Properties

Label 170.2.k.a.121.2
Level $170$
Weight $2$
Character 170.121
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 121.2
Root \(0.382683 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 170.121
Dual form 170.2.k.a.111.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.52334 - 0.630986i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(-1.52334 - 0.630986i) q^{6} +(1.24830 - 3.01367i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.198912 + 0.198912i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.52334 - 0.630986i) q^{3} +1.00000i q^{4} +(0.382683 + 0.923880i) q^{5} +(-1.52334 - 0.630986i) q^{6} +(1.24830 - 3.01367i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.198912 + 0.198912i) q^{9} +(0.382683 - 0.923880i) q^{10} +(3.58012 + 1.48294i) q^{11} +(0.630986 + 1.52334i) q^{12} -0.386874i q^{13} +(-3.01367 + 1.24830i) q^{14} +(1.16591 + 1.16591i) q^{15} -1.00000 q^{16} +(-3.76118 - 1.68925i) q^{17} +0.281305 q^{18} +(-3.89715 - 3.89715i) q^{19} +(-0.923880 + 0.382683i) q^{20} -5.37849i q^{21} +(-1.48294 - 3.58012i) q^{22} +(6.91082 + 2.86256i) q^{23} +(0.630986 - 1.52334i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-0.273561 + 0.273561i) q^{26} +(-2.07046 + 4.99853i) q^{27} +(3.01367 + 1.24830i) q^{28} +(0.192641 + 0.465076i) q^{29} -1.64885i q^{30} +(-10.2715 + 4.25457i) q^{31} +(0.707107 + 0.707107i) q^{32} +6.38944 q^{33} +(1.46508 + 3.85403i) q^{34} +3.26197 q^{35} +(-0.198912 - 0.198912i) q^{36} +(1.12132 - 0.464466i) q^{37} +5.51140i q^{38} +(-0.244112 - 0.589339i) q^{39} +(0.923880 + 0.382683i) q^{40} +(-3.32023 + 8.01575i) q^{41} +(-3.80317 + 3.80317i) q^{42} +(0.190043 - 0.190043i) q^{43} +(-1.48294 + 3.58012i) q^{44} +(-0.259892 - 0.107651i) q^{45} +(-2.86256 - 6.91082i) q^{46} +5.12906i q^{47} +(-1.52334 + 0.630986i) q^{48} +(-2.57420 - 2.57420i) q^{49} +1.00000 q^{50} +(-6.79543 - 0.200039i) q^{51} +0.386874 q^{52} +(-0.609919 - 0.609919i) q^{53} +(4.99853 - 2.07046i) q^{54} +3.87510i q^{55} +(-1.24830 - 3.01367i) q^{56} +(-8.39572 - 3.47762i) q^{57} +(0.192641 - 0.465076i) q^{58} +(-6.03300 + 6.03300i) q^{59} +(-1.16591 + 1.16591i) q^{60} +(2.59120 - 6.25570i) q^{61} +(10.2715 + 4.25457i) q^{62} +(0.351153 + 0.847759i) q^{63} -1.00000i q^{64} +(0.357425 - 0.148050i) q^{65} +(-4.51802 - 4.51802i) q^{66} -2.38009 q^{67} +(1.68925 - 3.76118i) q^{68} +12.3337 q^{69} +(-2.30656 - 2.30656i) q^{70} +(8.21885 - 3.40436i) q^{71} +0.281305i q^{72} +(-2.69971 - 6.51767i) q^{73} +(-1.12132 - 0.464466i) q^{74} +(-0.630986 + 1.52334i) q^{75} +(3.89715 - 3.89715i) q^{76} +(8.93816 - 8.93816i) q^{77} +(-0.244112 + 0.589339i) q^{78} +(4.55215 + 1.88556i) q^{79} +(-0.382683 - 0.923880i) q^{80} +8.07695i q^{81} +(8.01575 - 3.32023i) q^{82} +(-4.21738 - 4.21738i) q^{83} +5.37849 q^{84} +(0.121320 - 4.12132i) q^{85} -0.268761 q^{86} +(0.586913 + 0.586913i) q^{87} +(3.58012 - 1.48294i) q^{88} -12.0479i q^{89} +(0.107651 + 0.259892i) q^{90} +(-1.16591 - 0.482936i) q^{91} +(-2.86256 + 6.91082i) q^{92} +(-12.9623 + 12.9623i) q^{93} +(3.62680 - 3.62680i) q^{94} +(2.10912 - 5.09187i) q^{95} +(1.52334 + 0.630986i) q^{96} +(-4.46961 - 10.7906i) q^{97} +3.64047i q^{98} +(-1.00711 + 0.417157i) 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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) 1.52334 0.630986i 0.879498 0.364300i 0.103196 0.994661i \(-0.467093\pi\)
0.776302 + 0.630361i \(0.217093\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0.382683 + 0.923880i 0.171141 + 0.413171i
\(6\) −1.52334 0.630986i −0.621899 0.257599i
\(7\) 1.24830 3.01367i 0.471814 1.13906i −0.491547 0.870851i \(-0.663568\pi\)
0.963361 0.268209i \(-0.0864317\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.198912 + 0.198912i −0.0663041 + 0.0663041i
\(10\) 0.382683 0.923880i 0.121015 0.292156i
\(11\) 3.58012 + 1.48294i 1.07945 + 0.447122i 0.850316 0.526273i \(-0.176411\pi\)
0.229133 + 0.973395i \(0.426411\pi\)
\(12\) 0.630986 + 1.52334i 0.182150 + 0.439749i
\(13\) 0.386874i 0.107300i −0.998560 0.0536498i \(-0.982915\pi\)
0.998560 0.0536498i \(-0.0170855\pi\)
\(14\) −3.01367 + 1.24830i −0.805437 + 0.333623i
\(15\) 1.16591 + 1.16591i 0.301037 + 0.301037i
\(16\) −1.00000 −0.250000
\(17\) −3.76118 1.68925i −0.912219 0.409702i
\(18\) 0.281305 0.0663041
\(19\) −3.89715 3.89715i −0.894067 0.894067i 0.100836 0.994903i \(-0.467848\pi\)
−0.994903 + 0.100836i \(0.967848\pi\)
\(20\) −0.923880 + 0.382683i −0.206586 + 0.0855706i
\(21\) 5.37849i 1.17368i
\(22\) −1.48294 3.58012i −0.316163 0.763285i
\(23\) 6.91082 + 2.86256i 1.44101 + 0.596884i 0.960042 0.279857i \(-0.0902869\pi\)
0.480964 + 0.876741i \(0.340287\pi\)
\(24\) 0.630986 1.52334i 0.128800 0.310950i
\(25\) −0.707107 + 0.707107i −0.141421 + 0.141421i
\(26\) −0.273561 + 0.273561i −0.0536498 + 0.0536498i
\(27\) −2.07046 + 4.99853i −0.398460 + 0.961967i
\(28\) 3.01367 + 1.24830i 0.569530 + 0.235907i
\(29\) 0.192641 + 0.465076i 0.0357725 + 0.0863624i 0.940756 0.339084i \(-0.110117\pi\)
−0.904984 + 0.425446i \(0.860117\pi\)
\(30\) 1.64885i 0.301037i
\(31\) −10.2715 + 4.25457i −1.84481 + 0.764144i −0.900781 + 0.434274i \(0.857005\pi\)
−0.944026 + 0.329871i \(0.892995\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 6.38944 1.11226
\(34\) 1.46508 + 3.85403i 0.251258 + 0.660961i
\(35\) 3.26197 0.551374
\(36\) −0.198912 0.198912i −0.0331521 0.0331521i
\(37\) 1.12132 0.464466i 0.184344 0.0763578i −0.288602 0.957449i \(-0.593191\pi\)
0.472946 + 0.881091i \(0.343191\pi\)
\(38\) 5.51140i 0.894067i
\(39\) −0.244112 0.589339i −0.0390892 0.0943698i
\(40\) 0.923880 + 0.382683i 0.146078 + 0.0605076i
\(41\) −3.32023 + 8.01575i −0.518533 + 1.25185i 0.420271 + 0.907399i \(0.361935\pi\)
−0.938804 + 0.344451i \(0.888065\pi\)
\(42\) −3.80317 + 3.80317i −0.586842 + 0.586842i
\(43\) 0.190043 0.190043i 0.0289813 0.0289813i −0.692468 0.721449i \(-0.743476\pi\)
0.721449 + 0.692468i \(0.243476\pi\)
\(44\) −1.48294 + 3.58012i −0.223561 + 0.539724i
\(45\) −0.259892 0.107651i −0.0387423 0.0160476i
\(46\) −2.86256 6.91082i −0.422061 1.01894i
\(47\) 5.12906i 0.748151i 0.927398 + 0.374075i \(0.122040\pi\)
−0.927398 + 0.374075i \(0.877960\pi\)
\(48\) −1.52334 + 0.630986i −0.219875 + 0.0910750i
\(49\) −2.57420 2.57420i −0.367743 0.367743i
\(50\) 1.00000 0.141421
\(51\) −6.79543 0.200039i −0.951550 0.0280110i
\(52\) 0.386874 0.0536498
\(53\) −0.609919 0.609919i −0.0837788 0.0837788i 0.663976 0.747754i \(-0.268868\pi\)
−0.747754 + 0.663976i \(0.768868\pi\)
\(54\) 4.99853 2.07046i 0.680214 0.281754i
\(55\) 3.87510i 0.522518i
\(56\) −1.24830 3.01367i −0.166811 0.402719i
\(57\) −8.39572 3.47762i −1.11204 0.460622i
\(58\) 0.192641 0.465076i 0.0252950 0.0610674i
\(59\) −6.03300 + 6.03300i −0.785430 + 0.785430i −0.980741 0.195311i \(-0.937428\pi\)
0.195311 + 0.980741i \(0.437428\pi\)
\(60\) −1.16591 + 1.16591i −0.150518 + 0.150518i
\(61\) 2.59120 6.25570i 0.331769 0.800960i −0.666683 0.745341i \(-0.732287\pi\)
0.998452 0.0556194i \(-0.0177133\pi\)
\(62\) 10.2715 + 4.25457i 1.30448 + 0.540332i
\(63\) 0.351153 + 0.847759i 0.0442412 + 0.106808i
\(64\) 1.00000i 0.125000i
\(65\) 0.357425 0.148050i 0.0443331 0.0183634i
\(66\) −4.51802 4.51802i −0.556130 0.556130i
\(67\) −2.38009 −0.290774 −0.145387 0.989375i \(-0.546443\pi\)
−0.145387 + 0.989375i \(0.546443\pi\)
\(68\) 1.68925 3.76118i 0.204851 0.456110i
\(69\) 12.3337 1.48481
\(70\) −2.30656 2.30656i −0.275687 0.275687i
\(71\) 8.21885 3.40436i 0.975398 0.404023i 0.162679 0.986679i \(-0.447986\pi\)
