0.189896 0.458449i
\(837\) 8.67275i 0.299774i
\(838\) −2.13132 0.882820i −0.0736251 0.0304965i
\(839\) −0.199693 0.482102i −0.00689418 0.0166440i 0.920395 0.390990i \(-0.127867\pi\)
−0.927289 + 0.374346i \(0.877867\pi\)
\(840\) 4.55487 1.88669i 0.157158 0.0650969i
\(841\) 14.4133 + 14.4133i 0.497011 + 0.497011i
\(842\) 2.90971 + 2.90971i 0.100275 + 0.100275i
\(843\) 21.6627 8.97297i 0.746102 0.309045i
\(844\) 4.79111 + 11.5668i 0.164917 + 0.398145i
\(845\) 8.61313 + 3.56767i 0.296301 + 0.122732i
\(846\) 0.249988i 0.00859478i
\(847\) −1.17392 + 2.83409i −0.0403363 + 0.0973805i
\(848\) −2.75378 + 2.75378i −0.0945651 + 0.0945651i
\(849\) 11.3979 0.391174
\(850\) −3.85403 + 1.46508i −0.132192 + 0.0502517i
\(851\) 52.0386 1.78386
\(852\) −9.75884 + 9.75884i −0.334332 + 0.334332i
\(853\) −7.00774 + 16.9182i −0.239941 + 0.579268i −0.997276 0.0737581i \(-0.976501\pi\)
0.757336 + 0.653026i \(0.226501\pi\)
\(854\) 33.1264i 1.13356i
\(855\) −9.05835 3.75209i −0.309789 0.128319i
\(856\) 7.73765 + 18.6803i 0.264468 + 0.638481i
\(857\) 11.0386 4.57235i 0.377073 0.156189i −0.186094 0.982532i \(-0.559583\pi\)
0.563167 + 0.826343i \(0.309583\pi\)
\(858\) 9.49948 + 9.49948i 0.324307 + 0.324307i
\(859\) −5.54403 5.54403i −0.189160 0.189160i 0.606173 0.795333i \(-0.292704\pi\)
−0.795333 + 0.606173i \(0.792704\pi\)
\(860\) −7.27564 + 3.01367i −0.248097 + 0.102765i
\(861\) −0.766384 1.85021i −0.0261183 0.0630551i
\(862\) 5.74309 + 2.37887i 0.195610 + 0.0810245i
\(863\) 29.2172i 0.994564i −0.867589 0.497282i \(-0.834331\pi\)
0.867589 0.497282i \(-0.165669\pi\)
\(864\) −0.764757 + 1.84629i −0.0260176 + 0.0628120i
\(865\) −1.65044 + 1.65044i −0.0561166 + 0.0561166i
\(866\) −2.15959 −0.0733858
\(867\) −12.6003 36.3305i −0.427927 1.23385i
\(868\) −9.45901 −0.321060
\(869\) −21.5697 + 21.5697i −0.731701 + 0.731701i
\(870\) 6.08300 14.6857i 0.206233 0.497891i
\(871\) 17.5213i 0.593687i
\(872\) 10.2687 + 4.25345i 0.347743 + 0.144040i
\(873\) −1.12741 2.72181i −0.0381571 0.0921193i
\(874\) −27.3057 + 11.3104i −0.923629 + 0.382580i
\(875\) −1.54120 1.54120i −0.0521019 0.0521019i
\(876\) −2.66092 2.66092i −0.0899043 0.0899043i
\(877\) −33.1725 + 13.7405i −1.12015 + 0.463983i −0.864423 0.502765i \(-0.832316\pi\)
−0.255731 + 0.966748i \(0.582316\pi\)
\(878\) −12.8375 30.9925i −0.433245 1.04595i
\(879\) −29.9821 12.4190i −1.01127 0.418882i
\(880\) 3.09719i 0.104406i
