Properties

Label 847.2.f.m.323.1
Level $847$
Weight $2$
Character 847.323
Analytic conductor $6.763$
Analytic rank $0$
Dimension $4$
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] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), not 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 323.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 847.323
Dual form 847.2.f.m.729.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.80902 + 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-2.23607 + 1.62460i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} +O(q^{10})\) \(q+(1.80902 + 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-2.23607 + 1.62460i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} +4.47214 q^{10} -3.70820 q^{12} +(2.61803 + 1.90211i) q^{13} +(0.690983 - 2.12663i) q^{14} +(0.763932 + 2.35114i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-2.61803 + 1.90211i) q^{17} +(1.01722 + 3.13068i) q^{18} +(-2.00000 + 6.15537i) q^{19} +(4.85410 + 3.52671i) q^{20} +1.23607 q^{21} +2.47214 q^{23} +(-2.23607 - 1.62460i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(2.23607 + 6.88191i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(2.42705 - 1.76336i) q^{28} +(-2.61803 - 8.05748i) q^{29} +(-1.70820 + 5.25731i) q^{30} +(2.23607 + 1.62460i) q^{31} +6.70820 q^{32} -7.23607 q^{34} +(-1.61803 - 1.17557i) q^{35} +(-1.36475 + 4.20025i) q^{36} +(-2.61803 - 8.05748i) q^{37} +(-11.7082 + 8.50651i) q^{38} +(-3.23607 + 2.35114i) q^{39} +(1.38197 + 4.25325i) q^{40} +(3.47214 - 10.6861i) q^{41} +(2.23607 + 1.62460i) q^{42} -8.00000 q^{43} +2.94427 q^{45} +(4.47214 + 3.24920i) q^{46} +(0.854102 - 2.62866i) q^{47} +(0.381966 + 1.17557i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-1.80902 + 1.31433i) q^{50} +(-1.23607 - 3.80423i) q^{51} +(-3.00000 + 9.23305i) q^{52} +(0.381966 + 0.277515i) q^{53} -12.3607 q^{54} +2.23607 q^{56} +(-6.47214 - 4.70228i) q^{57} +(5.85410 - 18.0171i) q^{58} +(-0.381966 - 1.17557i) q^{59} +(-6.00000 + 4.35926i) q^{60} +(-5.85410 + 4.25325i) q^{61} +(1.90983 + 5.87785i) q^{62} +(0.454915 - 1.40008i) q^{63} +(10.5172 + 7.64121i) q^{64} +6.47214 q^{65} +14.4721 q^{67} +(-7.85410 - 5.70634i) q^{68} +(-0.944272 + 2.90617i) q^{69} +(-1.38197 - 4.25325i) q^{70} +(8.47214 - 6.15537i) q^{71} +(-2.66312 + 1.93487i) q^{72} +(0.236068 + 0.726543i) q^{73} +(5.85410 - 18.0171i) q^{74} +(-1.00000 - 0.726543i) q^{75} -19.4164 q^{76} -8.94427 q^{78} +(-7.23607 - 5.25731i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-0.746711 - 2.29814i) q^{81} +(20.3262 - 14.7679i) q^{82} +(-9.23607 + 6.71040i) q^{83} +(1.14590 + 3.52671i) q^{84} +(-2.00000 + 6.15537i) q^{85} +(-14.4721 - 10.5146i) q^{86} +10.4721 q^{87} +2.00000 q^{89} +(5.32624 + 3.86974i) q^{90} +(1.00000 - 3.07768i) q^{91} +(2.29180 + 7.05342i) q^{92} +(-2.76393 + 2.00811i) q^{93} +(5.00000 - 3.63271i) q^{94} +(4.00000 + 12.3107i) q^{95} +(-2.56231 + 7.88597i) q^{96} +(-14.0902 - 10.2371i) q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} + q^{7} - 5 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 5 q^{2} - 6 q^{3} - 3 q^{4} + 2 q^{5} + q^{7} - 5 q^{8} + 7 q^{9} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 12 q^{15} + q^{16} - 6 q^{17} - 25 q^{18} - 8 q^{19} + 6 q^{20} - 4 q^{21} - 8 q^{23} + q^{25} + 3 q^{28} - 6 q^{29} + 20 q^{30} - 20 q^{34} - 2 q^{35} - 39 q^{36} - 6 q^{37} - 20 q^{38} - 4 q^{39} + 10 q^{40} - 4 q^{41} - 32 q^{43} - 24 q^{45} - 10 q^{47} + 6 q^{48} - q^{49} - 5 q^{50} + 4 q^{51} - 12 q^{52} + 6 q^{53} + 40 q^{54} - 8 q^{57} + 10 q^{58} - 6 q^{59} - 24 q^{60} - 10 q^{61} + 30 q^{62} + 13 q^{63} + 13 q^{64} + 8 q^{65} + 40 q^{67} - 18 q^{68} + 32 q^{69} - 10 q^{70} + 16 q^{71} + 5 q^{72} - 8 q^{73} + 10 q^{74} - 4 q^{75} - 24 q^{76} - 20 q^{79} - 2 q^{80} - 41 q^{81} + 50 q^{82} - 28 q^{83} + 18 q^{84} - 8 q^{85} - 40 q^{86} + 24 q^{87} + 8 q^{89} - 10 q^{90} + 4 q^{91} + 36 q^{92} - 20 q^{93} + 20 q^{94} + 16 q^{95} + 30 q^{96} - 34 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.80902 + 1.31433i 1.27917 + 0.929370i 0.999528 0.0307347i \(-0.00978469\pi\)
0.279641 + 0.960105i \(0.409785\pi\)
\(3\) −0.381966 + 1.17557i −0.220528 + 0.678716i 0.778187 + 0.628033i \(0.216140\pi\)
−0.998715 + 0.0506828i \(0.983860\pi\)
\(4\) 0.927051 + 2.85317i 0.463525 + 1.42658i
\(5\) 1.61803 1.17557i 0.723607 0.525731i −0.163928 0.986472i \(-0.552416\pi\)
0.887535 + 0.460741i \(0.152416\pi\)
\(6\) −2.23607 + 1.62460i −0.912871 + 0.663240i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) −0.690983 + 2.12663i −0.244299 + 0.751876i
\(9\) 1.19098 + 0.865300i 0.396994 + 0.288433i
\(10\) 4.47214 1.41421
\(11\) 0 0
\(12\) −3.70820 −1.07047
\(13\) 2.61803 + 1.90211i 0.726112 + 0.527551i 0.888331 0.459204i \(-0.151865\pi\)
−0.162219 + 0.986755i \(0.551865\pi\)
\(14\) 0.690983 2.12663i 0.184673 0.568365i
\(15\) 0.763932 + 2.35114i 0.197246 + 0.607062i
\(16\) 0.809017 0.587785i 0.202254 0.146946i
\(17\) −2.61803 + 1.90211i −0.634967 + 0.461330i −0.858117 0.513454i \(-0.828366\pi\)
0.223151 + 0.974784i \(0.428366\pi\)
\(18\) 1.01722 + 3.13068i 0.239761 + 0.737909i
\(19\) −2.00000 + 6.15537i −0.458831 + 1.41214i 0.407746 + 0.913095i \(0.366315\pi\)
−0.866577 + 0.499043i \(0.833685\pi\)
\(20\) 4.85410 + 3.52671i 1.08541 + 0.788597i
\(21\) 1.23607 0.269732
\(22\) 0 0
\(23\) 2.47214 0.515476 0.257738 0.966215i \(-0.417023\pi\)
0.257738 + 0.966215i \(0.417023\pi\)
\(24\) −2.23607 1.62460i −0.456435 0.331620i
\(25\) −0.309017 + 0.951057i −0.0618034 + 0.190211i
\(26\) 2.23607 + 6.88191i 0.438529 + 1.34965i
\(27\) −4.47214 + 3.24920i −0.860663 + 0.625308i
\(28\) 2.42705 1.76336i 0.458670 0.333243i
\(29\) −2.61803 8.05748i −0.486157 1.49624i −0.830299 0.557319i \(-0.811830\pi\)
0.344142 0.938918i \(-0.388170\pi\)
\(30\) −1.70820 + 5.25731i −0.311874 + 0.959849i
\(31\) 2.23607 + 1.62460i 0.401610 + 0.291787i 0.770196 0.637807i \(-0.220158\pi\)
−0.368587 + 0.929593i \(0.620158\pi\)
\(32\) 6.70820 1.18585
\(33\) 0 0
\(34\) −7.23607 −1.24098
\(35\) −1.61803 1.17557i −0.273498 0.198708i
\(36\) −1.36475 + 4.20025i −0.227458 + 0.700042i
\(37\) −2.61803 8.05748i −0.430402 1.32464i −0.897726 0.440555i \(-0.854782\pi\)
0.467323 0.884086i \(-0.345218\pi\)
\(38\) −11.7082 + 8.50651i −1.89932 + 1.37994i
\(39\) −3.23607 + 2.35114i −0.518186 + 0.376484i
\(40\) 1.38197 + 4.25325i 0.218508 + 0.672499i
\(41\) 3.47214 10.6861i 0.542257 1.66889i −0.185168 0.982707i \(-0.559283\pi\)
0.727425 0.686187i \(-0.240717\pi\)
\(42\) 2.23607 + 1.62460i 0.345033 + 0.250681i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 2.94427 0.438906
\(46\) 4.47214 + 3.24920i 0.659380 + 0.479068i
\(47\) 0.854102 2.62866i 0.124584 0.383429i −0.869241 0.494388i \(-0.835392\pi\)
0.993825 + 0.110959i \(0.0353922\pi\)