0.812719 + 0.582656i \(0.197986\pi\)
\(72\) 0.281305i 0.0331521i
\(73\) −2.69971 6.51767i −0.315977 0.762836i −0.999460 0.0328692i \(-0.989536\pi\)
0.683483 0.729967i \(-0.260464\pi\)
\(74\) −1.12132 0.464466i −0.130351 0.0539931i
\(75\) −0.630986 + 1.52334i −0.0728600 + 0.175900i
\(76\) 3.89715 3.89715i 0.447034 0.447034i
\(77\) 8.93816 8.93816i 1.01860 1.01860i
\(78\) −0.244112 + 0.589339i −0.0276403 + 0.0667295i
\(79\) 4.55215 + 1.88556i 0.512157 + 0.212142i 0.623768 0.781610i \(-0.285601\pi\)
−0.111611 + 0.993752i \(0.535601\pi\)
\(80\) −0.382683 0.923880i −0.0427853 0.103293i
\(81\) 8.07695i 0.897439i
\(82\) 8.01575 3.32023i 0.885192 0.366658i
\(83\) −4.21738 4.21738i −0.462918 0.462918i 0.436693 0.899611i \(-0.356150\pi\)
−0.899611 + 0.436693i \(0.856150\pi\)
\(84\) 5.37849 0.586842
\(85\) 0.121320 4.12132i 0.0131590 0.447020i
\(86\) −0.268761 −0.0289813
\(87\) 0.586913 + 0.586913i 0.0629236 + 0.0629236i
\(88\) 3.58012 1.48294i 0.381643 0.158082i
\(89\) 12.0479i 1.27707i −0.769591 0.638537i \(-0.779540\pi\)
0.769591 0.638537i \(-0.220460\pi\)
\(90\) 0.107651 + 0.259892i 0.0113474 + 0.0273950i
\(91\) −1.16591 0.482936i −0.122221 0.0506255i
\(92\) −2.86256 + 6.91082i −0.298442 + 0.720503i
\(93\) −12.9623 + 12.9623i −1.34413 + 1.34413i
\(94\) 3.62680 3.62680i 0.374075 0.374075i
\(95\) 2.10912 5.09187i 0.216391 0.522415i
\(96\) 1.52334 + 0.630986i 0.155475 + 0.0643998i
\(97\) −4.46961 10.7906i −0.453820 1.09562i −0.970858 0.239656i \(-0.922965\pi\)
0.517037 0.855963i \(-0.327035\pi\)
\(98\) 3.64047i 0.367743i
\(99\) −1.00711 + 0.417157i −0.101218 + 0.0419258i
\(100\) −0.707107 0.707107i −0.0707107 0.0707107i
\(101\) −5.24718 −0.522114 −0.261057 0.965323i \(-0.584071\pi\)
−0.261057 + 0.965323i \(0.584071\pi\)
\(102\) 4.66364 + 4.94654i 0.461769 + 0.489780i
\(103\) 16.8149 1.65682 0.828408 0.560125i \(-0.189247\pi\)
0.828408 + 0.560125i \(0.189247\pi\)
\(104\) −0.273561 0.273561i −0.0268249 0.0268249i
\(105\) 4.96908 2.05826i 0.484932 0.200866i
\(106\) 0.862555i 0.0837788i
\(107\) −3.91601 9.45410i −0.378575 0.913962i −0.992233 0.124390i \(-0.960303\pi\)
0.613658 0.789572i \(-0.289697\pi\)
\(108\) −4.99853 2.07046i −0.480984 0.199230i
\(109\) 4.07387 9.83519i 0.390206 0.942040i −0.599689 0.800233i \(-0.704709\pi\)
0.989894 0.141807i \(-0.0452911\pi\)
\(110\) 2.74011 2.74011i 0.261259 0.261259i
\(111\) 1.41508 1.41508i 0.134313 0.134313i
\(112\) −1.24830 + 3.01367i −0.117954 + 0.284765i
\(113\) −10.9369 4.53022i −1.02886 0.426167i −0.196558 0.980492i \(-0.562976\pi\)
−0.832300 + 0.554325i \(0.812976\pi\)
\(114\) 3.47762 + 8.39572i 0.325709 + 0.786331i
\(115\) 7.48022i 0.697534i
\(116\) −0.465076 + 0.192641i −0.0431812 + 0.0178862i
\(117\) 0.0769540 + 0.0769540i 0.00711440 + 0.00711440i
\(118\) 8.53195 0.785430
\(119\) −9.78592 + 9.22625i −0.897074 + 0.845769i
\(120\) 1.64885 0.150518
\(121\) 2.84002 + 2.84002i 0.258183 + 0.258183i
\(122\) −6.25570 + 2.59120i −0.566365 + 0.234596i
\(123\) 14.3057i 1.28990i
\(124\) −4.25457 10.2715i −0.382072 0.922404i
\(125\) −0.923880 0.382683i −0.0826343 0.0342282i
\(126\) 0.351153 0.847759i 0.0312832 0.0755244i
\(127\) −2.97116 + 2.97116i −0.263648 + 0.263648i −0.826534 0.562886i \(-0.809691\pi\)
0.562886 + 0.826534i \(0.309691\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0.169585 0.409413i 0.0149311 0.0360468i
\(130\) −0.357425 0.148050i −0.0313482 0.0129849i
\(131\) 7.73878 + 18.6831i 0.676140 + 1.63235i 0.770984 + 0.636855i \(0.219765\pi\)
−0.0948433 + 0.995492i \(0.530235\pi\)
\(132\) 6.38944i 0.556130i
\(133\) −16.6095 + 6.87990i −1.44023 + 0.596563i
\(134\) 1.68297 + 1.68297i 0.145387 + 0.145387i
\(135\) −5.41037 −0.465650
\(136\) −3.85403 + 1.46508i −0.330480 + 0.125629i
\(137\) 9.83591 0.840338 0.420169 0.907446i \(-0.361971\pi\)
0.420169 + 0.907446i \(0.361971\pi\)
\(138\) −8.72126 8.72126i −0.742403 0.742403i
\(139\) −1.15496 + 0.478400i −0.0979624 + 0.0405774i −0.431126 0.902292i \(-0.641884\pi\)
0.333164 + 0.942869i \(0.391884\pi\)
\(140\) 3.26197i 0.275687i
\(141\) 3.23637 + 7.81329i 0.272551 + 0.657997i
\(142\) −8.21885 3.40436i −0.689711 0.285688i
\(143\) 0.573709 1.38506i 0.0479760 0.115824i
\(144\) 0.198912 0.198912i 0.0165760 0.0165760i
\(145\) −0.355953 + 0.355953i −0.0295603 + 0.0295603i
\(146\) −2.69971 + 6.51767i −0.223429 + 0.539406i
\(147\) −5.54565 2.29708i −0.457398 0.189460i
\(148\) 0.464466 + 1.12132i 0.0381789 + 0.0921720i
\(149\) 9.68125i 0.793119i 0.918009 + 0.396559i \(0.129796\pi\)
−0.918009 + 0.396559i \(0.870204\pi\)
\(150\) 1.52334 0.630986i 0.124380 0.0515198i
\(151\) 7.70193 + 7.70193i 0.626774 + 0.626774i 0.947255 0.320481i \(-0.103844\pi\)
−0.320481 + 0.947255i \(0.603844\pi\)
\(152\) −5.51140 −0.447034
\(153\) 1.08416 0.412132i 0.0876489 0.0333189i
\(154\) −12.6405 −1.01860
\(155\) −7.86143 7.86143i −0.631445 0.631445i
\(156\) 0.589339 0.244112i 0.0471849 0.0195446i
\(157\) 7.93497i 0.633280i 0.948546 + 0.316640i \(0.102555\pi\)
−0.948546 + 0.316640i \(0.897445\pi\)
\(158\) −1.88556 4.55215i −0.150007 0.362149i
\(159\) −1.31396 0.544260i −0.104204 0.0431627i
\(160\) −0.382683 + 0.923880i −0.0302538 + 0.0730391i
\(161\) 17.2536 17.2536i 1.35977 1.35977i
\(162\) 5.71127 5.71127i 0.448720 0.448720i
\(163\) 8.35691 20.1754i 0.654564 1.58026i −0.151520 0.988454i \(-0.548417\pi\)
0.806083 0.591802i \(-0.201583\pi\)
\(164\) −8.01575 3.32023i −0.625925 0.259267i
\(165\) 2.44513 + 5.90308i 0.190353 + 0.459554i
\(166\) 5.96428i 0.462918i
\(167\) 17.9066 7.41716i 1.38565 0.573957i 0.439667 0.898161i \(-0.355096\pi\)
0.945987 + 0.324204i \(0.105096\pi\)
\(168\) −3.80317 3.80317i −0.293421 0.293421i
\(169\) 12.8503 0.988487
\(170\) −3.00000 + 2.82843i −0.230089 + 0.216930i
\(171\) 1.55038 0.118561
\(172\) 0.190043 + 0.190043i 0.0144906 + 0.0144906i
\(173\) −11.5551 + 4.78629i −0.878520 + 0.363895i −0.775923 0.630828i \(-0.782715\pi\)
−0.102598 + 0.994723i \(0.532715\pi\)
\(174\) 0.830020i 0.0629236i
\(175\) 1.24830 + 3.01367i 0.0943628 + 0.227812i
\(176\) −3.58012 1.48294i −0.269862 0.111781i
\(177\) −5.38355 + 12.9970i −0.404652 + 0.976916i
\(178\) −8.51915 + 8.51915i −0.638537 + 0.638537i
\(179\) −12.1689 + 12.1689i −0.909550 + 0.909550i −0.996236 0.0866859i \(-0.972372\pi\)
0.0866859 + 0.996236i \(0.472372\pi\)
\(180\) 0.107651 0.259892i 0.00802380 0.0193712i
\(181\) 19.4600 + 8.06061i 1.44645 + 0.599140i 0.961353 0.275319i \(-0.0887835\pi\)
0.485099 + 0.874459i \(0.338783\pi\)
\(182\) 0.482936 + 1.16591i 0.0357976 + 0.0864230i
\(183\) 11.1645i 0.825307i
\(184\) 6.91082 2.86256i 0.509472 0.211030i
\(185\) 0.858221 + 0.858221i 0.0630977 + 0.0630977i
\(186\) 18.3314 1.34413
\(187\) −10.9604 11.6253i −0.801506 0.850126i
\(188\) −5.12906 −0.374075
\(189\) 12.4794 + 12.4794i 0.907740 + 0.907740i
\(190\) −5.09187 + 2.10912i −0.369403 + 0.153012i
\(191\) 14.2761i 1.03298i −0.856292 0.516491i \(-0.827238\pi\)
0.856292 0.516491i \(-0.172762\pi\)
\(192\) −0.630986 1.52334i −0.0455375 0.109937i
\(193\) −19.1829 7.94581i −1.38081 0.571952i −0.436115 0.899891i \(-0.643646\pi\)
−0.944699 + 0.327939i \(0.893646\pi\)
\(194\) −4.46961 + 10.7906i −0.320899 + 0.774720i
\(195\) 0.451061 0.451061i 0.0323011 0.0323011i
\(196\) 2.57420 2.57420i 0.183871 0.183871i
\(197\) 5.95147 14.3681i 0.424025 1.02369i −0.557123 0.830430i \(-0.688095\pi\)
0.981148 0.193257i \(-0.0619050\pi\)
\(198\) 1.00711 + 0.417157i 0.0715719 + 0.0296460i
\(199\) 0.959134 + 2.31555i 0.0679912 + 0.164145i 0.954222 0.299098i \(-0.0966857\pi\)