\(881\) 11.9967 28.9626i 0.404179 0.975773i −0.582462 0.812858i \(-0.697910\pi\)
0.986640 0.162915i \(-0.0520896\pi\)
\(882\) 3.36651 3.36651i 0.113356 0.113356i
\(883\) 7.04521 0.237090 0.118545 0.992949i \(-0.462177\pi\)
0.118545 + 0.992949i \(0.462177\pi\)
\(884\) −7.39052 + 2.80944i −0.248570 + 0.0944917i
\(885\) −22.0634 −0.741652
\(886\) 12.6173 12.6173i 0.423886 0.423886i
\(887\) 3.87848 9.36347i 0.130227 0.314395i −0.845295 0.534301i \(-0.820575\pi\)
0.975521 + 0.219906i \(0.0705750\pi\)
\(888\) 18.4496i 0.619127i
\(889\) −28.1251 11.6498i −0.943286 0.390722i
\(890\) −3.71904 8.97856i −0.124663 0.300962i
\(891\) 31.1035 12.8835i 1.04200 0.431613i
\(892\) −0.416933 0.416933i −0.0139599 0.0139599i
\(893\) −0.386896 0.386896i −0.0129470 0.0129470i
\(894\) 30.2166 12.5161i 1.01059 0.418602i
\(895\) 3.89949 + 9.41421i 0.130346 + 0.314682i
\(896\) −2.01367 0.834089i −0.0672720 0.0278650i
\(897\) 27.6741i 0.924012i
\(898\) 13.0074 31.4026i 0.434062 1.04792i
\(899\) −21.5650 + 21.5650i −0.719232 + 0.719232i
\(900\) −2.11652 −0.0705507
\(901\) −6.57865 + 14.6476i −0.219167 + 0.487984i
\(902\) −1.25810 −0.0418900
\(903\) 27.4537 27.4537i 0.913603 0.913603i
\(904\) −4.70338 + 11.3550i −0.156432 + 0.377661i
\(905\) 2.23946i 0.0744420i
\(906\) −18.1510 7.51838i −0.603025 0.249781i
\(907\) 19.9266 + 48.1070i 0.661651 + 1.59737i 0.795215 + 0.606327i \(0.207358\pi\)
−0.133564 + 0.991040i \(0.542642\pi\)
\(908\) −16.1927 + 6.70725i −0.537375 + 0.222588i
\(909\) −8.73925 8.73925i −0.289863 0.289863i
\(910\) −2.95541 2.95541i −0.0979709 0.0979709i
\(911\) −24.5429 + 10.1660i −0.813143 + 0.336815i −0.750207 0.661203i \(-0.770046\pi\)
−0.0629355 + 0.998018i \(0.520046\pi\)
\(912\) 4.00995 + 9.68087i 0.132783 + 0.320565i
\(913\) 23.8768 + 9.89010i 0.790207 + 0.327314i
\(914\) 19.0823i 0.631188i
\(915\) −13.1562 + 31.7618i −0.434929 + 1.05001i
\(916\) −11.6753 + 11.6753i −0.385764 + 0.385764i
\(917\) −27.4204 −0.905502
\(918\) −0.242447 + 8.23608i −0.00800196 + 0.271831i
\(919\) 21.1045 0.696174 0.348087 0.937462i \(-0.386831\pi\)
0.348087 + 0.937462i \(0.386831\pi\)
\(920\) −4.51140 + 4.51140i −0.148737 + 0.148737i
\(921\) 20.5714 49.6639i 0.677852 1.63648i
\(922\) 26.3710i 0.868483i
\(923\) 10.8094 + 4.47740i 0.355795 + 0.147375i
\(924\) 5.84343 + 14.1073i 0.192235 + 0.464095i
\(925\) −7.53553 + 3.12132i −0.247767 + 0.102628i
\(926\) 8.17845 + 8.17845i 0.268761 + 0.268761i