\(48\) 0.381966 + 1.17557i 0.0551320 + 0.169679i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) −1.80902 + 1.31433i −0.255834 + 0.185874i
\(51\) −1.23607 3.80423i −0.173084 0.532698i
\(52\) −3.00000 + 9.23305i −0.416025 + 1.28039i
\(53\) 0.381966 + 0.277515i 0.0524671 + 0.0381196i 0.613710 0.789532i \(-0.289677\pi\)
−0.561243 + 0.827651i \(0.689677\pi\)
\(54\) −12.3607 −1.68208
\(55\) 0 0
\(56\) 2.23607 0.298807
\(57\) −6.47214 4.70228i −0.857255 0.622832i
\(58\) 5.85410 18.0171i 0.768681 2.36576i
\(59\) −0.381966 1.17557i −0.0497277 0.153046i 0.923109 0.384538i \(-0.125639\pi\)
−0.972837 + 0.231492i \(0.925639\pi\)
\(60\) −6.00000 + 4.35926i −0.774597 + 0.562777i
\(61\) −5.85410 + 4.25325i −0.749541 + 0.544573i −0.895685 0.444690i \(-0.853314\pi\)
0.146144 + 0.989263i \(0.453314\pi\)
\(62\) 1.90983 + 5.87785i 0.242549 + 0.746488i
\(63\) 0.454915 1.40008i 0.0573139 0.176394i
\(64\) 10.5172 + 7.64121i 1.31465 + 0.955151i
\(65\) 6.47214 0.802770
\(66\) 0 0
\(67\) 14.4721 1.76805 0.884026 0.467437i \(-0.154823\pi\)
0.884026 + 0.467437i \(0.154823\pi\)
\(68\) −7.85410 5.70634i −0.952450 0.691995i
\(69\) −0.944272 + 2.90617i −0.113677 + 0.349862i
\(70\) −1.38197 4.25325i −0.165177 0.508361i
\(71\) 8.47214 6.15537i 1.00546 0.730508i 0.0422061 0.999109i \(-0.486561\pi\)
0.963251 + 0.268601i \(0.0865614\pi\)
\(72\) −2.66312 + 1.93487i −0.313852 + 0.228027i
\(73\) 0.236068 + 0.726543i 0.0276297 + 0.0850354i 0.963920 0.266190i \(-0.0857650\pi\)
−0.936291 + 0.351226i \(0.885765\pi\)
\(74\) 5.85410 18.0171i 0.680526 2.09444i
\(75\) −1.00000 0.726543i −0.115470 0.0838939i
\(76\) −19.4164 −2.22721
\(77\) 0 0
\(78\) −8.94427 −1.01274
\(79\) −7.23607 5.25731i −0.814121 0.591494i 0.100901 0.994896i \(-0.467827\pi\)
−0.915023 + 0.403403i \(0.867827\pi\)
\(80\) 0.618034 1.90211i 0.0690983 0.212663i
\(81\) −0.746711 2.29814i −0.0829679 0.255349i
\(82\) 20.3262 14.7679i 2.24466 1.63084i
\(83\) −9.23607 + 6.71040i −1.01379 + 0.736562i −0.965001 0.262247i \(-0.915536\pi\)
−0.0487895 + 0.998809i \(0.515536\pi\)
\(84\) 1.14590 + 3.52671i 0.125028 + 0.384796i
\(85\) −2.00000 + 6.15537i −0.216930 + 0.667643i
\(86\) −14.4721 10.5146i −1.56057 1.13382i
\(87\) 10.4721 1.12273
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 5.32624 + 3.86974i 0.561435 + 0.407906i
\(91\) 1.00000 3.07768i 0.104828 0.322629i
\(92\) 2.29180 + 7.05342i 0.238936 + 0.735370i
\(93\) −2.76393 + 2.00811i −0.286606 + 0.208232i
\(94\) 5.00000 3.63271i 0.515711 0.374686i
\(95\) 4.00000 + 12.3107i 0.410391 + 1.26305i
\(96\) −2.56231 + 7.88597i −0.261514 + 0.804858i
\(97\) −14.0902 10.2371i −1.43064 1.03942i −0.989897 0.141787i \(-0.954715\pi\)
−0.440743 0.897633i \(-0.645285\pi\)
\(98\) −2.23607 −0.225877
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) −3.85410 2.80017i −0.383497 0.278627i 0.379288 0.925279i \(-0.376169\pi\)
−0.762786 + 0.646651i \(0.776169\pi\)
\(102\) 2.76393 8.50651i 0.273670 0.842270i
\(103\) 2.38197 + 7.33094i 0.234702 + 0.722339i 0.997161 + 0.0753019i \(0.0239920\pi\)
−0.762459 + 0.647037i \(0.776008\pi\)
\(104\) −5.85410 + 4.25325i −0.574042 + 0.417066i
\(105\) 2.00000 1.45309i 0.195180 0.141807i
\(106\) 0.326238 + 1.00406i 0.0316870 + 0.0975226i
\(107\) 1.23607 3.80423i 0.119495 0.367768i −0.873363 0.487070i \(-0.838066\pi\)
0.992858 + 0.119302i \(0.0380656\pi\)
\(108\) −13.4164 9.74759i −1.29099 0.937962i
\(109\) 4.47214 0.428353 0.214176 0.976795i \(-0.431293\pi\)
0.214176 + 0.976795i \(0.431293\pi\)
\(110\) 0 0
\(111\) 10.4721 0.993971
\(112\) −0.809017 0.587785i −0.0764449 0.0555405i
\(113\) 0.618034 1.90211i 0.0581397 0.178936i −0.917769 0.397114i \(-0.870012\pi\)
0.975909 + 0.218179i \(0.0700116\pi\)
\(114\) −5.52786 17.0130i −0.517732 1.59341i
\(115\) 4.00000 2.90617i 0.373002 0.271002i
\(116\) 20.5623 14.9394i 1.90916 1.38709i
\(117\) 1.47214 + 4.53077i 0.136099 + 0.418870i
\(118\) 0.854102 2.62866i 0.0786265 0.241987i
\(119\) 2.61803 + 1.90211i 0.239995 + 0.174366i
\(120\) −5.52786 −0.504623
\(121\) 0 0
\(122\) −16.1803 −1.46490
\(123\) 11.2361 + 8.16348i 1.01312 + 0.736076i
\(124\) −2.56231 + 7.88597i −0.230102 + 0.708181i
\(125\) 3.70820 + 11.4127i 0.331672 + 1.02078i
\(126\) 2.66312 1.93487i 0.237249 0.172372i
\(127\) 2.47214 1.79611i 0.219367 0.159379i −0.472675 0.881237i \(-0.656712\pi\)
0.692041 + 0.721858i \(0.256712\pi\)
\(128\) 4.83688 + 14.8864i 0.427524 + 1.31578i
\(129\) 3.05573 9.40456i 0.269042 0.828026i
\(130\) 11.7082 + 8.50651i 1.02688 + 0.746070i
\(131\) −21.8885 −1.91241 −0.956205 0.292696i \(-0.905448\pi\)
−0.956205 + 0.292696i \(0.905448\pi\)
\(132\) 0 0
\(133\) 6.47214 0.561205
\(134\) 26.1803 + 19.0211i 2.26164 + 1.64318i
\(135\) −3.41641 + 10.5146i −0.294038 + 0.904955i
\(136\) −2.23607 6.88191i −0.191741 0.590119i
\(137\) −13.3262 + 9.68208i −1.13854 + 0.827196i −0.986915 0.161243i \(-0.948450\pi\)
−0.151623 + 0.988438i \(0.548450\pi\)
\(138\) −5.52786 + 4.01623i −0.470563 + 0.341884i
\(139\) 0.472136 + 1.45309i 0.0400460 + 0.123249i 0.969081 0.246743i \(-0.0793604\pi\)
−0.929035 + 0.369992i \(0.879360\pi\)
\(140\) 1.85410 5.70634i 0.156700 0.482274i
\(141\) 2.76393 + 2.00811i 0.232765 + 0.169114i
\(142\) 23.4164 1.96506
\(143\) 0 0
\(144\) 1.47214 0.122678
\(145\) −13.7082 9.95959i −1.13840 0.827099i
\(146\) −0.527864 + 1.62460i −0.0436863 + 0.134453i
\(147\) −0.381966 1.17557i −0.0315040 0.0969594i
\(148\) 20.5623 14.9394i 1.69021 1.22801i
\(149\) 11.3262 8.22899i 0.927882 0.674145i −0.0175917 0.999845i \(-0.505600\pi\)
0.945473 + 0.325700i \(0.105600\pi\)
\(150\) −0.854102 2.62866i −0.0697371 0.214629i
\(151\) −2.76393 + 8.50651i −0.224926 + 0.692250i 0.773374 + 0.633951i \(0.218568\pi\)
−0.998299 + 0.0582992i \(0.981432\pi\)
\(152\) −11.7082 8.50651i −0.949661 0.689969i
\(153\) −4.76393 −0.385141
\(154\) 0 0
\(155\) 5.52786 0.444009
\(156\) −9.70820 7.05342i −0.777278 0.564726i
\(157\) 3.38197 10.4086i 0.269910 0.830698i −0.720611 0.693340i \(-0.756139\pi\)
0.990521 0.137359i \(-0.0438614\pi\)
\(158\) −6.18034 19.0211i −0.491681 1.51324i
\(159\) −0.472136 + 0.343027i −0.0374428 + 0.0272038i
\(160\) 10.8541 7.88597i 0.858092 0.623440i
\(161\) −0.763932 2.35114i −0.0602063 0.185296i
\(162\) 1.66970 5.13880i 0.131184 0.403742i
\(163\) 2.76393 + 2.00811i 0.216488 + 0.157288i 0.690744 0.723099i \(-0.257283\pi\)
−0.474256 + 0.880387i \(0.657283\pi\)
\(164\) 33.7082 2.63217
\(165\) 0 0
\(166\) −25.5279 −1.98135
\(167\) 4.00000 + 2.90617i 0.309529 + 0.224886i 0.731694 0.681633i \(-0.238730\pi\)
−0.422165 + 0.906519i \(0.638730\pi\)
\(168\) −0.854102 + 2.62866i −0.0658954 + 0.202805i
\(169\) −0.781153 2.40414i −0.0600887 0.184934i
\(170\) −11.7082 + 8.50651i −0.897978 + 0.652419i
\(171\) −7.70820 + 5.60034i −0.589461 + 0.428269i
\(172\) −7.41641 22.8254i −0.565496 1.74042i