−0.886231 + 0.463243i \(0.846686\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −3.62567 + 1.50180i −0.255735 + 0.105929i
\(202\) 3.71031 + 3.71031i 0.261057 + 0.261057i
\(203\) 1.64206 0.115250
\(204\) 0.200039 6.79543i 0.0140055 0.475775i
\(205\) −8.67619 −0.605971
\(206\) −11.8899 11.8899i −0.828408 0.828408i
\(207\) −1.94405 + 0.805250i −0.135120 + 0.0559687i
\(208\) 0.386874i 0.0268249i
\(209\) −8.17306 19.7315i −0.565342 1.36486i
\(210\) −4.96908 2.05826i −0.342899 0.142033i
\(211\) −4.86897 + 11.7547i −0.335194 + 0.809229i 0.662969 + 0.748646i \(0.269296\pi\)
−0.998163 + 0.0605828i \(0.980704\pi\)
\(212\) 0.609919 0.609919i 0.0418894 0.0418894i
\(213\) 10.3720 10.3720i 0.710676 0.710676i
\(214\) −3.91601 + 9.45410i −0.267693 + 0.646269i
\(215\) 0.248303 + 0.102850i 0.0169341 + 0.00701434i
\(216\) 2.07046 + 4.99853i 0.140877 + 0.340107i
\(217\) 36.2658i 2.46188i
\(218\) −9.83519 + 4.07387i −0.666123 + 0.275917i
\(219\) −8.22513 8.22513i −0.555802 0.555802i
\(220\) −3.87510 −0.261259
\(221\) −0.653526 + 1.45510i −0.0439609 + 0.0978807i
\(222\) −2.00122 −0.134313
\(223\) −0.243767 0.243767i −0.0163238 0.0163238i 0.698898 0.715222i \(-0.253674\pi\)
−0.715222 + 0.698898i \(0.753674\pi\)
\(224\) 3.01367 1.24830i 0.201359 0.0834057i
\(225\) 0.281305i 0.0187536i
\(226\) 4.53022 + 10.9369i 0.301346 + 0.727513i
\(227\) 14.2037 + 5.88336i 0.942732 + 0.390492i 0.800494 0.599340i \(-0.204570\pi\)
0.142237 + 0.989833i \(0.454570\pi\)
\(228\) 3.47762 8.39572i 0.230311 0.556020i
\(229\) 4.74517 4.74517i 0.313570 0.313570i −0.532721 0.846291i \(-0.678831\pi\)
0.846291 + 0.532721i \(0.178831\pi\)
\(230\) 5.28931 5.28931i 0.348767 0.348767i
\(231\) 7.97596 19.2557i 0.524780 1.26693i
\(232\) 0.465076 + 0.192641i 0.0305337 + 0.0126475i
\(233\) 0.594799 + 1.43597i 0.0389666 + 0.0940736i 0.942165 0.335150i \(-0.108787\pi\)
−0.903198 + 0.429224i \(0.858787\pi\)
\(234\) 0.108829i 0.00711440i
\(235\) −4.73864 + 1.96281i −0.309115 + 0.128039i
\(236\) −6.03300 6.03300i −0.392715 0.392715i
\(237\) 8.12421 0.527724
\(238\) 13.4436 + 0.395744i 0.871421 + 0.0256523i
\(239\) 11.7012 0.756890 0.378445 0.925624i \(-0.376459\pi\)
0.378445 + 0.925624i \(0.376459\pi\)
\(240\) −1.16591 1.16591i −0.0752592 0.0752592i
\(241\) −25.2129 + 10.4435i −1.62411 + 0.672728i −0.994553 0.104228i \(-0.966763\pi\)
−0.629555 + 0.776956i \(0.716763\pi\)
\(242\) 4.01639i 0.258183i
\(243\) −1.11493 2.69167i −0.0715226 0.172671i
\(244\) 6.25570 + 2.59120i 0.400480 + 0.165884i
\(245\) 1.39315 3.36335i 0.0890048 0.214877i
\(246\) 10.1157 10.1157i 0.644951 0.644951i
\(247\) −1.50771 + 1.50771i −0.0959330 + 0.0959330i
\(248\) −4.25457 + 10.2715i −0.270166 + 0.652238i
\(249\) −9.08560 3.76338i −0.575776 0.238494i
\(250\) 0.382683 + 0.923880i 0.0242030 + 0.0584313i
\(251\) 15.8596i 1.00105i −0.865723 0.500523i \(-0.833141\pi\)
0.865723 0.500523i \(-0.166859\pi\)
\(252\) −0.847759 + 0.351153i −0.0534038 + 0.0221206i
\(253\) 20.4966 + 20.4966i 1.28861 + 1.28861i
\(254\) 4.20186 0.263648
\(255\) −2.41569 6.35471i −0.151276 0.397947i
\(256\) 1.00000 0.0625000
\(257\) 20.9077 + 20.9077i 1.30419 + 1.30419i 0.925542 + 0.378645i \(0.123610\pi\)
0.378645 + 0.925542i \(0.376390\pi\)
\(258\) −0.409413 + 0.169585i −0.0254890 + 0.0105579i
\(259\) 3.95908i 0.246005i
\(260\) 0.148050 + 0.357425i 0.00918169 + 0.0221666i
\(261\) −0.130828 0.0541907i −0.00809804 0.00335432i
\(262\) 7.73878 18.6831i 0.478103 1.15424i
\(263\) 15.1865 15.1865i 0.936437 0.936437i −0.0616599 0.998097i \(-0.519639\pi\)
0.998097 + 0.0616599i \(0.0196394\pi\)
\(264\) 4.51802 4.51802i 0.278065 0.278065i
\(265\) 0.330086 0.796897i 0.0202770 0.0489530i
\(266\) 16.6095 + 6.87990i 1.01840 + 0.421834i
\(267\) −7.60205 18.3530i −0.465238 1.12318i
\(268\) 2.38009i 0.145387i
\(269\) −27.8132 + 11.5206i −1.69580 + 0.702424i −0.999877 0.0156895i \(-0.995006\pi\)
−0.695926 + 0.718114i \(0.745006\pi\)
\(270\) 3.82571 + 3.82571i 0.232825 + 0.232825i
\(271\) 19.4876 1.18379 0.591893 0.806017i \(-0.298381\pi\)
0.591893 + 0.806017i \(0.298381\pi\)
\(272\) 3.76118 + 1.68925i 0.228055 + 0.102426i
\(273\) −2.08080 −0.125936
\(274\) −6.95504 6.95504i −0.420169 0.420169i
\(275\) −3.58012 + 1.48294i −0.215890 + 0.0894244i
\(276\) 12.3337i 0.742403i
\(277\) −4.02214 9.71031i −0.241667 0.583436i 0.755781 0.654824i \(-0.227257\pi\)
−0.997449 + 0.0713877i \(0.977257\pi\)
\(278\) 1.15496 + 0.478400i 0.0692699 + 0.0286925i
\(279\) 1.19683 2.88941i 0.0716524 0.172984i
\(280\) 2.30656 2.30656i 0.137844 0.137844i
\(281\) −1.46953 + 1.46953i −0.0876648 + 0.0876648i −0.749579 0.661915i \(-0.769744\pi\)
0.661915 + 0.749579i \(0.269744\pi\)
\(282\) 3.23637 7.81329i 0.192723 0.465274i
\(283\) −21.5603 8.93056i −1.28163 0.530867i −0.365147 0.930950i \(-0.618981\pi\)
−0.916479 + 0.400083i \(0.868981\pi\)
\(284\) 3.40436 + 8.21885i 0.202012 + 0.487699i
\(285\) 9.08746i 0.538294i
\(286\) −1.38506 + 0.573709i −0.0819002 + 0.0339242i
\(287\) 20.0122 + 20.0122i 1.18128 + 1.18128i
\(288\) −0.281305 −0.0165760
\(289\) 11.2929 + 12.7071i 0.664288 + 0.747477i
\(290\) 0.503394 0.0295603
\(291\) −13.6174 13.6174i −0.798268 0.798268i
\(292\) 6.51767 2.69971i 0.381418 0.157989i
\(293\) 3.46701i 0.202545i −0.994859 0.101273i \(-0.967709\pi\)
0.994859 0.101273i \(-0.0322914\pi\)
\(294\) 2.29708 + 5.54565i 0.133969 + 0.323429i
\(295\) −7.88250 3.26504i −0.458937 0.190098i
\(296\) 0.464466 1.12132i 0.0269965 0.0651754i
\(297\) −14.8250 + 14.8250i −0.860234 + 0.860234i
\(298\) 6.84568 6.84568i 0.396559 0.396559i
\(299\) 1.10745 2.67362i 0.0640454 0.154619i
\(300\) −1.52334 0.630986i −0.0879498 0.0364300i
\(301\) −0.335495 0.809957i −0.0193376 0.0466852i
\(302\) 10.8922i 0.626774i
\(303\) −7.99321 + 3.31090i −0.459198 + 0.190206i
\(304\) 3.89715 + 3.89715i 0.223517 + 0.223517i
\(305\) 6.77112 0.387713
\(306\) −1.05804 0.475193i −0.0604839 0.0271650i
\(307\) 0.0492977 0.00281357 0.00140678 0.999999i \(-0.499552\pi\)
0.00140678 + 0.999999i \(0.499552\pi\)
\(308\) 8.93816 + 8.93816i 0.509299 + 0.509299i
\(309\) 25.6147 10.6099i 1.45717 0.603578i
\(310\) 11.1177i 0.631445i
\(311\) −6.55093 15.8153i −0.371469 0.896806i −0.993502 0.113815i \(-0.963693\pi\)
0.622033 0.782991i \(-0.286307\pi\)
\(312\) −0.589339 0.244112i −0.0333648 0.0138201i
\(313\) −5.89235 + 14.2254i −0.333055 + 0.804067i 0.665291 + 0.746584i \(0.268307\pi\)
−0.998347 + 0.0574826i \(0.981693\pi\)
\(314\) 5.61087 5.61087i 0.316640 0.316640i
\(315\) −0.648847 + 0.648847i −0.0365584 + 0.0365584i
\(316\) −1.88556 + 4.55215i −0.106071 + 0.256078i
\(317\) −25.4894 10.5581i −1.43163 0.593000i −0.473876 0.880591i \(-0.657146\pi\)
−0.957753 + 0.287591i \(0.907146\pi\)
\(318\) 0.544260 + 1.31396i 0.0305206 + 0.0736833i
\(319\) 1.95070i 0.109218i
\(320\) 0.923880 0.382683i 0.0516464 0.0213927i
\(321\) −11.9308 11.9308i −0.665913 0.665913i
\(322\) −24.4003 −1.35977
\(323\) 8.07462 + 21.2411i 0.449284 + 1.18189i
\(324\) −8.07695 −0.448720
\(325\) 0.273561 + 0.273561i 0.0151744 + 0.0151744i
\(326\) −20.1754 + 8.35691i −1.11741 + 0.462846i
\(327\) 17.5528i 0.970675i
\(328\) 3.32023 + 8.01575i 0.183329 + 0.442596i
\(329\) 15.4573 + 6.40262i 0.852189 + 0.352988i
\(330\) 2.44513 5.90308i 0.134600 0.324954i
\(331\) −0.548939 + 0.548939i −0.0301724 + 0.0301724i −0.722032 0.691860i \(-0.756792\pi\)
0.691860 + 0.722032i \(0.256792\pi\)
\(332\) 4.21738 4.21738i 0.231459 0.231459i
\(333\) −0.130656 + 0.315433i −0.00715993 + 0.0172856i