\(927\) 22.3560 + 22.3560i 0.734267 + 0.734267i
\(928\) −6.49242 + 2.68925i −0.213124 + 0.0882788i
\(929\) −13.4185 32.3951i −0.440246 1.06285i −0.975862 0.218387i \(-0.929921\pi\)
0.535616 0.844462i \(-0.320079\pi\)
\(930\) 9.06933 + 3.75664i 0.297395 + 0.123185i
\(931\) 10.4204i 0.341514i
\(932\) 7.93116 19.1475i 0.259794 0.627197i
\(933\) −45.3907 + 45.3907i −1.48602 + 1.48602i
\(934\) 0.772529 0.0252779
\(935\) −4.53762 11.9367i −0.148396 0.390370i
\(936\) −4.05866 −0.132661
\(937\) 5.36321 5.36321i 0.175208 0.175208i −0.614055 0.789263i \(-0.710463\pi\)
0.789263 + 0.614055i \(0.210463\pi\)
\(938\) −7.62113 + 18.3990i −0.248839 + 0.600750i
\(939\) 19.4776i 0.635626i
\(940\) −0.109122 0.0451999i −0.00355917 0.00147426i
\(941\) −14.0258 33.8613i −0.457228 1.10385i −0.969515 0.245032i \(-0.921202\pi\)
0.512287 0.858814i \(-0.328798\pi\)
\(942\) −34.1912 + 14.1625i −1.11401 + 0.461438i
\(943\) 1.83256 + 1.83256i 0.0596763 + 0.0596763i
\(944\) 6.89715 + 6.89715i 0.224483 + 0.224483i
\(945\) −4.02413 + 1.66685i −0.130905 + 0.0542226i
\(946\) −9.33390 22.5340i −0.303471 0.732645i
\(947\) 55.6670 + 23.0580i 1.80893 + 0.749285i 0.982503 + 0.186249i \(0.0596331\pi\)
0.826432 + 0.563036i \(0.190367\pi\)
\(948\) 22.2781i 0.723560i
\(949\) −1.22084 + 2.94737i −0.0396302 + 0.0956758i
\(950\) 3.27564 3.27564i 0.106276 0.106276i
\(951\) 20.4772 0.664018
\(952\) −8.98275 0.264427i −0.291133 0.00857014i
\(953\) 39.9833 1.29518 0.647592 0.761987i \(-0.275776\pi\)
0.647592 + 0.761987i \(0.275776\pi\)
\(954\) −5.82843 + 5.82843i −0.188702 + 0.188702i
\(955\) 4.68344 11.3068i 0.151553 0.365880i
\(956\) 17.3225i 0.560251i
\(957\) 45.4843 + 18.8402i 1.47030 + 0.609017i
\(958\) 2.38229 + 5.75135i 0.0769682 + 0.185818i
\(959\) −20.2280 + 8.37870i −0.653195 + 0.270562i
\(960\) 1.59946 + 1.59946i 0.0516222 + 0.0516222i
\(961\) 8.60258 + 8.60258i 0.277503 + 0.277503i
\(962\) −14.4502 + 5.98547i −0.465893 + 0.192979i
\(963\) 16.3769 + 39.5373i 0.527738 + 1.27407i
\(964\) −25.5397 10.5789i −0.822578 0.340723i
\(965\) 23.5326i 0.757543i
\(966\) 12.0372 29.0604i 0.387291 0.935004i
\(967\) 21.2217 21.2217i 0.682443 0.682443i −0.278107 0.960550i \(-0.589707\pi\)
0.960550 + 0.278107i \(0.0897071\pi\)
\(968\) −1.40743 −0.0452364
\(969\) 29.6377 + 31.4355i 0.952099 + 1.00985i
\(970\) 1.39194 0.0446925
\(971\) −40.6704 + 40.6704i −1.30518 + 1.30518i −0.380322 + 0.924854i \(0.624187\pi\)