\(173\) 3.94427 12.1392i 0.299877 0.922928i −0.681662 0.731667i \(-0.738742\pi\)
0.981539 0.191261i \(-0.0612575\pi\)
\(174\) 18.9443 + 13.7638i 1.43616 + 1.04343i
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 1.52786 0.114841
\(178\) 3.61803 + 2.62866i 0.271183 + 0.197026i
\(179\) −2.76393 + 8.50651i −0.206586 + 0.635806i 0.793059 + 0.609145i \(0.208487\pi\)
−0.999645 + 0.0266609i \(0.991513\pi\)
\(180\) 2.72949 + 8.40051i 0.203444 + 0.626137i
\(181\) 20.5623 14.9394i 1.52838 1.11044i 0.571256 0.820772i \(-0.306456\pi\)
0.957128 0.289664i \(-0.0935436\pi\)
\(182\) 5.85410 4.25325i 0.433935 0.315272i
\(183\) −2.76393 8.50651i −0.204316 0.628819i
\(184\) −1.70820 + 5.25731i −0.125930 + 0.387574i
\(185\) −13.7082 9.95959i −1.00785 0.732244i
\(186\) −7.63932 −0.560142
\(187\) 0 0
\(188\) 8.29180 0.604741
\(189\) 4.47214 + 3.24920i 0.325300 + 0.236344i
\(190\) −8.94427 + 27.5276i −0.648886 + 1.99706i
\(191\) −0.944272 2.90617i −0.0683251 0.210283i 0.911064 0.412264i \(-0.135262\pi\)
−0.979389 + 0.201981i \(0.935262\pi\)
\(192\) −13.0000 + 9.44505i −0.938194 + 0.681638i
\(193\) 9.61803 6.98791i 0.692321 0.503001i −0.185101 0.982719i \(-0.559261\pi\)
0.877422 + 0.479719i \(0.159261\pi\)
\(194\) −12.0344 37.0382i −0.864023 2.65919i
\(195\) −2.47214 + 7.60845i −0.177033 + 0.544853i
\(196\) −2.42705 1.76336i −0.173361 0.125954i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) −2.18034 −0.154560 −0.0772801 0.997009i \(-0.524624\pi\)
−0.0772801 + 0.997009i \(0.524624\pi\)
\(200\) −1.80902 1.31433i −0.127917 0.0929370i
\(201\) −5.52786 + 17.0130i −0.389905 + 1.20001i
\(202\) −3.29180 10.1311i −0.231610 0.712822i
\(203\) −6.85410 + 4.97980i −0.481064 + 0.349513i
\(204\) 9.70820 7.05342i 0.679710 0.493838i
\(205\) −6.94427 21.3723i −0.485009 1.49270i
\(206\) −5.32624 + 16.3925i −0.371097 + 1.14212i
\(207\) 2.94427 + 2.13914i 0.204641 + 0.148680i
\(208\) 3.23607 0.224381
\(209\) 0 0
\(210\) 5.52786 0.381459
\(211\) −11.2361 8.16348i −0.773523 0.561997i 0.129505 0.991579i \(-0.458661\pi\)
−0.903028 + 0.429582i \(0.858661\pi\)
\(212\) −0.437694 + 1.34708i −0.0300610 + 0.0925181i
\(213\) 4.00000 + 12.3107i 0.274075 + 0.843518i
\(214\) 7.23607 5.25731i 0.494647 0.359382i
\(215\) −12.9443 + 9.40456i −0.882792 + 0.641386i
\(216\) −3.81966 11.7557i −0.259895 0.799874i
\(217\) 0.854102 2.62866i 0.0579802 0.178445i
\(218\) 8.09017 + 5.87785i 0.547935 + 0.398098i
\(219\) −0.944272 −0.0638080
\(220\) 0 0
\(221\) −10.4721 −0.704432
\(222\) 18.9443 + 13.7638i 1.27146 + 0.923767i
\(223\) −3.14590 + 9.68208i −0.210665 + 0.648360i 0.788768 + 0.614691i \(0.210719\pi\)
−0.999433 + 0.0336691i \(0.989281\pi\)
\(224\) −2.07295 6.37988i −0.138505 0.426274i
\(225\) −1.19098 + 0.865300i −0.0793989 + 0.0576867i
\(226\) 3.61803 2.62866i 0.240668 0.174856i
\(227\) −1.81966 5.60034i −0.120775 0.371707i 0.872333 0.488913i \(-0.162606\pi\)
−0.993108 + 0.117205i \(0.962606\pi\)
\(228\) 7.41641 22.8254i 0.491164 1.51165i
\(229\) 3.61803 + 2.62866i 0.239086 + 0.173706i 0.700876 0.713283i \(-0.252793\pi\)
−0.461790 + 0.886989i \(0.652793\pi\)
\(230\) 11.0557 0.728993
\(231\) 0 0
\(232\) 18.9443 1.24375
\(233\) 7.61803 + 5.53483i 0.499074 + 0.362598i 0.808663 0.588272i \(-0.200192\pi\)
−0.309589 + 0.950870i \(0.600192\pi\)
\(234\) −3.29180 + 10.1311i −0.215191 + 0.662291i
\(235\) −1.70820 5.25731i −0.111431 0.342949i
\(236\) 3.00000 2.17963i 0.195283 0.141882i
\(237\) 8.94427 6.49839i 0.580993 0.422116i
\(238\) 2.23607 + 6.88191i 0.144943 + 0.446088i
\(239\) 3.05573 9.40456i 0.197659 0.608331i −0.802277 0.596952i \(-0.796378\pi\)
0.999935 0.0113783i \(-0.00362189\pi\)
\(240\) 2.00000 + 1.45309i 0.129099 + 0.0937962i
\(241\) 13.1246 0.845431 0.422715 0.906263i \(-0.361077\pi\)
0.422715 + 0.906263i \(0.361077\pi\)
\(242\) 0 0
\(243\) −13.5967 −0.872232
\(244\) −17.5623 12.7598i −1.12431 0.816860i
\(245\) −0.618034 + 1.90211i −0.0394847 + 0.121522i
\(246\) 9.59675 + 29.5358i 0.611866 + 1.88313i
\(247\) −16.9443 + 12.3107i −1.07814 + 0.783313i
\(248\) −5.00000 + 3.63271i −0.317500 + 0.230677i
\(249\) −4.36068 13.4208i −0.276347 0.850508i
\(250\) −8.29180 + 25.5195i −0.524419 + 1.61400i
\(251\) −3.47214 2.52265i −0.219159 0.159229i 0.472789 0.881176i \(-0.343247\pi\)
−0.691948 + 0.721947i \(0.743247\pi\)
\(252\) 4.41641 0.278208
\(253\) 0 0
\(254\) 6.83282 0.428729
\(255\) −6.47214 4.70228i −0.405301 0.294468i
\(256\) −2.78115 + 8.55951i −0.173822 + 0.534969i
\(257\) −1.85410 5.70634i −0.115656 0.355952i 0.876428 0.481534i \(-0.159920\pi\)
−0.992083 + 0.125582i \(0.959920\pi\)
\(258\) 17.8885 12.9968i 1.11369 0.809145i
\(259\) −6.85410 + 4.97980i −0.425893 + 0.309430i
\(260\) 6.00000 + 18.4661i 0.372104 + 1.14522i
\(261\) 3.85410 11.8617i 0.238563 0.734221i
\(262\) −39.5967 28.7687i −2.44630 1.77734i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0.944272 0.0580062
\(266\) 11.7082 + 8.50651i 0.717876 + 0.521567i
\(267\) −0.763932 + 2.35114i −0.0467519 + 0.143887i
\(268\) 13.4164 + 41.2915i 0.819538 + 2.52228i
\(269\) −10.8541 + 7.88597i −0.661786 + 0.480816i −0.867266 0.497846i \(-0.834125\pi\)
0.205479 + 0.978661i \(0.434125\pi\)
\(270\) −20.0000 + 14.5309i −1.21716 + 0.884319i
\(271\) 3.23607 + 9.95959i 0.196577 + 0.605002i 0.999955 + 0.00953205i \(0.00303419\pi\)
−0.803377 + 0.595470i \(0.796966\pi\)
\(272\) −1.00000 + 3.07768i −0.0606339 + 0.186612i
\(273\) 3.23607 + 2.35114i 0.195856 + 0.142298i
\(274\) −36.8328 −2.22515
\(275\) 0 0
\(276\) −9.16718 −0.551800
\(277\) −16.0902 11.6902i −0.966765 0.702396i −0.0120527 0.999927i \(-0.503837\pi\)
−0.954712 + 0.297532i \(0.903837\pi\)
\(278\) −1.05573 + 3.24920i −0.0633184 + 0.194874i
\(279\) 1.25735 + 3.86974i 0.0752758 + 0.231675i
\(280\) 3.61803 2.62866i 0.216219 0.157092i
\(281\) −2.85410 + 2.07363i −0.170261 + 0.123702i −0.669653 0.742674i \(-0.733557\pi\)
0.499391 + 0.866377i \(0.333557\pi\)
\(282\) 2.36068 + 7.26543i 0.140576 + 0.432650i
\(283\) −9.23607 + 28.4257i −0.549027 + 1.68973i 0.162190 + 0.986760i \(0.448144\pi\)
−0.711217 + 0.702973i \(0.751856\pi\)
\(284\) 25.4164 + 18.4661i 1.50819 + 1.09576i
\(285\) −16.0000 −0.947758
\(286\) 0 0
\(287\) −11.2361 −0.663244
\(288\) 7.98936 + 5.80461i 0.470777 + 0.342040i
\(289\) −2.01722 + 6.20837i −0.118660 + 0.365198i
\(290\) −11.7082 36.0341i −0.687529 2.11600i
\(291\) 17.4164 12.6538i 1.02097 0.741777i
\(292\) −1.85410 + 1.34708i −0.108503 + 0.0788321i
\(293\) 7.76393 + 23.8949i 0.453574 + 1.39596i 0.872801 + 0.488075i \(0.162301\pi\)
−0.419228 + 0.907881i \(0.637699\pi\)
\(294\) 0.854102 2.62866i 0.0498122 0.153306i
\(295\) −2.00000 1.45309i −0.116445 0.0846019i
\(296\) 18.9443 1.10111
\(297\) 0 0
\(298\) 31.3050 1.81345
\(299\) 6.47214 + 4.70228i 0.374293 + 0.271940i
\(300\) 1.14590 3.52671i 0.0661585 0.203615i
\(301\) 2.47214 + 7.60845i 0.142492 + 0.438544i