\(334\) −17.9066 7.41716i −0.979806 0.405849i
\(335\) −0.910819 2.19891i −0.0497634 0.120139i
\(336\) 5.37849i 0.293421i
\(337\) 25.0517 10.3768i 1.36465 0.565258i 0.424320 0.905512i \(-0.360513\pi\)
0.940333 + 0.340254i \(0.110513\pi\)
\(338\) −9.08655 9.08655i −0.494243 0.494243i
\(339\) −19.5191 −1.06013
\(340\) 4.12132 + 0.121320i 0.223510 + 0.00657952i
\(341\) −43.0823 −2.33304
\(342\) −1.09629 1.09629i −0.0592804 0.0592804i
\(343\) 10.1245 4.19372i 0.546673 0.226439i
\(344\) 0.268761i 0.0144906i
\(345\) 4.71991 + 11.3949i 0.254112 + 0.613480i
\(346\) 11.5551 + 4.78629i 0.621208 + 0.257313i
\(347\) −8.07218 + 19.4880i −0.433337 + 1.04617i 0.544867 + 0.838523i \(0.316580\pi\)
−0.978204 + 0.207646i \(0.933420\pi\)
\(348\) −0.586913 + 0.586913i −0.0314618 + 0.0314618i
\(349\) −9.17504 + 9.17504i −0.491129 + 0.491129i −0.908662 0.417533i \(-0.862895\pi\)
0.417533 + 0.908662i \(0.362895\pi\)
\(350\) 1.24830 3.01367i 0.0667246 0.161087i
\(351\) 1.93380 + 0.801007i 0.103219 + 0.0427546i
\(352\) 1.48294 + 3.58012i 0.0790408 + 0.190821i
\(353\) 15.7415i 0.837837i −0.908024 0.418919i \(-0.862409\pi\)
0.908024 0.418919i \(-0.137591\pi\)
\(354\) 12.9970 5.38355i 0.690784 0.286132i
\(355\) 6.29044 + 6.29044i 0.333862 + 0.333862i
\(356\) 12.0479 0.638537
\(357\) −9.08560 + 20.2295i −0.480861 + 1.07066i
\(358\) 17.2095 0.909550
\(359\) −3.09805 3.09805i −0.163509 0.163509i 0.620610 0.784119i \(-0.286885\pi\)
−0.784119 + 0.620610i \(0.786885\pi\)
\(360\) −0.259892 + 0.107651i −0.0136975 + 0.00567368i
\(361\) 11.3755i 0.598713i
\(362\) −8.06061 19.4600i −0.423656 1.02280i
\(363\) 6.11831 + 2.53429i 0.321128 + 0.133016i
\(364\) 0.482936 1.16591i 0.0253127 0.0611103i
\(365\) 4.98841 4.98841i 0.261105 0.261105i
\(366\) −7.89452 + 7.89452i −0.412653 + 0.412653i
\(367\) −8.40289 + 20.2864i −0.438627 + 1.05894i 0.537796 + 0.843075i \(0.319257\pi\)
−0.976423 + 0.215865i \(0.930743\pi\)
\(368\) −6.91082 2.86256i −0.360251 0.149221i
\(369\) −0.933997 2.25487i −0.0486219 0.117384i
\(370\) 1.21371i 0.0630977i
\(371\) −2.59946 + 1.07673i −0.134957 + 0.0559010i
\(372\) −12.9623 12.9623i −0.672063 0.672063i
\(373\) −34.7421 −1.79888 −0.899440 0.437045i \(-0.856025\pi\)
−0.899440 + 0.437045i \(0.856025\pi\)
\(374\) −0.470128 + 15.9705i −0.0243098 + 0.825816i
\(375\) −1.64885 −0.0851461
\(376\) 3.62680 + 3.62680i 0.187038 + 0.187038i
\(377\) 0.179926 0.0745277i 0.00926665 0.00383837i
\(378\) 17.6485i 0.907740i
\(379\) 4.06600 + 9.81620i 0.208857 + 0.504224i 0.993244 0.116047i \(-0.0370224\pi\)
−0.784387 + 0.620272i \(0.787022\pi\)
\(380\) 5.09187 + 2.10912i 0.261207 + 0.108196i
\(381\) −2.65131 + 6.40084i −0.135831 + 0.327925i
\(382\) −10.0947 + 10.0947i −0.516491 + 0.516491i
\(383\) −3.92646 + 3.92646i −0.200633 + 0.200633i −0.800271 0.599638i \(-0.795311\pi\)
0.599638 + 0.800271i \(0.295311\pi\)
\(384\) −0.630986 + 1.52334i −0.0321999 + 0.0777374i
\(385\) 11.6783 + 4.83730i 0.595180 + 0.246531i
\(386\) 7.94581 + 19.1829i 0.404431 + 0.976383i
\(387\) 0.0756037i 0.00384315i
\(388\) 10.7906 4.46961i 0.547810 0.226910i
\(389\) −6.26679 6.26679i −0.317739 0.317739i 0.530159 0.847898i \(-0.322132\pi\)
−0.847898 + 0.530159i \(0.822132\pi\)
\(390\) −0.637896 −0.0323011
\(391\) −21.1572 22.4407i −1.06997 1.13487i
\(392\) −3.64047 −0.183871
\(393\) 23.5775 + 23.5775i 1.18933 + 1.18933i
\(394\) −14.3681 + 5.95147i −0.723856 + 0.299831i
\(395\) 4.92721i 0.247915i
\(396\) −0.417157 1.00711i −0.0209629 0.0506089i
\(397\) 4.68003 + 1.93853i 0.234884 + 0.0972922i 0.497021 0.867739i \(-0.334427\pi\)
−0.262137 + 0.965031i \(0.584427\pi\)
\(398\) 0.959134 2.31555i 0.0480770 0.116068i
\(399\) −20.9608 + 20.9608i −1.04935 + 1.04935i
\(400\) 0.707107 0.707107i 0.0353553 0.0353553i
\(401\) −1.49473 + 3.60859i −0.0746431 + 0.180204i −0.956797 0.290757i \(-0.906093\pi\)
0.882154 + 0.470961i \(0.156093\pi\)
\(402\) 3.62567 + 1.50180i 0.180832 + 0.0749030i
\(403\) 1.64598 + 3.97376i 0.0819923 + 0.197947i
\(404\) 5.24718i 0.261057i
\(405\) −7.46213 + 3.09092i −0.370796 + 0.153589i
\(406\) −1.16111 1.16111i −0.0576249 0.0576249i
\(407\) 4.70324 0.233131
\(408\) −4.94654 + 4.66364i −0.244890 + 0.230885i
\(409\) 35.1203 1.73659 0.868295 0.496049i \(-0.165216\pi\)
0.868295 + 0.496049i \(0.165216\pi\)
\(410\) 6.13499 + 6.13499i 0.302986 + 0.302986i
\(411\) 14.9834 6.20632i 0.739076 0.306135i
\(412\) 16.8149i 0.828408i
\(413\) 10.6505 + 25.7125i 0.524075 + 1.26523i
\(414\) 1.94405 + 0.805250i 0.0955446 + 0.0395759i
\(415\) 2.28243 5.51028i 0.112040 0.270489i
\(416\) 0.273561 0.273561i 0.0134124 0.0134124i
\(417\) −1.45753 + 1.45753i −0.0713754 + 0.0713754i
\(418\) −8.17306 + 19.7315i −0.399757 + 0.965099i
\(419\) −21.1715 8.76953i −1.03430 0.428420i −0.200035 0.979789i \(-0.564106\pi\)
−0.834261 + 0.551369i \(0.814106\pi\)
\(420\) 2.05826 + 4.96908i 0.100433 + 0.242466i
\(421\) 28.3500i 1.38170i −0.723000 0.690848i \(-0.757237\pi\)
0.723000 0.690848i \(-0.242763\pi\)
\(422\) 11.7547 4.86897i 0.572211 0.237018i
\(423\) −1.02023 1.02023i −0.0496055 0.0496055i
\(424\) −0.862555 −0.0418894
\(425\) 3.85403 1.46508i 0.186948 0.0710666i
\(426\) −14.6682 −0.710676
\(427\) −15.6180 15.6180i −0.755809 0.755809i
\(428\) 9.45410 3.91601i 0.456981 0.189288i
\(429\) 2.47191i 0.119345i
\(430\) −0.102850 0.248303i −0.00495989 0.0119742i
\(431\) 17.1728 + 7.11320i 0.827184 + 0.342631i 0.755787 0.654817i \(-0.227254\pi\)
0.0713968 + 0.997448i \(0.477254\pi\)
\(432\) 2.07046 4.99853i 0.0996150 0.240492i
\(433\) 7.09542 7.09542i 0.340984 0.340984i −0.515753 0.856737i \(-0.672488\pi\)
0.856737 + 0.515753i \(0.172488\pi\)
\(434\) 25.6438 25.6438i 1.23094 1.23094i
\(435\) −0.317635 + 0.766838i −0.0152294 + 0.0367671i
\(436\) 9.83519 + 4.07387i 0.471020 + 0.195103i
\(437\) −15.7767 38.0883i −0.754701 1.82201i
\(438\) 11.6321i 0.555802i
\(439\) 33.3356 13.8081i 1.59102 0.659023i 0.600912 0.799315i \(-0.294804\pi\)
0.990110 + 0.140293i \(0.0448043\pi\)
\(440\) 2.74011 + 2.74011i 0.130630 + 0.130630i
\(441\) 1.02408 0.0487657
\(442\) 1.49102 0.566800i 0.0709208 0.0269599i
\(443\) −1.26810 −0.0602493 −0.0301247 0.999546i \(-0.509590\pi\)
−0.0301247 + 0.999546i \(0.509590\pi\)
\(444\) 1.41508 + 1.41508i 0.0671565 + 0.0671565i
\(445\) 11.1308 4.61053i 0.527650 0.218560i
\(446\) 0.344739i 0.0163238i
\(447\) 6.10874 + 14.7478i 0.288933 + 0.697547i
\(448\) −3.01367 1.24830i −0.142383 0.0589768i
\(449\) 1.76923 4.27131i 0.0834953 0.201576i −0.876618 0.481187i \(-0.840206\pi\)
0.960113 + 0.279612i \(0.0902057\pi\)
\(450\) −0.198912 + 0.198912i −0.00937682 + 0.00937682i
\(451\) −23.7737 + 23.7737i −1.11946 + 1.11946i
\(452\) 4.53022 10.9369i 0.213083 0.514429i
\(453\) 16.5924 + 6.87282i 0.779581 + 0.322913i
\(454\) −5.88336 14.2037i −0.276120 0.666612i
\(455\) 1.26197i 0.0591622i
\(456\) −8.39572 + 3.47762i −0.393165 + 0.162854i
\(457\) −3.84756 3.84756i −0.179981 0.179981i 0.611366 0.791348i \(-0.290620\pi\)
−0.791348 + 0.611366i \(0.790620\pi\)
\(458\) −6.71069 −0.313570
\(459\) 16.2311 15.3028i 0.757603 0.714275i
\(460\) −7.48022 −0.348767
\(461\) −0.930680 0.930680i −0.0433461 0.0433461i 0.685102 0.728448i \(-0.259758\pi\)
−0.728448 + 0.685102i \(0.759758\pi\)
\(462\) −19.2557 + 7.97596i −0.895855 + 0.371075i
\(463\) 11.2825i 0.524343i 0.965021 + 0.262172i \(0.0844387\pi\)
−0.965021 + 0.262172i \(0.915561\pi\)
\(464\) −0.192641 0.465076i −0.00894312 0.0215906i
\(465\) −16.9360 7.01514i −0.785390 0.325319i
\(466\) 0.594799 1.43597i 0.0275535 0.0665201i