−0.924854 + 0.380322i \(0.875813\pi\)
\(972\) −7.11493 + 17.1770i −0.228211 + 0.550951i
\(973\) 2.98361i 0.0956502i
\(974\) −6.54146 2.70956i −0.209602 0.0868200i
\(975\) 1.65992 + 4.00740i 0.0531599 + 0.128339i
\(976\) 14.0416 5.81623i 0.449461 0.186173i
\(977\) −27.3214 27.3214i −0.874088 0.874088i 0.118827 0.992915i \(-0.462087\pi\)
−0.992915 + 0.118827i \(0.962087\pi\)
\(978\) 18.6702 + 18.6702i 0.597009 + 0.597009i
\(979\) 27.8083 11.5186i 0.888757 0.368135i
\(980\) 0.860819 + 2.07820i 0.0274979 + 0.0663857i
\(981\) 21.7340 + 9.00251i 0.693913 + 0.287428i
\(982\) 42.1770i 1.34592i
\(983\) 14.1239 34.0981i 0.450483 1.08756i −0.521656 0.853156i \(-0.674686\pi\)
0.972139 0.234406i \(-0.0753144\pi\)
\(984\) 0.649709 0.649709i 0.0207120 0.0207120i
\(985\) 27.0277 0.861173
\(986\) −21.0820 + 19.8763i −0.671388 + 0.632991i
\(987\) 0.582315 0.0185353
\(988\) 6.28140 6.28140i 0.199838 0.199838i
\(989\) −19.2275 + 46.4192i −0.611398 + 1.47605i
\(990\) 6.55526i 0.208340i
\(991\) −29.2718 12.1248i −0.929850 0.385156i −0.134228 0.990950i \(-0.542856\pi\)
−0.795621 + 0.605794i \(0.792856\pi\)
\(992\) −1.66078 4.00948i −0.0527298 0.127301i
\(993\) 6.10921 2.53052i 0.193870 0.0803036i
\(994\) 9.40338 + 9.40338i 0.298257 + 0.298257i
\(995\) 12.3728 + 12.3728i 0.392245 + 0.392245i
\(996\) −17.4380 + 7.22304i −0.552543 + 0.228871i
\(997\) 3.09573 + 7.47375i 0.0980427 + 0.236696i 0.965289 0.261183i \(-0.0841125\pi\)
−0.867247 + 0.497879i \(0.834112\pi\)
\(998\) −30.6592 12.6995i −0.970500 0.401994i
\(999\) 16.2998i 0.515703i
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 170.2.k.a.161.2 yes 8
5.2 odd 4 850.2.o.c.399.1 8
5.3 odd 4 850.2.o.f.399.2 8
5.4 even 2 850.2.l.d.501.1 8
17.6 odd 16 2890.2.b.p.2311.2 8
17.7 odd 16 2890.2.a.bf.1.1 4
17.10 odd 16 2890.2.a.bc.1.4 4
17.11 odd 16 2890.2.b.p.2311.7 8
17.15 even 8 inner 170.2.k.a.151.2 8
85.32 odd 8 850.2.o.f.49.2 8
85.49 even 8 850.2.l.d.151.1 8
85.83 odd 8 850.2.o.c.49.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.k.a.151.2 8 17.15 even 8 inner
170.2.k.a.161.2 yes 8 1.1 even 1 trivial
850.2.l.d.151.1 8 85.49 even 8
850.2.l.d.501.1 8 5.4 even 2
850.2.o.c.49.1 8 85.83 odd 8
850.2.o.c.399.1 8 5.2 odd 4
850.2.o.f.49.2 8 85.32 odd 8
850.2.o.f.399.2 8 5.3 odd 4
2890.2.a.bc.1.4 4 17.10 odd 16
2890.2.a.bf.1.1 4 17.7 odd 16
2890.2.b.p.2311.2 8 17.6 odd 16
2890.2.b.p.2311.7 8 17.11 odd 16