\(302\) −16.1803 + 11.7557i −0.931074 + 0.676465i
\(303\) 4.76393 3.46120i 0.273681 0.198841i
\(304\) 2.00000 + 6.15537i 0.114708 + 0.353035i
\(305\) −4.47214 + 13.7638i −0.256074 + 0.788114i
\(306\) −8.61803 6.26137i −0.492660 0.357939i
\(307\) 8.94427 0.510477 0.255238 0.966878i \(-0.417846\pi\)
0.255238 + 0.966878i \(0.417846\pi\)
\(308\) 0 0
\(309\) −9.52786 −0.542021
\(310\) 10.0000 + 7.26543i 0.567962 + 0.412648i
\(311\) −2.56231 + 7.88597i −0.145295 + 0.447172i −0.997049 0.0767701i \(-0.975539\pi\)
0.851754 + 0.523942i \(0.175539\pi\)
\(312\) −2.76393 8.50651i −0.156477 0.481586i
\(313\) −12.0902 + 8.78402i −0.683377 + 0.496502i −0.874476 0.485068i \(-0.838795\pi\)
0.191099 + 0.981571i \(0.438795\pi\)
\(314\) 19.7984 14.3844i 1.11729 0.811756i
\(315\) −0.909830 2.80017i −0.0512631 0.157772i
\(316\) 8.29180 25.5195i 0.466450 1.43559i
\(317\) −11.3262 8.22899i −0.636145 0.462186i 0.222379 0.974960i \(-0.428618\pi\)
−0.858524 + 0.512774i \(0.828618\pi\)
\(318\) −1.30495 −0.0731781
\(319\) 0 0
\(320\) 26.0000 1.45344
\(321\) 4.00000 + 2.90617i 0.223258 + 0.162207i
\(322\) 1.70820 5.25731i 0.0951945 0.292978i
\(323\) −6.47214 19.9192i −0.360119 1.10833i
\(324\) 5.86475 4.26099i 0.325819 0.236721i
\(325\) −2.61803 + 1.90211i −0.145222 + 0.105510i
\(326\) 2.36068 + 7.26543i 0.130746 + 0.402395i
\(327\) −1.70820 + 5.25731i −0.0944639 + 0.290730i
\(328\) 20.3262 + 14.7679i 1.12233 + 0.815420i
\(329\) −2.76393 −0.152381
\(330\) 0 0
\(331\) −13.8885 −0.763383 −0.381692 0.924290i \(-0.624658\pi\)
−0.381692 + 0.924290i \(0.624658\pi\)
\(332\) −27.7082 20.1312i −1.52069 1.10484i
\(333\) 3.85410 11.8617i 0.211203 0.650017i
\(334\) 3.41641 + 10.5146i 0.186938 + 0.575335i
\(335\) 23.4164 17.0130i 1.27938 0.929520i
\(336\) 1.00000 0.726543i 0.0545545 0.0396361i
\(337\) 3.56231 + 10.9637i 0.194051 + 0.597228i 0.999986 + 0.00522430i \(0.00166295\pi\)
−0.805935 + 0.592004i \(0.798337\pi\)
\(338\) 1.74671 5.37582i 0.0950086 0.292406i
\(339\) 2.00000 + 1.45309i 0.108625 + 0.0789207i
\(340\) −19.4164 −1.05300
\(341\) 0 0
\(342\) −21.3050 −1.15204
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) 5.52786 17.0130i 0.298042 0.917280i
\(345\) 1.88854 + 5.81234i 0.101676 + 0.312926i
\(346\) 23.0902 16.7760i 1.24134 0.901883i
\(347\) 16.9443 12.3107i 0.909616 0.660875i −0.0313016 0.999510i \(-0.509965\pi\)
0.940918 + 0.338635i \(0.109965\pi\)
\(348\) 9.70820 + 29.8788i 0.520414 + 1.60167i
\(349\) 2.23607 6.88191i 0.119694 0.368380i −0.873203 0.487356i \(-0.837961\pi\)
0.992897 + 0.118976i \(0.0379612\pi\)
\(350\) 1.80902 + 1.31433i 0.0966960 + 0.0702538i
\(351\) −17.8885 −0.954820
\(352\) 0 0
\(353\) 19.8885 1.05856 0.529280 0.848447i \(-0.322462\pi\)
0.529280 + 0.848447i \(0.322462\pi\)
\(354\) 2.76393 + 2.00811i 0.146901 + 0.106730i
\(355\) 6.47214 19.9192i 0.343505 1.05720i
\(356\) 1.85410 + 5.70634i 0.0982672 + 0.302435i
\(357\) −3.23607 + 2.35114i −0.171271 + 0.124436i
\(358\) −16.1803 + 11.7557i −0.855158 + 0.621308i
\(359\) 7.70820 + 23.7234i 0.406823 + 1.25207i 0.919363 + 0.393410i \(0.128705\pi\)
−0.512540 + 0.858664i \(0.671295\pi\)
\(360\) −2.03444 + 6.26137i −0.107225 + 0.330003i
\(361\) −18.5172 13.4535i −0.974591 0.708082i
\(362\) 56.8328 2.98707
\(363\) 0 0
\(364\) 9.70820 0.508848
\(365\) 1.23607 + 0.898056i 0.0646988 + 0.0470064i
\(366\) 6.18034 19.0211i 0.323052 0.994250i
\(367\) −7.14590 21.9928i −0.373013 1.14802i −0.944810 0.327620i \(-0.893753\pi\)
0.571797 0.820395i \(-0.306247\pi\)
\(368\) 2.00000 1.45309i 0.104257 0.0757473i
\(369\) 13.3820 9.72257i 0.696637 0.506137i
\(370\) −11.7082 36.0341i −0.608681 1.87333i
\(371\) 0.145898 0.449028i 0.00757465 0.0233124i
\(372\) −8.29180 6.02434i −0.429910 0.312348i
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) −14.8328 −0.765963
\(376\) 5.00000 + 3.63271i 0.257855 + 0.187343i
\(377\) 8.47214 26.0746i 0.436337 1.34291i
\(378\) 3.81966 + 11.7557i 0.196462 + 0.604648i
\(379\) −30.1803 + 21.9273i −1.55026 + 1.12633i −0.606795 + 0.794859i \(0.707545\pi\)
−0.943465 + 0.331471i \(0.892455\pi\)
\(380\) −31.4164 + 22.8254i −1.61163 + 1.17092i
\(381\) 1.16718 + 3.59222i 0.0597967 + 0.184035i
\(382\) 2.11146 6.49839i 0.108031 0.332487i
\(383\) 3.76393 + 2.73466i 0.192328 + 0.139734i 0.679782 0.733414i \(-0.262074\pi\)
−0.487454 + 0.873149i \(0.662074\pi\)
\(384\) −19.3475 −0.987324
\(385\) 0 0
\(386\) 26.5836 1.35307
\(387\) −9.52786 6.92240i −0.484329 0.351885i
\(388\) 16.1459 49.6920i 0.819684 2.52273i
\(389\) 4.90983 + 15.1109i 0.248938 + 0.766153i 0.994964 + 0.100236i \(0.0319597\pi\)
−0.746025 + 0.665917i \(0.768040\pi\)
\(390\) −14.4721 + 10.5146i −0.732825 + 0.532429i
\(391\) −6.47214 + 4.70228i −0.327310 + 0.237805i
\(392\) −0.690983 2.12663i −0.0348999 0.107411i
\(393\) 8.36068 25.7315i 0.421741 1.29798i
\(394\) 3.61803 + 2.62866i 0.182274 + 0.132430i
\(395\) −17.8885 −0.900070
\(396\) 0 0
\(397\) −35.8885 −1.80119 −0.900597 0.434655i \(-0.856870\pi\)
−0.900597 + 0.434655i \(0.856870\pi\)
\(398\) −3.94427 2.86568i −0.197708 0.143644i
\(399\) −2.47214 + 7.60845i −0.123762 + 0.380899i
\(400\) 0.309017 + 0.951057i 0.0154508 + 0.0475528i
\(401\) −18.5623 + 13.4863i −0.926957 + 0.673474i −0.945246 0.326359i \(-0.894178\pi\)
0.0182886 + 0.999833i \(0.494178\pi\)
\(402\) −32.3607 + 23.5114i −1.61400 + 1.17264i
\(403\) 2.76393 + 8.50651i 0.137681 + 0.423739i
\(404\) 4.41641 13.5923i 0.219725 0.676242i
\(405\) −3.90983 2.84066i −0.194281 0.141153i
\(406\) −18.9443 −0.940188
\(407\) 0 0
\(408\) 8.94427 0.442807
\(409\) 7.38197 + 5.36331i 0.365015 + 0.265199i 0.755141 0.655563i \(-0.227569\pi\)
−0.390126 + 0.920762i \(0.627569\pi\)
\(410\) 15.5279 47.7899i 0.766867 2.36017i
\(411\) −6.29180 19.3642i −0.310351 0.955163i
\(412\) −18.7082 + 13.5923i −0.921687 + 0.669645i
\(413\) −1.00000 + 0.726543i −0.0492068 + 0.0357508i
\(414\) 2.51471 + 7.73948i 0.123591 + 0.380375i
\(415\) −7.05573 + 21.7153i −0.346352 + 1.06596i
\(416\) 17.5623 + 12.7598i 0.861063 + 0.625599i
\(417\) −1.88854 −0.0924824
\(418\) 0 0
\(419\) 24.6525 1.20435 0.602176 0.798363i \(-0.294300\pi\)
0.602176 + 0.798363i \(0.294300\pi\)
\(420\) 6.00000 + 4.35926i 0.292770 + 0.212710i
\(421\) 6.90983 21.2663i 0.336765 1.03645i −0.629082 0.777339i \(-0.716569\pi\)
0.965846 0.259116i \(-0.0834310\pi\)
\(422\) −9.59675 29.5358i −0.467162 1.43778i
\(423\) 3.29180 2.39163i 0.160053 0.116285i
\(424\) −0.854102 + 0.620541i −0.0414789 + 0.0301362i
\(425\) −1.00000 3.07768i −0.0485071 0.149290i
\(426\) −8.94427 + 27.5276i −0.433351 + 1.33372i
\(427\) 5.85410 + 4.25325i 0.283300 + 0.205829i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −35.7771 −1.72532
\(431\) 9.70820 + 7.05342i 0.467628 + 0.339751i 0.796516 0.604617i \(-0.206674\pi\)
−0.328888 + 0.944369i \(0.606674\pi\)
\(432\) −1.70820 + 5.25731i −0.0821860 + 0.252942i