\(467\) −15.4555 + 15.4555i −0.715195 + 0.715195i −0.967617 0.252422i \(-0.918773\pi\)
0.252422 + 0.967617i \(0.418773\pi\)
\(468\) −0.0769540 + 0.0769540i −0.00355720 + 0.00355720i
\(469\) −2.97107 + 7.17279i −0.137191 + 0.331209i
\(470\) 4.73864 + 1.96281i 0.218577 + 0.0905376i
\(471\) 5.00686 + 12.0876i 0.230704 + 0.556969i
\(472\) 8.53195i 0.392715i
\(473\) 0.962198 0.398556i 0.0442419 0.0183256i
\(474\) −5.74468 5.74468i −0.263862 0.263862i
\(475\) 5.51140 0.252880
\(476\) −9.22625 9.78592i −0.422885 0.448537i
\(477\) 0.242641 0.0111098
\(478\) −8.27403 8.27403i −0.378445 0.378445i
\(479\) −4.04430 + 1.67520i −0.184789 + 0.0765420i −0.473159 0.880977i \(-0.656886\pi\)
0.288371 + 0.957519i \(0.406886\pi\)
\(480\) 1.64885i 0.0752592i
\(481\) −0.179690 0.433810i −0.00819315 0.0197800i
\(482\) 25.2129 + 10.4435i 1.14842 + 0.475690i
\(483\) 15.3962 37.1698i 0.700553 1.69128i
\(484\) −2.84002 + 2.84002i −0.129092 + 0.129092i
\(485\) 8.25877 8.25877i 0.375011 0.375011i
\(486\) −1.11493 + 2.69167i −0.0505741 + 0.122097i
\(487\) −18.3854 7.61547i −0.833121 0.345090i −0.0749834 0.997185i \(-0.523890\pi\)
−0.758137 + 0.652095i \(0.773890\pi\)
\(488\) −2.59120 6.25570i −0.117298 0.283182i
\(489\) 36.0069i 1.62829i
\(490\) −3.36335 + 1.39315i −0.151941 + 0.0629359i
\(491\) 18.4660 + 18.4660i 0.833361 + 0.833361i 0.987975 0.154614i \(-0.0494134\pi\)
−0.154614 + 0.987975i \(0.549413\pi\)
\(492\) −14.3057 −0.644951
\(493\) 0.0610720 2.07465i 0.00275054 0.0934375i
\(494\) 2.13222 0.0959330
\(495\) −0.770805 0.770805i −0.0346451 0.0346451i
\(496\) 10.2715 4.25457i 0.461202 0.191036i
\(497\) 29.0186i 1.30166i
\(498\) 3.76338 + 9.08560i 0.168641 + 0.407135i
\(499\) 0.991395 + 0.410649i 0.0443809 + 0.0183832i 0.404763 0.914421i \(-0.367354\pi\)
−0.360383 + 0.932805i \(0.617354\pi\)
\(500\) 0.382683 0.923880i 0.0171141 0.0413171i
\(501\) 22.5976 22.5976i 1.00959 1.00959i
\(502\) −11.2144 + 11.2144i −0.500523 + 0.500523i
\(503\) −6.48860 + 15.6649i −0.289312 + 0.698462i −0.999987 0.00505889i \(-0.998390\pi\)
0.710675 + 0.703521i \(0.248390\pi\)
\(504\) 0.847759 + 0.351153i 0.0377622 + 0.0156416i
\(505\) −2.00801 4.84776i −0.0893552 0.215722i
\(506\) 28.9866i 1.28861i
\(507\) 19.5754 8.10838i 0.869372 0.360106i
\(508\) −2.97116 2.97116i −0.131824 0.131824i
\(509\) −13.4425 −0.595830 −0.297915 0.954592i \(-0.596291\pi\)
−0.297915 + 0.954592i \(0.596291\pi\)
\(510\) −2.78531 + 6.20160i −0.123336 + 0.274612i
\(511\) −23.0122 −1.01800
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 27.5489 11.4111i 1.21631 0.503814i
\(514\) 29.5680i 1.30419i
\(515\) 6.43476 + 15.5349i 0.283550 + 0.684549i
\(516\) 0.409413 + 0.169585i 0.0180234 + 0.00746554i
\(517\) −7.60607 + 18.3627i −0.334515 + 0.807590i
\(518\) −2.79949 + 2.79949i −0.123003 + 0.123003i
\(519\) −14.5823 + 14.5823i −0.640090 + 0.640090i
\(520\) 0.148050 0.357425i 0.00649244 0.0156741i
\(521\) −4.37555 1.81241i −0.191696 0.0794032i 0.284770 0.958596i \(-0.408083\pi\)
−0.476467 + 0.879193i \(0.658083\pi\)
\(522\) 0.0541907 + 0.130828i 0.00237186 + 0.00572618i
\(523\) 0.534337i 0.0233649i −0.999932 0.0116825i \(-0.996281\pi\)
0.999932 0.0116825i \(-0.00371873\pi\)
\(524\) −18.6831 + 7.73878i −0.816174 + 0.338070i
\(525\) 3.80317 + 3.80317i 0.165984 + 0.165984i
\(526\) −21.4769 −0.936437
\(527\) 45.8198 + 1.34881i 1.99594 + 0.0587550i
\(528\) −6.38944 −0.278065
\(529\) 23.3017 + 23.3017i 1.01312 + 1.01312i
\(530\) −0.796897 + 0.330086i −0.0346150 + 0.0143380i
\(531\) 2.40008i 0.104154i
\(532\) −6.87990 16.6095i −0.298281 0.720115i
\(533\) 3.10109 + 1.28451i 0.134323 + 0.0556384i
\(534\) −7.60205 + 18.3530i −0.328973 + 0.794211i
\(535\) 7.23585 7.23585i 0.312833 0.312833i
\(536\) −1.68297 + 1.68297i −0.0726934 + 0.0726934i
\(537\) −10.8590 + 26.2158i −0.468598 + 1.13130i
\(538\) 27.8132 + 11.5206i 1.19911 + 0.496689i
\(539\) −5.39858 13.0333i −0.232533 0.561385i
\(540\) 5.41037i 0.232825i
\(541\) −3.87392 + 1.60463i −0.166553 + 0.0689884i −0.464402 0.885624i \(-0.653731\pi\)
0.297849 + 0.954613i \(0.403731\pi\)
\(542\) −13.7798 13.7798i −0.591893 0.591893i
\(543\) 34.7303 1.49042
\(544\) −1.46508 3.85403i −0.0628146 0.165240i
\(545\) 10.6455 0.456004
\(546\) 1.47135 + 1.47135i 0.0629679 + 0.0629679i
\(547\) 21.6550 8.96980i 0.925901 0.383521i 0.131779 0.991279i \(-0.457931\pi\)
0.794122 + 0.607758i \(0.207931\pi\)
\(548\) 9.83591i 0.420169i
\(549\) 0.728915 + 1.75976i 0.0311093 + 0.0751046i
\(550\) 3.58012 + 1.48294i 0.152657 + 0.0632326i
\(551\) 1.06172 2.56322i 0.0452308 0.109197i
\(552\) 8.72126 8.72126i 0.371202 0.371202i
\(553\) 11.3649 11.3649i 0.483285 0.483285i
\(554\) −4.02214 + 9.71031i −0.170885 + 0.412552i
\(555\) 1.84889 + 0.765833i 0.0784808 + 0.0325078i
\(556\) −0.478400 1.15496i −0.0202887 0.0489812i
\(557\) 28.1590i 1.19313i −0.802563 0.596567i \(-0.796531\pi\)
0.802563 0.596567i \(-0.203469\pi\)
\(558\) −2.88941 + 1.19683i −0.122318 + 0.0506659i
\(559\) −0.0735226 0.0735226i −0.00310968 0.00310968i
\(560\) −3.26197 −0.137844
\(561\) −24.0318 10.7933i −1.01462 0.455695i
\(562\) 2.07823 0.0876648
\(563\) 9.54033 + 9.54033i 0.402077 + 0.402077i 0.878964 0.476887i \(-0.158235\pi\)
−0.476887 + 0.878964i \(0.658235\pi\)
\(564\) −7.81329 + 3.23637i −0.328999 + 0.136276i
\(565\) 11.8380i 0.498030i
\(566\) 8.93056 + 21.5603i 0.375379 + 0.906246i
\(567\) 24.3413 + 10.0825i 1.02224 + 0.423425i
\(568\) 3.40436 8.21885i 0.142844 0.344855i
\(569\) −2.03477 + 2.03477i −0.0853018 + 0.0853018i −0.748470 0.663168i \(-0.769211\pi\)
0.663168 + 0.748470i \(0.269211\pi\)
\(570\) −6.42580 + 6.42580i −0.269147 + 0.269147i
\(571\) 14.5080 35.0255i 0.607142 1.46577i −0.258953 0.965890i \(-0.583377\pi\)
0.866095 0.499880i \(-0.166623\pi\)
\(572\) 1.38506 + 0.573709i 0.0579122 + 0.0239880i
\(573\) −9.00803 21.7473i −0.376316 0.908507i
\(574\) 28.3015i 1.18128i
\(575\) −6.91082 + 2.86256i −0.288201 + 0.119377i
\(576\) 0.198912 + 0.198912i 0.00828802 + 0.00828802i
\(577\) −32.0749 −1.33529 −0.667647 0.744478i \(-0.732698\pi\)
−0.667647 + 0.744478i \(0.732698\pi\)
\(578\) 1.00000 16.9706i 0.0415945 0.705882i
\(579\) −34.2357 −1.42279
\(580\) −0.355953 0.355953i −0.0147802 0.0147802i
\(581\) −17.9744 + 7.44523i −0.745702 + 0.308880i
\(582\) 19.2580i 0.798268i
\(583\) −1.27911 3.08805i −0.0529755 0.127894i
\(584\) −6.51767 2.69971i −0.269703 0.111715i
\(585\) −0.0416472 + 0.100545i −0.00172190 + 0.00415704i
\(586\) −2.45155 + 2.45155i −0.101273 + 0.101273i
\(587\) 15.5504 15.5504i 0.641833 0.641833i −0.309173 0.951006i \(-0.600052\pi\)
0.951006 + 0.309173i \(0.100052\pi\)
\(588\) 2.29708 5.54565i 0.0947301 0.228699i
\(589\) 56.6101 + 23.4487i 2.33258 + 0.966186i
\(590\) 3.26504 + 7.88250i 0.134419 + 0.324517i
\(591\) 25.6428i 1.05480i
\(592\) −1.12132 + 0.464466i −0.0460860 + 0.0190894i
\(593\) 15.0634 + 15.0634i 0.618579 + 0.618579i 0.945167 0.326588i \(-0.105899\pi\)
−0.326588 + 0.945167i \(0.605899\pi\)
\(594\) 20.9657 0.860234
\(595\) −12.2689 5.51028i −0.502974 0.225899i
\(596\) −9.68125 −0.396559
\(597\) 2.92217 + 2.92217i 0.119596 + 0.119596i
\(598\) −2.67362 + 1.10745i −0.109332 + 0.0452869i
\(599\) 46.7012i 1.90816i 0.299552 + 0.954080i \(0.403163\pi\)
−0.299552 + 0.954080i \(0.596837\pi\)
\(600\) 0.630986 + 1.52334i 0.0257599 + 0.0621899i
\(601\) −25.2665 10.4657i −1.03064 0.426905i −0.197697 0.980263i \(-0.563346\pi\)
−0.832943 + 0.553358i \(0.813346\pi\)
\(602\) −0.335495 + 0.809957i −0.0136738 + 0.0330114i
\(603\) 0.473428 0.473428i 0.0192795 0.0192795i