\(433\) −2.61803 8.05748i −0.125815 0.387218i 0.868234 0.496155i \(-0.165255\pi\)
−0.994049 + 0.108937i \(0.965255\pi\)
\(434\) 5.00000 3.63271i 0.240008 0.174376i
\(435\) 16.9443 12.3107i 0.812416 0.590255i
\(436\) 4.14590 + 12.7598i 0.198553 + 0.611082i
\(437\) −4.94427 + 15.2169i −0.236517 + 0.727923i
\(438\) −1.70820 1.24108i −0.0816211 0.0593012i
\(439\) −10.4721 −0.499808 −0.249904 0.968271i \(-0.580399\pi\)
−0.249904 + 0.968271i \(0.580399\pi\)
\(440\) 0 0
\(441\) −1.47214 −0.0701017
\(442\) −18.9443 13.7638i −0.901087 0.654678i
\(443\) −7.70820 + 23.7234i −0.366228 + 1.12713i 0.582981 + 0.812486i \(0.301886\pi\)
−0.949209 + 0.314647i \(0.898114\pi\)
\(444\) 9.70820 + 29.8788i 0.460731 + 1.41798i
\(445\) 3.23607 2.35114i 0.153404 0.111455i
\(446\) −18.4164 + 13.3803i −0.872042 + 0.633576i
\(447\) 5.34752 + 16.4580i 0.252929 + 0.778436i
\(448\) 4.01722 12.3637i 0.189796 0.584132i
\(449\) 23.0344 + 16.7355i 1.08706 + 0.789797i 0.978901 0.204336i \(-0.0655036\pi\)
0.108162 + 0.994133i \(0.465504\pi\)
\(450\) −3.29180 −0.155177
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −8.94427 6.49839i −0.420239 0.305321i
\(454\) 4.06888 12.5227i 0.190962 0.587721i
\(455\) −2.00000 6.15537i −0.0937614 0.288568i
\(456\) 14.4721 10.5146i 0.677720 0.492392i
\(457\) −23.3262 + 16.9475i −1.09116 + 0.792771i −0.979594 0.200987i \(-0.935585\pi\)
−0.111561 + 0.993758i \(0.535585\pi\)
\(458\) 3.09017 + 9.51057i 0.144394 + 0.444400i
\(459\) 5.52786 17.0130i 0.258019 0.794100i
\(460\) 12.0000 + 8.71851i 0.559503 + 0.406503i
\(461\) 12.1803 0.567295 0.283647 0.958929i \(-0.408455\pi\)
0.283647 + 0.958929i \(0.408455\pi\)
\(462\) 0 0
\(463\) −5.52786 −0.256902 −0.128451 0.991716i \(-0.541000\pi\)
−0.128451 + 0.991716i \(0.541000\pi\)
\(464\) −6.85410 4.97980i −0.318194 0.231181i
\(465\) −2.11146 + 6.49839i −0.0979164 + 0.301356i
\(466\) 6.50658 + 20.0252i 0.301411 + 0.927649i
\(467\) −19.4721 + 14.1473i −0.901063 + 0.654661i −0.938739 0.344629i \(-0.888005\pi\)
0.0376758 + 0.999290i \(0.488005\pi\)
\(468\) −11.5623 + 8.40051i −0.534468 + 0.388314i
\(469\) −4.47214 13.7638i −0.206504 0.635554i
\(470\) 3.81966 11.7557i 0.176188 0.542250i
\(471\) 10.9443 + 7.95148i 0.504285 + 0.366385i
\(472\) 2.76393 0.127220
\(473\) 0 0
\(474\) 24.7214 1.13549
\(475\) −5.23607 3.80423i −0.240247 0.174550i
\(476\) −3.00000 + 9.23305i −0.137505 + 0.423196i
\(477\) 0.214782 + 0.661030i 0.00983418 + 0.0302665i
\(478\) 17.8885 12.9968i 0.818203 0.594459i
\(479\) 10.9443 7.95148i 0.500057 0.363312i −0.308982 0.951068i \(-0.599988\pi\)
0.809039 + 0.587756i \(0.199988\pi\)
\(480\) 5.12461 + 15.7719i 0.233905 + 0.719887i
\(481\) 8.47214 26.0746i 0.386296 1.18890i
\(482\) 23.7426 + 17.2500i 1.08145 + 0.785718i
\(483\) 3.05573 0.139040
\(484\) 0 0
\(485\) −34.8328 −1.58168
\(486\) −24.5967 17.8706i −1.11573 0.810626i
\(487\) −11.2361 + 34.5811i −0.509155 + 1.56702i 0.284517 + 0.958671i \(0.408167\pi\)
−0.793672 + 0.608346i \(0.791833\pi\)
\(488\) −5.00000 15.3884i −0.226339 0.696601i
\(489\) −3.41641 + 2.48217i −0.154495 + 0.112247i
\(490\) −3.61803 + 2.62866i −0.163446 + 0.118751i
\(491\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(492\) −12.8754 + 39.6264i −0.580467 + 1.78649i
\(493\) 22.1803 + 16.1150i 0.998952 + 0.725781i
\(494\) −46.8328 −2.10711
\(495\) 0 0
\(496\) 2.76393 0.124104
\(497\) −8.47214 6.15537i −0.380027 0.276106i
\(498\) 9.75078 30.0098i 0.436943 1.34477i
\(499\) 0.472136 + 1.45309i 0.0211357 + 0.0650490i 0.961068 0.276312i \(-0.0891122\pi\)
−0.939932 + 0.341361i \(0.889112\pi\)
\(500\) −29.1246 + 21.1603i −1.30249 + 0.946316i
\(501\) −4.94427 + 3.59222i −0.220894 + 0.160489i
\(502\) −2.96556 9.12705i −0.132359 0.407360i
\(503\) −7.23607 + 22.2703i −0.322640 + 0.992985i 0.649854 + 0.760059i \(0.274830\pi\)
−0.972494 + 0.232926i \(0.925170\pi\)
\(504\) 2.66312 + 1.93487i 0.118625 + 0.0861859i
\(505\) −9.52786 −0.423984
\(506\) 0 0
\(507\) 3.12461 0.138769
\(508\) 7.41641 + 5.38834i 0.329050 + 0.239069i
\(509\) 12.5066 38.4913i 0.554344 1.70610i −0.143324 0.989676i \(-0.545779\pi\)
0.697669 0.716421i \(-0.254221\pi\)
\(510\) −5.52786 17.0130i −0.244778 0.753349i
\(511\) 0.618034 0.449028i 0.0273402 0.0198638i
\(512\) 9.04508 6.57164i 0.399740 0.290428i
\(513\) −11.0557 34.0260i −0.488122 1.50229i
\(514\) 4.14590 12.7598i 0.182868 0.562809i
\(515\) 12.4721 + 9.06154i 0.549588 + 0.399299i
\(516\) 29.6656 1.30596
\(517\) 0 0
\(518\) −18.9443 −0.832364
\(519\) 12.7639 + 9.27354i 0.560274 + 0.407063i
\(520\) −4.47214 + 13.7638i −0.196116 + 0.603583i
\(521\) 9.38197 + 28.8747i 0.411031 + 1.26502i 0.915753 + 0.401742i \(0.131595\pi\)
−0.504721 + 0.863282i \(0.668405\pi\)
\(522\) 22.5623 16.3925i 0.987525 0.717479i
\(523\) 35.5967 25.8626i 1.55654 1.13089i 0.617759 0.786367i \(-0.288041\pi\)
0.938778 0.344523i \(-0.111959\pi\)
\(524\) −20.2918 62.4517i −0.886451 2.72822i
\(525\) −0.381966 + 1.17557i −0.0166704 + 0.0513061i
\(526\) 0 0
\(527\) −8.94427 −0.389619
\(528\) 0 0
\(529\) −16.8885 −0.734285
\(530\) 1.70820 + 1.24108i 0.0741996 + 0.0539092i
\(531\) 0.562306 1.73060i 0.0244020 0.0751016i
\(532\) 6.00000 + 18.4661i 0.260133 + 0.800607i
\(533\) 29.4164 21.3723i 1.27417 0.925736i
\(534\) −4.47214 + 3.24920i −0.193528 + 0.140607i
\(535\) −2.47214 7.60845i −0.106880 0.328942i
\(536\) −10.0000 + 30.7768i −0.431934 + 1.32936i
\(537\) −8.94427 6.49839i −0.385974 0.280426i
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) −33.1672 −1.42729
\(541\) 16.8541 + 12.2452i 0.724614 + 0.526463i 0.887855 0.460123i \(-0.152195\pi\)
−0.163241 + 0.986586i \(0.552195\pi\)
\(542\) −7.23607 + 22.2703i −0.310816 + 0.956592i
\(543\) 9.70820 + 29.8788i 0.416619 + 1.28222i
\(544\) −17.5623 + 12.7598i −0.752978 + 0.547070i
\(545\) 7.23607 5.25731i 0.309959 0.225198i
\(546\) 2.76393 + 8.50651i 0.118285 + 0.364045i
\(547\) −8.65248 + 26.6296i −0.369953 + 1.13860i 0.576868 + 0.816838i \(0.304275\pi\)
−0.946821 + 0.321761i \(0.895725\pi\)
\(548\) −39.9787 29.0462i −1.70781 1.24079i
\(549\) −10.6525 −0.454637
\(550\) 0 0
\(551\) 54.8328 2.33596
\(552\) −5.52786 4.01623i −0.235282 0.170942i
\(553\) −2.76393 + 8.50651i −0.117534 + 0.361734i
\(554\) −13.7426 42.2955i −0.583869 1.79696i
\(555\) 16.9443 12.3107i 0.719244 0.522562i
\(556\) −3.70820 + 2.69417i −0.157263 + 0.114258i
\(557\) 12.0344 + 37.0382i 0.509916 + 1.56936i 0.792346 + 0.610071i \(0.208859\pi\)
−0.282431 + 0.959288i \(0.591141\pi\)
\(558\) −2.81153 + 8.65300i −0.119022 + 0.366311i
\(559\) −20.9443 15.2169i −0.885848 0.643606i
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) −7.88854 −0.332758
\(563\) 10.1803 + 7.39645i 0.429050 + 0.311723i 0.781269 0.624194i \(-0.214573\pi\)
−0.352219 + 0.935918i \(0.614573\pi\)
\(564\) −3.16718 + 9.74759i −0.133363 + 0.410448i