\(604\) −7.70193 + 7.70193i −0.313387 + 0.313387i
\(605\) −1.53701 + 3.71066i −0.0624882 + 0.150860i
\(606\) 7.99321 + 3.31090i 0.324702 + 0.134496i
\(607\) 7.51669 + 18.1469i 0.305093 + 0.736560i 0.999850 + 0.0173153i \(0.00551189\pi\)
−0.694757 + 0.719245i \(0.744488\pi\)
\(608\) 5.51140i 0.223517i
\(609\) 2.50141 1.03612i 0.101362 0.0419855i
\(610\) −4.78791 4.78791i −0.193857 0.193857i
\(611\) 1.98430 0.0802763
\(612\) 0.412132 + 1.08416i 0.0166595 + 0.0438244i
\(613\) 4.06372 0.164132 0.0820661 0.996627i \(-0.473848\pi\)
0.0820661 + 0.996627i \(0.473848\pi\)
\(614\) −0.0348588 0.0348588i −0.00140678 0.00140678i
\(615\) −13.2167 + 5.47455i −0.532951 + 0.220755i
\(616\) 12.6405i 0.509299i
\(617\) 10.2233 + 24.6812i 0.411574 + 0.993629i 0.984715 + 0.174172i \(0.0557248\pi\)
−0.573141 + 0.819457i \(0.694275\pi\)
\(618\) −25.6147 10.6099i −1.03037 0.426794i
\(619\) −3.79149 + 9.15346i −0.152393 + 0.367909i −0.981577 0.191067i \(-0.938805\pi\)
0.829184 + 0.558975i \(0.188805\pi\)
\(620\) 7.86143 7.86143i 0.315723 0.315723i
\(621\) −28.6171 + 28.6171i −1.14837 + 1.14837i
\(622\) −6.55093 + 15.8153i −0.262668 + 0.634137i
\(623\) −36.3084 15.0394i −1.45466 0.602541i
\(624\) 0.244112 + 0.589339i 0.00977231 + 0.0235924i
\(625\) 1.00000i 0.0400000i
\(626\) 14.2254 5.89235i 0.568561 0.235506i
\(627\) −24.9006 24.9006i −0.994435 0.994435i
\(628\) −7.93497 −0.316640
\(629\) −5.00208 0.147248i −0.199446 0.00587114i
\(630\) 0.917608 0.0365584
\(631\) −14.0357 14.0357i −0.558753 0.558753i 0.370199 0.928952i \(-0.379289\pi\)
−0.928952 + 0.370199i \(0.879289\pi\)
\(632\) 4.55215 1.88556i 0.181075 0.0750036i
\(633\) 20.9787i 0.833827i
\(634\) 10.5581 + 25.4894i 0.419315 + 1.01232i
\(635\) −3.88201 1.60798i −0.154053 0.0638108i
\(636\) 0.544260 1.31396i 0.0215813 0.0521019i
\(637\) −0.995890 + 0.995890i −0.0394586 + 0.0394586i
\(638\) 1.37935 1.37935i 0.0546092 0.0546092i
\(639\) −0.957662 + 2.31200i −0.0378845 + 0.0914614i
\(640\) −0.923880 0.382683i −0.0365195 0.0151269i
\(641\) 6.29557 + 15.1989i 0.248660 + 0.600319i 0.998091 0.0617642i \(-0.0196727\pi\)
−0.749431 + 0.662083i \(0.769673\pi\)
\(642\) 16.8727i 0.665913i
\(643\) 5.04875 2.09126i 0.199103 0.0824713i −0.280904 0.959736i \(-0.590634\pi\)
0.480007 + 0.877265i \(0.340634\pi\)
\(644\) 17.2536 + 17.2536i 0.679887 + 0.679887i
\(645\) 0.443146 0.0174489
\(646\) 9.31012 20.7294i 0.366302 0.815586i
\(647\) −18.0212 −0.708488 −0.354244 0.935153i \(-0.615262\pi\)
−0.354244 + 0.935153i \(0.615262\pi\)
\(648\) 5.71127 + 5.71127i 0.224360 + 0.224360i
\(649\) −30.5455 + 12.6523i −1.19901 + 0.496648i
\(650\) 0.386874i 0.0151744i
\(651\) 22.8832 + 55.2449i 0.896863 + 2.16522i
\(652\) 20.1754 + 8.35691i 0.790128 + 0.327282i
\(653\) 1.07011 2.58348i 0.0418768 0.101099i −0.901557 0.432660i \(-0.857575\pi\)
0.943434 + 0.331560i \(0.107575\pi\)
\(654\) −12.4117 + 12.4117i −0.485337 + 0.485337i
\(655\) −14.2994 + 14.2994i −0.558724 + 0.558724i
\(656\) 3.32023 8.01575i 0.129633 0.312962i
\(657\) 1.83345 + 0.759440i 0.0715297 + 0.0296286i
\(658\) −6.40262 15.4573i −0.249600 0.602588i
\(659\) 39.8730i 1.55323i 0.629975 + 0.776616i \(0.283065\pi\)
−0.629975 + 0.776616i \(0.716935\pi\)
\(660\) −5.90308 + 2.44513i −0.229777 + 0.0951767i
\(661\) 15.0252 + 15.0252i 0.584414 + 0.584414i 0.936113 0.351699i \(-0.114396\pi\)
−0.351699 + 0.936113i \(0.614396\pi\)
\(662\) 0.776318 0.0301724
\(663\) −0.0773898 + 2.62897i −0.00300557 + 0.102101i
\(664\) −5.96428 −0.231459
\(665\) −12.7124 12.7124i −0.492966 0.492966i
\(666\) 0.315433 0.130656i 0.0122228 0.00506283i
\(667\) 3.76550i 0.145801i
\(668\) 7.41716 + 17.9066i 0.286978 + 0.692827i
\(669\) −0.525153 0.217525i −0.0203036 0.00841001i
\(670\) −0.910819 + 2.19891i −0.0351880 + 0.0849514i
\(671\) 18.5536 18.5536i 0.716254 0.716254i
\(672\) 3.80317 3.80317i 0.146710 0.146710i
\(673\) −3.09140 + 7.46331i −0.119165 + 0.287690i −0.972195 0.234172i \(-0.924762\pi\)
0.853030 + 0.521861i \(0.174762\pi\)
\(674\) −25.0517 10.3768i −0.964956 0.399698i
\(675\) −2.07046 4.99853i −0.0796920 0.192393i
\(676\) 12.8503i 0.494243i
\(677\) −14.9417 + 6.18907i −0.574258 + 0.237865i −0.650862 0.759196i \(-0.725592\pi\)
0.0766041 + 0.997062i \(0.475592\pi\)
\(678\) 13.8021 + 13.8021i 0.530066 + 0.530066i
\(679\) −38.0987 −1.46209
\(680\) −2.82843 3.00000i −0.108465 0.115045i
\(681\) 25.3493 0.971387
\(682\) 30.4638 + 30.4638i 1.16652 + 1.16652i
\(683\) −21.6024 + 8.94801i −0.826593 + 0.342386i −0.755553 0.655087i \(-0.772632\pi\)
−0.0710401 + 0.997473i \(0.522632\pi\)
\(684\) 1.55038i 0.0592804i
\(685\) 3.76404 + 9.08719i 0.143817 + 0.347204i
\(686\) −10.1245 4.19372i −0.386556 0.160117i
\(687\) 4.23435 10.2226i 0.161551 0.390018i
\(688\) −0.190043 + 0.190043i −0.00724531 + 0.00724531i
\(689\) −0.235962 + 0.235962i −0.00898942 + 0.00898942i
\(690\) 4.71991 11.3949i 0.179684 0.433796i
\(691\) 28.6113 + 11.8512i 1.08842 + 0.450840i 0.853457 0.521164i \(-0.174502\pi\)
0.234967 + 0.972003i \(0.424502\pi\)
\(692\) −4.78629 11.5551i −0.181948 0.439260i
\(693\) 3.55582i 0.135074i
\(694\) 19.4880 8.07218i 0.739753 0.306416i
\(695\) −0.883968 0.883968i −0.0335308 0.0335308i
\(696\) 0.830020 0.0314618
\(697\) 26.0286 24.5400i 0.985902 0.929517i
\(698\) 12.9755 0.491129
\(699\) 1.81216 + 1.81216i 0.0685421 + 0.0685421i
\(700\) −3.01367 + 1.24830i −0.113906 + 0.0471814i
\(701\) 14.5668i 0.550179i 0.961419 + 0.275090i \(0.0887075\pi\)
−0.961419 + 0.275090i \(0.911292\pi\)
\(702\) −0.801007 1.93380i −0.0302320 0.0729866i
\(703\) −6.18005 2.55986i −0.233085 0.0965469i
\(704\) 1.48294 3.58012i 0.0558903 0.134931i
\(705\) −5.98003 + 5.98003i −0.225221 + 0.225221i
\(706\) −11.1309 + 11.1309i −0.418919 + 0.418919i
\(707\) −6.55007 + 15.8133i −0.246341 + 0.594719i
\(708\) −12.9970 5.38355i −0.488458 0.202326i
\(709\) −16.7641 40.4722i −0.629590 1.51996i −0.840134 0.542380i \(-0.817523\pi\)
0.210544 0.977584i \(-0.432477\pi\)
\(710\) 8.89602i 0.333862i
\(711\) −1.28054 + 0.530417i −0.0480240 + 0.0198922i
\(712\) −8.51915 8.51915i −0.319268 0.319268i
\(713\) −83.1631 −3.11448
\(714\) 20.7289 7.87990i 0.775759 0.294898i
\(715\) 1.49918 0.0560660
\(716\) −12.1689 12.1689i −0.454775 0.454775i
\(717\) 17.8249 7.38332i 0.665684 0.275735i
\(718\) 4.38130i 0.163509i
\(719\) −14.5402 35.1032i −0.542258 1.30913i −0.923126 0.384498i \(-0.874375\pi\)
0.380867 0.924630i \(-0.375625\pi\)
\(720\) 0.259892 + 0.107651i 0.00968559 + 0.00401190i
\(721\) 20.9900 50.6744i 0.781709 1.88721i
\(722\) 8.04373 8.04373i 0.299357 0.299357i
\(723\) −31.8180 + 31.8180i −1.18333 + 1.18333i
\(724\) −8.06061 + 19.4600i −0.299570 + 0.723226i
\(725\) −0.465076 0.192641i −0.0172725 0.00715449i
\(726\) −2.53429 6.11831i −0.0940562 0.227072i
\(727\) 18.6950i 0.693360i 0.937984 + 0.346680i \(0.112691\pi\)
−0.937984 + 0.346680i \(0.887309\pi\)
\(728\) −1.16591 + 0.482936i −0.0432115 + 0.0178988i
\(729\) −20.5306 20.5306i −0.760393 0.760393i
\(730\) −7.05468 −0.261105
\(731\) −1.03581 + 0.393755i −0.0383109 + 0.0145636i
\(732\) 11.1645 0.412653
\(733\) −25.3096 25.3096i −0.934832 0.934832i 0.0631706 0.998003i \(-0.479879\pi\)
−0.998003 + 0.0631706i \(0.979879\pi\)
\(734\) 20.2864 8.40289i 0.748784 0.310156i
\(735\) 6.00257i 0.221408i
\(736\) 2.86256 + 6.91082i 0.105515 + 0.254736i
\(737\) −8.52100 3.52951i −0.313875 0.130011i
\(738\) −0.933997 + 2.25487i −0.0343809 + 0.0830028i
\(739\) 2.72089 2.72089i 0.100089 0.100089i −0.655289 0.755378i \(-0.727453\pi\)
0.755378 + 0.655289i \(0.227453\pi\)
\(740\) −0.858221 + 0.858221i −0.0315488 + 0.0315488i
\(741\) −1.34540 + 3.24808i −0.0494245 + 0.119321i
\(742\) 2.59946 + 1.07673i 0.0954290 + 0.0395280i
\(743\) 10.2614 + 24.7732i 0.376453 + 0.908839i 0.992625 + 0.121227i \(0.0386828\pi\)
−0.616172 + 0.787612i \(0.711317\pi\)
\(744\) 18.3314i 0.672063i
\(745\) −8.94431 + 3.70485i −0.327694 + 0.135735i
\(746\) 24.5664 + 24.5664i 0.899440 + 0.899440i
\(747\) 1.67778 0.0613867
\(748\) 11.6253 10.9604i 0.425063 0.400753i
\(749\) −33.3799 −1.21967
\(750\) 1.16591 + 1.16591i 0.0425730 + 0.0425730i
\(751\) −8.19609 + 3.39493i −0.299080 + 0.123883i −0.527177 0.849755i \(-0.676750\pi\)
0.228097 + 0.973638i \(0.426750\pi\)
\(752\) 5.12906i 0.187038i
\(753\) −10.0072 24.1594i −0.364681 0.880418i
\(754\) −0.179926 0.0745277i −0.00655251 0.00271414i
\(755\) −4.16826 + 10.0631i −0.151698 + 0.366232i
\(756\) −12.4794 + 12.4794i −0.453870 + 0.453870i
\(757\) −1.40238 + 1.40238i −0.0509705 + 0.0509705i −0.732133 0.681162i \(-0.761475\pi\)
0.681162 + 0.732133i \(0.261475\pi\)
\(758\) 4.06600 9.81620i 0.147684 0.356540i
\(759\) 44.1563 + 18.2901i 1.60277 + 0.663890i
\(760\) −2.10912 5.09187i −0.0765059 0.184702i
\(761\) 8.91397i 0.323131i 0.986862 + 0.161566i \(0.0516544\pi\)
−0.986862 + 0.161566i \(0.948346\pi\)
\(762\) 6.40084 2.65131i 0.231878 0.0960469i
\(763\) −24.5546 24.5546i −0.888936 0.888936i
\(764\) 14.2761 0.516491
\(765\) 0.795649 + 0.843914i 0.0287668 + 0.0305118i
\(766\) 5.55285 0.200633
\(767\) 2.33401 + 2.33401i 0.0842763 + 0.0842763i
\(768\) 1.52334 0.630986i 0.0549686 0.0227688i
\(769\) 48.4038i 1.74549i −0.488180 0.872743i \(-0.662339\pi\)
0.488180 0.872743i \(-0.337661\pi\)
\(770\) −4.83730 11.6783i −0.174324 0.420856i
\(771\) 45.0419 + 18.6570i 1.62215 + 0.671915i
\(772\) 7.94581 19.1829i 0.285976 0.690407i
\(773\) 13.5594 13.5594i 0.487699 0.487699i −0.419881 0.907579i \(-0.637928\pi\)
0.907579 + 0.419881i \(0.137928\pi\)
\(774\) 0.0534599 0.0534599i 0.00192158 0.00192158i
\(775\) 4.25457 10.2715i 0.152829 0.368961i
\(776\) −10.7906 4.46961i −0.387360 0.160450i
\(777\) −2.49813 6.03101i −0.0896198 0.216361i
\(778\) 8.86259i 0.317739i
\(779\) 44.1780 18.2991i 1.58284 0.655635i
\(780\) 0.451061 + 0.451061i 0.0161506 + 0.0161506i
\(781\) 34.4730 1.23354
\(782\) −0.907502 + 30.8284i −0.0324522 + 1.10242i
\(783\) −2.72355 −0.0973317
\(784\) 2.57420 + 2.57420i 0.0919356 + 0.0919356i
\(785\) −7.33096 + 3.03658i −0.261653 + 0.108380i
\(786\) 33.3436i 1.18933i
\(787\) −13.0796 31.5770i −0.466238 1.12560i −0.965793 0.259316i \(-0.916503\pi\)
0.499555 0.866282i \(-0.333497\pi\)
\(788\) 14.3681 + 5.95147i 0.511843 + 0.212012i
\(789\) 13.5516 32.7165i 0.482451 1.16474i
\(790\) 3.48406 3.48406i 0.123957 0.123957i
\(791\) −27.3052 + 27.3052i −0.970860 + 0.970860i
\(792\) −0.417157 + 1.00711i −0.0148230 + 0.0357859i
\(793\) −2.42017 1.00247i −0.0859427 0.0355986i
\(794\) −1.93853 4.68003i −0.0687959 0.166088i
\(795\) 1.42222i 0.0504410i
\(796\) −2.31555 + 0.959134i −0.0820726 + 0.0339956i
\(797\) 12.2144 + 12.2144i 0.432656 + 0.432656i 0.889531 0.456875i \(-0.151031\pi\)
−0.456875 + 0.889531i \(0.651031\pi\)
\(798\) 29.6430 1.04935
\(799\) 8.66425 19.2913i 0.306519 0.682478i
\(800\) −1.00000 −0.0353553
\(801\) 2.39647 + 2.39647i 0.0846753 + 0.0846753i
\(802\) 3.60859 1.49473i 0.127424 0.0527806i
\(803\) 27.3376i 0.964722i
\(804\) −1.50180 3.62567i −0.0529645 0.127868i
\(805\) 22.5429 + 9.33758i 0.794533 + 0.329106i
\(806\) 1.64598 3.97376i 0.0579773 0.139970i
\(807\) −35.0995 + 35.0995i −1.23556 + 1.23556i
\(808\) −3.71031 + 3.71031i −0.130528 + 0.130528i
\(809\) 3.34288 8.07043i 0.117529 0.283741i −0.854157 0.520015i \(-0.825926\pi\)
0.971686 + 0.236274i \(0.0759263\pi\)
\(810\) 7.46213 + 3.09092i 0.262193 + 0.108604i
\(811\) 7.81129 + 18.8581i 0.274291 + 0.662198i 0.999658 0.0261652i \(-0.00832960\pi\)
−0.725366 + 0.688363i \(0.758330\pi\)
\(812\) 1.64206i 0.0576249i
\(813\) 29.6861 12.2964i 1.04114 0.431253i
\(814\) −3.32569 3.32569i −0.116565 0.116565i
\(815\) 21.8377 0.764940
\(816\) 6.79543 + 0.200039i 0.237887 + 0.00700275i
\(817\) −1.48125 −0.0518224
\(818\) −24.8338 24.8338i −0.868295 0.868295i
\(819\) 0.327976 0.135852i 0.0114604 0.00474706i
\(820\) 8.67619i 0.302986i
\(821\) 21.1824 + 51.1388i 0.739270 + 1.78475i 0.608834 + 0.793298i \(0.291638\pi\)
0.130436 + 0.991457i \(0.458362\pi\)
\(822\) −14.9834 6.20632i −0.522606 0.216470i
\(823\) 5.83962 14.0981i 0.203556 0.491429i −0.788827 0.614615i \(-0.789311\pi\)
0.992384 + 0.123187i \(0.0393114\pi\)
\(824\) 11.8899 11.8899i 0.414204 0.414204i
\(825\) −4.51802 + 4.51802i −0.157297 + 0.157297i
\(826\) 10.6505 25.7125i 0.370577 0.894652i
\(827\) −27.8773 11.5472i −0.969389 0.401534i −0.158904 0.987294i \(-0.550796\pi\)
−0.810484 + 0.585760i \(0.800796\pi\)
\(828\) −0.805250 1.94405i −0.0279844 0.0675602i
\(829\) 45.3366i 1.57460i 0.616567 + 0.787302i \(0.288523\pi\)
−0.616567 + 0.787302i \(0.711477\pi\)
\(830\) −5.51028 + 2.28243i −0.191264 + 0.0792243i
\(831\) −12.2542 12.2542i −0.425092 0.425092i
\(832\) −0.386874 −0.0134124
\(833\) 5.33356 + 14.0305i 0.184797 + 0.486127i
\(834\) 2.06126 0.0713754
\(835\) 13.7051 + 13.7051i 0.474285 + 0.474285i
\(836\) 19.7315 8.17306i 0.682428 0.282671i
\(837\) 60.1511i 2.07912i
\(838\) 8.76953 + 21.1715i 0.302938 + 0.731358i
\(839\) 13.9838 + 5.79230i 0.482776 + 0.199972i 0.610779 0.791801i \(-0.290857\pi\)
−0.128003 + 0.991774i \(0.540857\pi\)
\(840\) 2.05826 4.96908i 0.0710167 0.171450i
\(841\) 20.3269 20.3269i 0.700928 0.700928i
\(842\) −20.0465 + 20.0465i −0.690848 + 0.690848i
\(843\) −1.31133 + 3.16584i −0.0451648 + 0.109037i
\(844\) −11.7547 4.86897i −0.404615 0.167597i
\(845\) 4.91761 + 11.8722i 0.169171 + 0.408415i
\(846\) 1.44283i 0.0496055i
\(847\) 12.1041 5.01367i 0.415901 0.172272i
\(848\) 0.609919 + 0.609919i 0.0209447 + 0.0209447i
\(849\) −38.4786 −1.32058
\(850\) −3.76118 1.68925i −0.129007 0.0579407i
\(851\) 9.07880 0.311217
\(852\) 10.3720 + 10.3720i 0.355338 + 0.355338i
\(853\) −10.8316 + 4.48661i −0.370868 + 0.153619i −0.560330 0.828269i \(-0.689326\pi\)
0.189462 + 0.981888i \(0.439326\pi\)
\(854\) 22.0872i 0.755809i
\(855\) 0.593306 + 1.43237i 0.0202906 + 0.0489859i
\(856\) −9.45410 3.91601i −0.323134 0.133847i
\(857\) 7.16039 17.2867i 0.244594 0.590503i −0.753134 0.657867i \(-0.771459\pi\)
0.997728 + 0.0673641i \(0.0214589\pi\)
\(858\) −1.74790 + 1.74790i −0.0596725 + 0.0596725i
\(859\) 24.0468 24.0468i 0.820465 0.820465i −0.165710 0.986175i \(-0.552991\pi\)
0.986175 + 0.165710i \(0.0529914\pi\)
\(860\) −0.102850 + 0.248303i −0.00350717 + 0.00846706i
\(861\) 43.1127 + 17.8578i 1.46928 + 0.608594i
\(862\) −7.11320 17.1728i −0.242277 0.584908i
\(863\) 4.32882i 0.147355i −0.997282 0.0736774i \(-0.976526\pi\)
0.997282 0.0736774i \(-0.0234735\pi\)
\(864\) −4.99853 + 2.07046i −0.170053 + 0.0704384i
\(865\) −8.84391 8.84391i −0.300702 0.300702i
\(866\) −10.0344 −0.340984
\(867\) 25.2209 + 12.2315i 0.856546 + 0.415404i
\(868\) −36.2658 −1.23094
\(869\) 13.5011 + 13.5011i 0.457993 + 0.457993i
\(870\) 0.766838 0.317635i 0.0259983 0.0107688i
\(871\) 0.920793i 0.0311999i
\(872\) −4.07387 9.83519i −0.137959 0.333061i
\(873\) 3.03544 + 1.25732i 0.102734 + 0.0425539i
\(874\) −15.7767 + 38.0883i −0.533655 + 1.28836i
\(875\) −2.30656 + 2.30656i −0.0779761 + 0.0779761i
\(876\) 8.22513 8.22513i 0.277901 0.277901i
\(877\) −14.0035 + 33.8074i −0.472864 + 1.14160i 0.490027 + 0.871707i \(0.336987\pi\)