\(565\) −1.23607 3.80423i −0.0520018 0.160045i
\(566\) −54.0689 + 39.2833i −2.27268 + 1.65120i
\(567\) −1.95492 + 1.42033i −0.0820987 + 0.0596482i
\(568\) 7.23607 + 22.2703i 0.303619 + 0.934442i
\(569\) −2.32624 + 7.15942i −0.0975210 + 0.300139i −0.987902 0.155076i \(-0.950438\pi\)
0.890382 + 0.455215i \(0.150438\pi\)
\(570\) −28.9443 21.0292i −1.21234 0.880818i
\(571\) 15.0557 0.630063 0.315031 0.949081i \(-0.397985\pi\)
0.315031 + 0.949081i \(0.397985\pi\)
\(572\) 0 0
\(573\) 3.77709 0.157790
\(574\) −20.3262 14.7679i −0.848401 0.616399i
\(575\) −0.763932 + 2.35114i −0.0318582 + 0.0980494i
\(576\) 5.91390 + 18.2011i 0.246412 + 0.758379i
\(577\) 15.7984 11.4782i 0.657695 0.477843i −0.208189 0.978089i \(-0.566757\pi\)
0.865884 + 0.500245i \(0.166757\pi\)
\(578\) −11.8090 + 8.57975i −0.491190 + 0.356871i
\(579\) 4.54102 + 13.9758i 0.188718 + 0.580815i
\(580\) 15.7082 48.3449i 0.652248 2.00741i
\(581\) 9.23607 + 6.71040i 0.383177 + 0.278394i
\(582\) 48.1378 1.99537
\(583\) 0 0
\(584\) −1.70820 −0.0706860
\(585\) 7.70820 + 5.60034i 0.318695 + 0.231545i
\(586\) −17.3607 + 53.4307i −0.717163 + 2.20720i
\(587\) 8.38197 + 25.7970i 0.345961 + 1.06476i 0.961067 + 0.276314i \(0.0891129\pi\)
−0.615107 + 0.788444i \(0.710887\pi\)
\(588\) 3.00000 2.17963i 0.123718 0.0898863i
\(589\) −14.4721 + 10.5146i −0.596314 + 0.433247i
\(590\) −1.70820 5.25731i −0.0703256 0.216440i
\(591\) −0.763932 + 2.35114i −0.0314240 + 0.0967130i
\(592\) −6.85410 4.97980i −0.281702 0.204668i
\(593\) 45.7082 1.87701 0.938505 0.345264i \(-0.112211\pi\)
0.938505 + 0.345264i \(0.112211\pi\)
\(594\) 0 0
\(595\) 6.47214 0.265332
\(596\) 33.9787 + 24.6870i 1.39182 + 1.01122i
\(597\) 0.832816 2.56314i 0.0340849 0.104902i
\(598\) 5.52786 + 17.0130i 0.226051 + 0.695714i
\(599\) 18.9443 13.7638i 0.774042 0.562374i −0.129143 0.991626i \(-0.541223\pi\)
0.903185 + 0.429252i \(0.141223\pi\)
\(600\) 2.23607 1.62460i 0.0912871 0.0663240i
\(601\) 11.4721 + 35.3076i 0.467958 + 1.44023i 0.855224 + 0.518259i \(0.173420\pi\)
−0.387266 + 0.921968i \(0.626580\pi\)
\(602\) −5.52786 + 17.0130i −0.225299 + 0.693399i
\(603\) 17.2361 + 12.5227i 0.701907 + 0.509965i
\(604\) −26.8328 −1.09181
\(605\) 0 0
\(606\) 13.1672 0.534880
\(607\) 10.4721 + 7.60845i 0.425051 + 0.308818i 0.779667 0.626194i \(-0.215388\pi\)
−0.354616 + 0.935012i \(0.615388\pi\)
\(608\) −13.4164 + 41.2915i −0.544107 + 1.67459i
\(609\) −3.23607 9.95959i −0.131132 0.403583i
\(610\) −26.1803 + 19.0211i −1.06001 + 0.770143i
\(611\) 7.23607 5.25731i 0.292740 0.212688i
\(612\) −4.41641 13.5923i −0.178523 0.549436i
\(613\) −4.72949 + 14.5559i −0.191022 + 0.587906i 0.808978 + 0.587839i \(0.200021\pi\)
−1.00000 6.68672e-5i \(0.999979\pi\)
\(614\) 16.1803 + 11.7557i 0.652985 + 0.474422i
\(615\) 27.7771 1.12008
\(616\) 0 0
\(617\) 6.58359 0.265045 0.132523 0.991180i \(-0.457692\pi\)
0.132523 + 0.991180i \(0.457692\pi\)
\(618\) −17.2361 12.5227i −0.693336 0.503738i
\(619\) 3.43769 10.5801i 0.138173 0.425252i −0.857897 0.513821i \(-0.828230\pi\)
0.996070 + 0.0885695i \(0.0282295\pi\)
\(620\) 5.12461 + 15.7719i 0.205809 + 0.633416i
\(621\) −11.0557 + 8.03246i −0.443651 + 0.322331i
\(622\) −15.0000 + 10.8981i −0.601445 + 0.436976i
\(623\) −0.618034 1.90211i −0.0247610 0.0762065i
\(624\) −1.23607 + 3.80423i −0.0494823 + 0.152291i
\(625\) 15.3713 + 11.1679i 0.614853 + 0.446717i
\(626\) −33.4164 −1.33559
\(627\) 0 0
\(628\) 32.8328 1.31017
\(629\) 22.1803 + 16.1150i 0.884388 + 0.642546i
\(630\) 2.03444 6.26137i 0.0810541 0.249459i
\(631\) −7.41641 22.8254i −0.295243 0.908663i −0.983140 0.182855i \(-0.941466\pi\)
0.687897 0.725808i \(-0.258534\pi\)
\(632\) 16.1803 11.7557i 0.643619 0.467617i
\(633\) 13.8885 10.0906i 0.552020 0.401066i
\(634\) −9.67376 29.7728i −0.384194 1.18243i
\(635\) 1.88854 5.81234i 0.0749446 0.230656i
\(636\) −1.41641 1.02908i −0.0561642 0.0408057i
\(637\) −3.23607 −0.128218
\(638\) 0 0
\(639\) 15.4164 0.609864
\(640\) 25.3262 + 18.4006i 1.00111 + 0.727347i
\(641\) −4.79837 + 14.7679i −0.189524 + 0.583296i −0.999997 0.00248057i \(-0.999210\pi\)
0.810473 + 0.585777i \(0.199210\pi\)
\(642\) 3.41641 + 10.5146i 0.134835 + 0.414979i
\(643\) −9.00000 + 6.53888i −0.354925 + 0.257868i −0.750932 0.660379i \(-0.770396\pi\)
0.396007 + 0.918247i \(0.370396\pi\)
\(644\) 6.00000 4.35926i 0.236433 0.171779i
\(645\) −6.11146 18.8091i −0.240638 0.740609i
\(646\) 14.4721 44.5407i 0.569399 1.75243i
\(647\) −29.1803 21.2008i −1.14720 0.833488i −0.159092 0.987264i \(-0.550857\pi\)
−0.988106 + 0.153776i \(0.950857\pi\)
\(648\) 5.40325 0.212260
\(649\) 0 0
\(650\) −7.23607 −0.283822
\(651\) 2.76393 + 2.00811i 0.108327 + 0.0787042i
\(652\) −3.16718 + 9.74759i −0.124037 + 0.381745i
\(653\) 7.74265 + 23.8294i 0.302993 + 0.932517i 0.980418 + 0.196925i \(0.0630957\pi\)
−0.677425 + 0.735592i \(0.736904\pi\)
\(654\) −10.0000 + 7.26543i −0.391031 + 0.284101i
\(655\) −35.4164 + 25.7315i −1.38383 + 1.00541i
\(656\) −3.47214 10.6861i −0.135564 0.417224i
\(657\) −0.347524 + 1.06957i −0.0135582 + 0.0417279i
\(658\) −5.00000 3.63271i −0.194920 0.141618i
\(659\) 17.8885 0.696839 0.348419 0.937339i \(-0.386719\pi\)
0.348419 + 0.937339i \(0.386719\pi\)
\(660\) 0 0
\(661\) −40.8328 −1.58821 −0.794106 0.607779i \(-0.792061\pi\)
−0.794106 + 0.607779i \(0.792061\pi\)
\(662\) −25.1246 18.2541i −0.976496 0.709466i
\(663\) 4.00000 12.3107i 0.155347 0.478109i
\(664\) −7.88854 24.2784i −0.306135 0.942186i
\(665\) 10.4721 7.60845i 0.406092 0.295043i
\(666\) 22.5623 16.3925i 0.874272 0.635195i
\(667\) −6.47214 19.9192i −0.250602 0.771274i
\(668\) −4.58359 + 14.1068i −0.177345 + 0.545810i
\(669\) −10.1803 7.39645i −0.393595 0.285963i
\(670\) 64.7214 2.50040
\(671\) 0 0
\(672\) 8.29180 0.319863
\(673\) −17.3262 12.5882i −0.667877 0.485241i 0.201437 0.979502i \(-0.435439\pi\)
−0.869314 + 0.494260i \(0.835439\pi\)
\(674\) −7.96556 + 24.5155i −0.306822 + 0.944301i
\(675\) −1.70820 5.25731i −0.0657488 0.202354i
\(676\) 6.13525 4.45752i 0.235971 0.171443i
\(677\) −7.85410 + 5.70634i −0.301858 + 0.219312i −0.728395 0.685158i \(-0.759733\pi\)
0.426537 + 0.904470i \(0.359733\pi\)
\(678\) 1.70820 + 5.25731i 0.0656032 + 0.201906i
\(679\) −5.38197 + 16.5640i −0.206541 + 0.635668i
\(680\) −11.7082 8.50651i −0.448989 0.326210i
\(681\) 7.27864 0.278918
\(682\) 0 0
\(683\) −5.88854 −0.225319 −0.112659 0.993634i \(-0.535937\pi\)
−0.112659 + 0.993634i \(0.535937\pi\)
\(684\) −23.1246 16.8010i −0.884192 0.642403i
\(685\) −10.1803 + 31.3319i −0.388971 + 1.19713i
\(686\) 0.690983 + 2.12663i 0.0263819 + 0.0811950i
\(687\) −4.47214 + 3.24920i −0.170623 + 0.123965i
\(688\) −6.47214 + 4.70228i −0.246748 + 0.179273i
\(689\) 0.472136 + 1.45309i 0.0179869 + 0.0553581i
\(690\) −4.22291 + 12.9968i −0.160764 + 0.494779i
\(691\) −15.0000 10.8981i −0.570627 0.414585i 0.264706 0.964329i \(-0.414725\pi\)