−0.962892 + 0.269888i \(0.913013\pi\)
\(878\) −33.3356 13.8081i −1.12502 0.466000i
\(879\) −2.18764 5.28143i −0.0737872 0.178138i
\(880\) 3.87510i 0.130630i
\(881\) −14.7746 + 6.11984i −0.497769 + 0.206183i −0.617420 0.786633i \(-0.711822\pi\)
0.119652 + 0.992816i \(0.461822\pi\)
\(882\) −0.724134 0.724134i −0.0243828 0.0243828i
\(883\) 9.64068 0.324435 0.162217 0.986755i \(-0.448135\pi\)
0.162217 + 0.986755i \(0.448135\pi\)
\(884\) −1.45510 0.653526i −0.0489404 0.0219804i
\(885\) −14.0679 −0.472887
\(886\) 0.896683 + 0.896683i 0.0301247 + 0.0301247i
\(887\) −19.4510 + 8.05687i −0.653101 + 0.270523i −0.684532 0.728983i \(-0.739993\pi\)
0.0314313 + 0.999506i \(0.489993\pi\)
\(888\) 2.00122i 0.0671565i
\(889\) 5.24519 + 12.6630i 0.175918 + 0.424704i
\(890\) −11.1308 4.61053i −0.373105 0.154545i
\(891\) −11.9776 + 28.9165i −0.401265 + 0.968739i
\(892\) 0.243767 0.243767i 0.00816192 0.00816192i
\(893\) 19.9887 19.9887i 0.668897 0.668897i
\(894\) 6.10874 14.7478i 0.204307 0.493240i
\(895\) −15.8995 6.58579i −0.531462 0.220139i
\(896\) 1.24830 + 3.01367i 0.0417029 + 0.100680i
\(897\) 4.77160i 0.159319i
\(898\) −4.27131 + 1.76923i −0.142535 + 0.0590401i
\(899\) −3.95740 3.95740i −0.131987 0.131987i
\(900\) 0.281305 0.00937682
\(901\) 1.26371 + 3.32431i 0.0421002 + 0.110749i
\(902\) 33.6211 1.11946
\(903\) −1.02214 1.02214i −0.0340148 0.0340148i
\(904\) −10.9369 + 4.53022i −0.363756 + 0.150673i
\(905\) 21.0634i 0.700170i
\(906\) −6.87282 16.5924i −0.228334 0.551247i
\(907\) −22.9245 9.49564i −0.761196 0.315298i −0.0318952 0.999491i \(-0.510154\pi\)
−0.729300 + 0.684194i \(0.760154\pi\)
\(908\) −5.88336 + 14.2037i −0.195246 + 0.471366i
\(909\) 1.04373 1.04373i 0.0346183 0.0346183i
\(910\) −0.892349 + 0.892349i −0.0295811 + 0.0295811i
\(911\) −0.193157 + 0.466323i −0.00639959 + 0.0154500i −0.927047 0.374945i \(-0.877662\pi\)
0.920647 + 0.390395i \(0.127662\pi\)
\(912\) 8.39572 + 3.47762i 0.278010 + 0.115155i
\(913\) −8.84464 21.3529i −0.292715 0.706677i
\(914\) 5.44127i 0.179981i
\(915\) 10.3147 4.27249i 0.340993 0.141244i
\(916\) 4.74517 + 4.74517i 0.156785 + 0.156785i
\(917\) 65.9649 2.17835
\(918\) −22.2979 0.656388i −0.735939 0.0216640i
\(919\) 20.9247 0.690243 0.345121 0.938558i \(-0.387838\pi\)
0.345121 + 0.938558i \(0.387838\pi\)
\(920\) 5.28931 + 5.28931i 0.174383 + 0.174383i
\(921\) 0.0750970 0.0311062i 0.00247453 0.00102498i
\(922\) 1.31618i 0.0433461i
\(923\) −1.31706 3.17966i −0.0433515 0.104660i
\(924\) 19.2557 + 7.97596i 0.633465 + 0.262390i
\(925\) −0.464466 + 1.12132i −0.0152716 + 0.0368688i
\(926\) 7.97795 7.97795i 0.262172 0.262172i
\(927\) −3.34468 + 3.34468i −0.109854 + 0.109854i
\(928\) −0.192641 + 0.465076i −0.00632374 + 0.0152669i
\(929\) −38.5898 15.9844i −1.26609 0.524432i −0.354318 0.935125i \(-0.615287\pi\)
−0.911774 + 0.410693i \(0.865287\pi\)
\(930\) 7.01514 + 16.9360i 0.230036 + 0.555355i
\(931\) 20.0641i 0.657573i
\(932\) −1.43597 + 0.594799i −0.0470368 + 0.0194833i
\(933\) −19.9585 19.9585i −0.653413 0.653413i
\(934\) 21.8574 0.715195
\(935\) 6.54600 14.5749i 0.214077 0.476651i
\(936\) 0.108829 0.00355720
\(937\) 18.9789 + 18.9789i 0.620014 + 0.620014i 0.945535 0.325521i \(-0.105540\pi\)
−0.325521 + 0.945535i \(0.605540\pi\)
\(938\) 7.17279 2.97107i 0.234200 0.0970088i
\(939\) 25.3880i 0.828507i
\(940\) −1.96281 4.73864i −0.0640197 0.154557i
\(941\) −47.1619 19.5351i −1.53743 0.636826i −0.556445 0.830885i \(-0.687835\pi\)
−0.980990 + 0.194058i \(0.937835\pi\)
\(942\) 5.00686 12.0876i 0.163132 0.393836i
\(943\) −45.8911 + 45.8911i −1.49442 + 1.49442i
\(944\) 6.03300 6.03300i 0.196357 0.196357i
\(945\) −6.75378 + 16.3051i −0.219700 + 0.530404i
\(946\) −0.962198 0.398556i −0.0312838 0.0129582i
\(947\) 7.76243 + 18.7402i 0.252245 + 0.608974i 0.998385 0.0568159i \(-0.0180948\pi\)
−0.746139 + 0.665790i \(0.768095\pi\)
\(948\) 8.12421i 0.263862i
\(949\) −2.52152 + 1.04445i −0.0818520 + 0.0339042i
\(950\) −3.89715 3.89715i −0.126440 0.126440i
\(951\) −45.4910 −1.47515
\(952\) −0.395744 + 13.4436i −0.0128261 + 0.435711i
\(953\) −42.9260 −1.39051 −0.695254 0.718764i \(-0.744708\pi\)
−0.695254 + 0.718764i \(0.744708\pi\)
\(954\) −0.171573 0.171573i −0.00555488 0.00555488i
\(955\) 13.1894 5.46323i 0.426799 0.176786i
\(956\) 11.7012i 0.378445i
\(957\) 1.23087 + 2.97157i 0.0397883 + 0.0960574i
\(958\) 4.04430 + 1.67520i 0.130665 + 0.0541233i
\(959\) 12.2782 29.6422i 0.396483 0.957196i
\(960\) 1.16591 1.16591i 0.0376296 0.0376296i
\(961\) 65.4810 65.4810i 2.11229 2.11229i
\(962\) −0.179690 + 0.433810i −0.00579343 + 0.0139866i
\(963\) 2.65948 + 1.10159i 0.0857006 + 0.0354983i
\(964\) −10.4435 25.2129i −0.336364 0.812054i
\(965\) 20.7634i 0.668398i
\(966\) −37.1698 + 15.3962i −1.19592 + 0.495366i
\(967\) −25.3012 25.3012i −0.813632 0.813632i 0.171545 0.985176i \(-0.445124\pi\)
−0.985176 + 0.171545i \(0.945124\pi\)
\(968\) 4.01639 0.129092
\(969\) 25.7032 + 27.2624i 0.825706 + 0.875794i
\(970\) −11.6797 −0.375011
\(971\) 34.0013 + 34.0013i 1.09115 + 1.09115i 0.995406 + 0.0957464i \(0.0305238\pi\)
0.0957464 + 0.995406i \(0.469476\pi\)
\(972\) 2.69167 1.11493i 0.0863354 0.0357613i
\(973\) 4.07786i 0.130730i
\(974\) 7.61547 + 18.3854i 0.244015 + 0.589105i
\(975\) 0.589339 + 0.244112i 0.0188740 + 0.00781785i
\(976\) −2.59120 + 6.25570i −0.0829422 + 0.200240i
\(977\) −16.9706 + 16.9706i −0.542937 + 0.542937i −0.924389 0.381452i \(-0.875424\pi\)
0.381452 + 0.924389i \(0.375424\pi\)
\(978\) −25.4608 + 25.4608i −0.814145 + 0.814145i
\(979\) 17.8663 43.1329i 0.571008 1.37853i
\(980\) 3.36335 + 1.39315i 0.107438 + 0.0445024i
\(981\) 1.14600 + 2.76668i 0.0365889 + 0.0883334i
\(982\) 26.1149i 0.833361i
\(983\) 38.9250 16.1233i 1.24152 0.514252i 0.337327 0.941387i \(-0.390477\pi\)
0.904188 + 0.427135i \(0.140477\pi\)
\(984\) 10.1157 + 10.1157i 0.322475 + 0.322475i
\(985\) 15.5519 0.495526
\(986\) −1.51018 + 1.42381i −0.0480940 + 0.0453435i
\(987\) 27.5866 0.878092
\(988\) −1.50771 1.50771i −0.0479665 0.0479665i
\(989\) 1.85736 0.769343i 0.0590606 0.0244637i
\(990\) 1.09008i 0.0346451i
\(991\) 6.27811 + 15.1567i 0.199431 + 0.481468i 0.991680 0.128730i \(-0.0410899\pi\)
−0.792249 + 0.610198i \(0.791090\pi\)
\(992\) −10.2715 4.25457i −0.326119 0.135083i
\(993\) −0.489846 + 1.18259i −0.0155448 + 0.0375284i
\(994\) −20.5192 + 20.5192i −0.650831 + 0.650831i
\(995\) −1.77225 + 1.77225i −0.0561840 + 0.0561840i
\(996\) 3.76338 9.08560i 0.119247 0.287888i
\(997\) −38.1614 15.8070i −1.20858 0.500611i −0.314820 0.949151i \(-0.601944\pi\)
−0.893763 + 0.448540i \(0.851944\pi\)
\(998\) −0.410649 0.991395i −0.0129989 0.0313821i
\(999\) 6.56661i 0.207758i
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.121.2 yes 8
5.2 odd 4 850.2.o.f.699.1 8
5.3 odd 4 850.2.o.c.699.2 8
5.4 even 2 850.2.l.d.801.1 8
17.3 odd 16 2890.2.a.bf.1.3 4
17.5 odd 16 2890.2.b.p.2311.6 8
17.9 even 8 inner 170.2.k.a.111.2 8
17.12 odd 16 2890.2.b.p.2311.3 8
17.14 odd 16 2890.2.a.bc.1.2 4
85.9 even 8 850.2.l.d.451.1 8
85.43 odd 8 850.2.o.f.349.1 8
85.77 odd 8 850.2.o.c.349.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.k.a.111.2 8 17.9 even 8 inner
170.2.k.a.121.2 yes 8 1.1 even 1 trivial
850.2.l.d.451.1 8 85.9 even 8
850.2.l.d.801.1 8 5.4 even 2
850.2.o.c.349.2 8 85.77 odd 8
850.2.o.c.699.2 8 5.3 odd 4
850.2.o.f.349.1 8 85.43 odd 8
850.2.o.f.699.1 8 5.2 odd 4
2890.2.a.bc.1.2 4 17.14 odd 16
2890.2.a.bf.1.3 4 17.3 odd 16
2890.2.b.p.2311.3 8 17.12 odd 16
2890.2.b.p.2311.6 8 17.5 odd 16