−0.835333 + 0.549744i \(0.814725\pi\)
\(692\) 38.2918 1.45564
\(693\) 0 0
\(694\) 46.8328 1.77775
\(695\) 2.47214 + 1.79611i 0.0937735 + 0.0681304i
\(696\) −7.23607 + 22.2703i −0.274282 + 0.844155i
\(697\) 11.2361 + 34.5811i 0.425596 + 1.30985i
\(698\) 13.0902 9.51057i 0.495470 0.359980i
\(699\) −9.41641 + 6.84142i −0.356161 + 0.258766i
\(700\) 0.927051 + 2.85317i 0.0350392 + 0.107840i
\(701\) 4.79837 14.7679i 0.181232 0.557775i −0.818631 0.574320i \(-0.805267\pi\)
0.999863 + 0.0165448i \(0.00526661\pi\)
\(702\) −32.3607 23.5114i −1.22138 0.887381i
\(703\) 54.8328 2.06806
\(704\) 0 0
\(705\) 6.83282 0.257339
\(706\) 35.9787 + 26.1401i 1.35408 + 0.983794i
\(707\) −1.47214 + 4.53077i −0.0553654 + 0.170397i
\(708\) 1.41641 + 4.35926i 0.0532319 + 0.163831i
\(709\) 12.0902 8.78402i 0.454056 0.329891i −0.337139 0.941455i \(-0.609459\pi\)
0.791195 + 0.611564i \(0.209459\pi\)
\(710\) 37.8885 27.5276i 1.42193 1.03309i
\(711\) −4.06888 12.5227i −0.152595 0.469639i
\(712\) −1.38197 + 4.25325i −0.0517914 + 0.159397i
\(713\) 5.52786 + 4.01623i 0.207020 + 0.150409i
\(714\) −8.94427 −0.334731
\(715\) 0 0
\(716\) −26.8328 −1.00279
\(717\) 9.88854 + 7.18445i 0.369294 + 0.268308i
\(718\) −17.2361 + 53.0472i −0.643244 + 1.97970i
\(719\) −15.9098 48.9654i −0.593337 1.82610i −0.562838 0.826567i \(-0.690290\pi\)
−0.0304986 0.999535i \(-0.509710\pi\)
\(720\) 2.38197 1.73060i 0.0887706 0.0644956i
\(721\) 6.23607 4.53077i 0.232243 0.168735i
\(722\) −15.8156 48.6754i −0.588595 1.81151i
\(723\) −5.01316 + 15.4289i −0.186441 + 0.573807i
\(724\) 61.6869 + 44.8182i 2.29258 + 1.66565i
\(725\) 8.47214 0.314647
\(726\) 0 0
\(727\) 25.0132 0.927687 0.463843 0.885917i \(-0.346470\pi\)
0.463843 + 0.885917i \(0.346470\pi\)
\(728\) 5.85410 + 4.25325i 0.216967 + 0.157636i
\(729\) 7.43363 22.8784i 0.275320 0.847347i
\(730\) 1.05573 + 3.24920i 0.0390742 + 0.120258i
\(731\) 20.9443 15.2169i 0.774652 0.562818i
\(732\) 21.7082 15.7719i 0.802358 0.582947i
\(733\) −2.70820 8.33499i −0.100030 0.307860i 0.888502 0.458873i \(-0.151747\pi\)
−0.988532 + 0.151013i \(0.951747\pi\)
\(734\) 15.9787 49.1774i 0.589785 1.81517i
\(735\) −2.00000 1.45309i −0.0737711 0.0535978i
\(736\) 16.5836 0.611279
\(737\) 0 0
\(738\) 36.9868 1.36150
\(739\) 20.1803 + 14.6619i 0.742346 + 0.539346i 0.893445 0.449173i \(-0.148281\pi\)
−0.151099 + 0.988519i \(0.548281\pi\)
\(740\) 15.7082 48.3449i 0.577445 1.77719i
\(741\) −8.00000 24.6215i −0.293887 0.904492i
\(742\) 0.854102 0.620541i 0.0313551 0.0227808i
\(743\) 1.52786 1.11006i 0.0560519 0.0407241i −0.559407 0.828893i \(-0.688971\pi\)
0.615458 + 0.788169i \(0.288971\pi\)
\(744\) −2.36068 7.26543i −0.0865467 0.266363i
\(745\) 8.65248 26.6296i 0.317002 0.975632i
\(746\) −10.8541 7.88597i −0.397397 0.288726i
\(747\) −16.8065 −0.614918
\(748\) 0 0
\(749\) −4.00000 −0.146157
\(750\) −26.8328 19.4952i −0.979796 0.711863i
\(751\) 9.12461 28.0827i 0.332962 1.02475i −0.634756 0.772713i \(-0.718899\pi\)
0.967717 0.252038i \(-0.0811008\pi\)
\(752\) −0.854102 2.62866i −0.0311459 0.0958572i
\(753\) 4.29180 3.11817i 0.156402 0.113633i
\(754\) 49.5967 36.0341i 1.80621 1.31229i
\(755\) 5.52786 + 17.0130i 0.201180 + 0.619167i
\(756\) −5.12461 + 15.7719i −0.186380 + 0.573620i
\(757\) −12.8541 9.33905i −0.467190 0.339434i 0.329155 0.944276i \(-0.393236\pi\)
−0.796345 + 0.604842i \(0.793236\pi\)
\(758\) −83.4164 −3.02982
\(759\) 0 0
\(760\) −28.9443 −1.04992
\(761\) −25.5623 18.5721i −0.926633 0.673238i 0.0185332 0.999828i \(-0.494100\pi\)
−0.945166 + 0.326590i \(0.894100\pi\)
\(762\) −2.60990 + 8.03246i −0.0945468 + 0.290985i
\(763\) −1.38197 4.25325i −0.0500305 0.153978i
\(764\) 7.41641 5.38834i 0.268316 0.194943i
\(765\) −7.70820 + 5.60034i −0.278691 + 0.202481i
\(766\) 3.21478 + 9.89408i 0.116155 + 0.357488i
\(767\) 1.23607 3.80423i 0.0446318 0.137363i
\(768\) −9.00000 6.53888i −0.324760 0.235952i
\(769\) −18.2918 −0.659619 −0.329810 0.944047i \(-0.606985\pi\)
−0.329810 + 0.944047i \(0.606985\pi\)
\(770\) 0 0
\(771\) 7.41641 0.267095
\(772\) 28.8541 + 20.9637i 1.03848 + 0.754501i
\(773\) −11.8541 + 36.4832i −0.426362 + 1.31221i 0.475321 + 0.879812i \(0.342332\pi\)
−0.901684 + 0.432396i \(0.857668\pi\)
\(774\) −8.13777 25.0455i −0.292506 0.900241i
\(775\) −2.23607 + 1.62460i −0.0803219 + 0.0583573i
\(776\) 31.5066 22.8909i 1.13102 0.821734i
\(777\) −3.23607 9.95959i −0.116093 0.357298i
\(778\) −10.9787 + 33.7890i −0.393606 + 1.21139i
\(779\) 58.8328 + 42.7445i 2.10790 + 1.53148i
\(780\) −24.0000 −0.859338
\(781\) 0 0
\(782\) −17.8885 −0.639693
\(783\) 37.8885 + 27.5276i 1.35403 + 0.983758i
\(784\) −0.309017 + 0.951057i −0.0110363 + 0.0339663i
\(785\) −6.76393 20.8172i −0.241415 0.742999i
\(786\) 48.9443 35.5601i 1.74578 1.26839i
\(787\) −35.1246 + 25.5195i −1.25206 + 0.909673i −0.998339 0.0576055i \(-0.981653\pi\)
−0.253718 + 0.967278i \(0.581653\pi\)
\(788\) 1.85410 + 5.70634i 0.0660496 + 0.203280i
\(789\) 0 0
\(790\) −32.3607 23.5114i −1.15134 0.836498i
\(791\) −2.00000 −0.0711118
\(792\) 0 0
\(793\) −23.4164 −0.831541
\(794\) −64.9230 47.1693i −2.30403 1.67398i
\(795\) −0.360680 + 1.11006i −0.0127920 + 0.0393697i
\(796\) −2.02129 6.22088i −0.0716426 0.220493i
\(797\) 12.0902 8.78402i 0.428256 0.311146i −0.352695 0.935738i \(-0.614735\pi\)
0.780951 + 0.624592i \(0.214735\pi\)
\(798\) −14.4721 + 10.5146i −0.512308 + 0.372214i
\(799\) 2.76393 + 8.50651i 0.0977809 + 0.300939i
\(800\) −2.07295 + 6.37988i −0.0732898 + 0.225563i
\(801\) 2.38197 + 1.73060i 0.0841626 + 0.0611477i
\(802\) −51.3050 −1.81164
\(803\) 0 0
\(804\) −53.6656 −1.89264
\(805\) −4.00000 2.90617i −0.140981 0.102429i
\(806\) −6.18034 + 19.0211i −0.217693 + 0.669991i
\(807\) −5.12461 15.7719i −0.180395 0.555198i
\(808\) 8.61803 6.26137i 0.303181 0.220274i
\(809\) 17.0344 12.3762i 0.598899 0.435126i −0.246589 0.969120i \(-0.579310\pi\)
0.845488 + 0.533995i \(0.179310\pi\)
\(810\) −3.33939 10.2776i −0.117334 0.361118i
\(811\) 10.7639 33.1280i 0.377973 1.16328i −0.563478 0.826131i \(-0.690537\pi\)
0.941451 0.337150i \(-0.109463\pi\)
\(812\) −20.5623 14.9394i −0.721595 0.524270i
\(813\) −12.9443 −0.453975
\(814\) 0 0
\(815\) 6.83282 0.239343
\(816\) −3.23607 2.35114i −0.113285 0.0823064i
\(817\) 16.0000 49.2429i 0.559769 1.72279i
\(818\) 6.30495 + 19.4046i 0.220447 + 0.678468i
\(819\) 3.85410 2.80017i 0.134673 0.0978458i
\(820\) 54.5410 39.6264i 1.90466 1.38381i
\(821\) −13.8541 42.6385i −0.483511 1.48810i −0.834125 0.551575i \(-0.814027\pi\)
0.350614 0.936520i \(-0.385973\pi\)
\(822\) 14.0689 43.2996i 0.490709 1.51025i
\(823\) 11.4164 + 8.29451i 0.397951 + 0.289128i 0.768706 0.639602i \(-0.220901\pi\)
−0.370755 + 0.928731i \(0.620901\pi\)
\(824\) −17.2361 −0.600447
\(825\) 0 0
\(826\) −2.76393 −0.0961695
\(827\) −10.4721 7.60845i −0.364152 0.264572i 0.390630 0.920548i \(-0.372257\pi\)
−0.754782 + 0.655976i \(0.772257\pi\)
\(828\) −3.37384 + 10.3836i −0.117249 + 0.360855i
\(829\) 11.3820 + 35.0301i 0.395312 + 1.21665i 0.928718 + 0.370786i \(0.120912\pi\)
−0.533406 + 0.845859i \(0.679088\pi\)
\(830\) −41.3050 + 30.0098i −1.43372 + 1.04166i
\(831\) 19.8885 14.4499i 0.689926 0.501261i
\(832\) 13.0000 + 40.0099i 0.450694 + 1.38709i
\(833\) 1.00000 3.07768i 0.0346479 0.106635i
\(834\) −3.41641 2.48217i −0.118301 0.0859504i
\(835\) 9.88854 0.342207
\(836\) 0 0
\(837\) −15.2786 −0.528107
\(838\) 44.5967 + 32.4014i 1.54057 + 1.11929i
\(839\) 13.6180 41.9120i 0.470147 1.44696i −0.382246 0.924061i \(-0.624849\pi\)
0.852393 0.522902i \(-0.175151\pi\)
\(840\) 1.70820 + 5.25731i 0.0589386 + 0.181394i
\(841\) −34.6074 + 25.1437i −1.19336 + 0.867026i
\(842\) 40.4508 29.3893i 1.39403 1.01282i
\(843\) −1.34752 4.14725i −0.0464112 0.142839i
\(844\) 12.8754 39.6264i 0.443189 1.36400i
\(845\) −4.09017 2.97168i −0.140706 0.102229i
\(846\) 9.09830 0.312806
\(847\) 0 0
\(848\) 0.472136 0.0162132
\(849\) −29.8885 21.7153i −1.02577 0.745267i
\(850\) 2.23607 6.88191i 0.0766965 0.236048i
\(851\) −6.47214 19.9192i −0.221862 0.682821i
\(852\) −31.4164 + 22.8254i −1.07631 + 0.781984i
\(853\) −24.7984 + 18.0171i −0.849080 + 0.616893i −0.924892 0.380229i \(-0.875845\pi\)
0.0758121 + 0.997122i \(0.475845\pi\)
\(854\) 5.00000 + 15.3884i 0.171096 + 0.526581i
\(855\) −5.88854 + 18.1231i −0.201384 + 0.619796i
\(856\) 7.23607 + 5.25731i 0.247324 + 0.179691i
\(857\) −15.2361 −0.520454 −0.260227 0.965547i \(-0.583797\pi\)
−0.260227 + 0.965547i \(0.583797\pi\)
\(858\) 0 0
\(859\) −26.5410 −0.905568 −0.452784 0.891620i \(-0.649569\pi\)
−0.452784 + 0.891620i \(0.649569\pi\)
\(860\) −38.8328 28.2137i −1.32419 0.962079i
\(861\) 4.29180 13.2088i 0.146264 0.450154i
\(862\) 8.29180 + 25.5195i 0.282420 + 0.869198i
\(863\) 2.47214 1.79611i 0.0841525 0.0611404i −0.544914 0.838492i \(-0.683438\pi\)
0.629066 + 0.777352i \(0.283438\pi\)
\(864\) −30.0000 + 21.7963i −1.02062 + 0.741524i
\(865\) −7.88854 24.2784i −0.268219 0.825492i
\(866\) 5.85410 18.0171i 0.198930 0.612245i
\(867\) −6.52786 4.74277i −0.221698 0.161073i
\(868\) 8.29180 0.281442
\(869\) 0 0
\(870\) 46.8328 1.58778
\(871\) 37.8885 + 27.5276i 1.28380 + 0.932738i
\(872\) −3.09017 + 9.51057i −0.104646 + 0.322068i
\(873\) −7.92299 24.3844i −0.268152 0.825288i
\(874\) −28.9443 + 21.0292i −0.979055 + 0.711325i
\(875\) 9.70820 7.05342i 0.328197 0.238449i
\(876\) −0.875388 2.69417i −0.0295766 0.0910275i
\(877\) −4.50658 + 13.8698i −0.152176 + 0.468351i −0.997864 0.0653278i \(-0.979191\pi\)
0.845688 + 0.533678i \(0.179191\pi\)
\(878\) −18.9443 13.7638i −0.639338 0.464506i
\(879\) −31.0557 −1.04748
\(880\) 0 0
\(881\) 2.58359 0.0870434 0.0435217 0.999052i \(-0.486142\pi\)
0.0435217 + 0.999052i \(0.486142\pi\)
\(882\) −2.66312 1.93487i −0.0896719 0.0651504i
\(883\) −2.76393 + 8.50651i −0.0930137 + 0.286267i −0.986731 0.162364i \(-0.948088\pi\)
0.893717 + 0.448631i \(0.148088\pi\)
\(884\) −9.70820 29.8788i −0.326522 1.00493i
\(885\) 2.47214 1.79611i 0.0830999 0.0603756i
\(886\) −45.1246 + 32.7849i −1.51599 + 1.10143i
\(887\) 1.34752 + 4.14725i 0.0452454 + 0.139251i 0.971127 0.238562i \(-0.0766761\pi\)
−0.925882 + 0.377813i \(0.876676\pi\)
\(888\) −7.23607 + 22.2703i −0.242827 + 0.747343i
\(889\) −2.47214 1.79611i −0.0829128 0.0602397i
\(890\) 8.94427 0.299813
\(891\) 0 0
\(892\) −30.5410 −1.02259
\(893\) 14.4721 + 10.5146i 0.484292 + 0.351858i
\(894\) −11.9574 + 36.8012i −0.399916 + 1.23082i
\(895\) 5.52786 + 17.0130i 0.184776 + 0.568682i
\(896\) 12.6631 9.20029i 0.423045 0.307360i
\(897\) −8.00000 + 5.81234i −0.267112 + 0.194068i
\(898\) 19.6738 + 60.5496i 0.656522 + 2.02057i
\(899\) 7.23607 22.2703i 0.241336 0.742757i
\(900\) −3.57295 2.59590i −0.119098 0.0865300i
\(901\) −1.52786 −0.0509005
\(902\) 0 0
\(903\) −9.88854 −0.329070
\(904\) 3.61803 + 2.62866i 0.120334 + 0.0874278i
\(905\) 15.7082 48.3449i 0.522158 1.60704i
\(906\) −7.63932 23.5114i −0.253799 0.781114i
\(907\) −18.1803 + 13.2088i −0.603668 + 0.438591i −0.847179 0.531308i \(-0.821701\pi\)
0.243511 + 0.969898i \(0.421701\pi\)
\(908\) 14.2918 10.3836i 0.474290 0.344592i
\(909\) −2.16718 6.66991i −0.0718810 0.221227i
\(910\) 4.47214 13.7638i 0.148250 0.456266i
\(911\) −34.3607 24.9645i −1.13842 0.827111i −0.151522 0.988454i \(-0.548417\pi\)
−0.986898 + 0.161343i \(0.948417\pi\)
\(912\) −8.00000 −0.264906
\(913\) 0 0
\(914\) −64.4721 −2.13255
\(915\) −14.4721 10.5146i −0.478434 0.347603i
\(916\) −4.14590 + 12.7598i −0.136984 + 0.421594i
\(917\) 6.76393 + 20.8172i 0.223365 + 0.687446i
\(918\) 32.3607 23.5114i 1.06806 0.775992i
\(919\) 33.8885 24.6215i 1.11788 0.812187i 0.133994 0.990982i \(-0.457220\pi\)
0.983886 + 0.178795i \(0.0572199\pi\)
\(920\) 3.41641 + 10.5146i 0.112636 + 0.346657i
\(921\) −3.41641 + 10.5146i −0.112574 + 0.346469i
\(922\) 22.0344 + 16.0090i 0.725666 + 0.527227i
\(923\) 33.8885 1.11546
\(924\) 0 0
\(925\) 8.47214 0.278562
\(926\) −10.0000 7.26543i −0.328620 0.238757i
\(927\) −3.50658 + 10.7921i −0.115171 + 0.354460i
\(928\) −17.5623 54.0512i −0.576511 1.77432i
\(929\) 42.2705 30.7113i 1.38685 1.00761i 0.390648 0.920540i \(-0.372251\pi\)
0.996203 0.0870656i \(-0.0277490\pi\)
\(930\) −12.3607 + 8.98056i −0.405323 + 0.294484i
\(931\) −2.00000 6.15537i −0.0655474 0.201734i
\(932\) −8.72949 + 26.8666i −0.285944 + 0.880045i
\(933\) −8.29180 6.02434i −0.271461 0.197228i
\(934\) −53.8197 −1.76103
\(935\) 0 0
\(936\) −10.6525 −0.348187
\(937\) −8.61803 6.26137i −0.281539 0.204550i 0.438049 0.898951i \(-0.355669\pi\)
−0.719588 + 0.694401i \(0.755669\pi\)
\(938\) 10.0000 30.7768i 0.326512 1.00490i
\(939\) −5.70820 17.5680i −0.186280 0.573311i
\(940\) 13.4164 9.74759i 0.437595 0.317931i
\(941\) 6.14590 4.46526i 0.200351 0.145563i −0.483087 0.875573i \(-0.660484\pi\)
0.683437 + 0.730009i \(0.260484\pi\)
\(942\) 9.34752 + 28.7687i 0.304559 + 0.937336i
\(943\) 8.58359 26.4176i 0.279520 0.860275i
\(944\) −1.00000 0.726543i −0.0325472 0.0236469i
\(945\) 11.0557 0.359643
\(946\) 0 0
\(947\) −5.16718 −0.167911 −0.0839555 0.996470i \(-0.526755\pi\)
−0.0839555 + 0.996470i \(0.526755\pi\)
\(948\) 26.8328 + 19.4952i 0.871489 + 0.633174i
\(949\) −0.763932 + 2.35114i −0.0247983 + 0.0763213i
\(950\) −4.47214 13.7638i −0.145095 0.446557i
\(951\) 14.0000 10.1716i 0.453981 0.329837i
\(952\) −5.85410 + 4.25325i −0.189733 + 0.137849i
\(953\) −7.09017 21.8213i −0.229673 0.706861i −0.997784 0.0665438i \(-0.978803\pi\)
0.768110 0.640317i \(-0.221197\pi\)
\(954\) −0.480267 + 1.47811i −0.0155492 + 0.0478555i
\(955\) −4.94427 3.59222i −0.159993 0.116242i
\(956\) 29.6656 0.959455
\(957\) 0 0
\(958\) 30.2492 0.977308
\(959\) 13.3262 + 9.68208i 0.430327 + 0.312651i
\(960\) −9.93112 + 30.5648i −0.320525 + 0.986476i
\(961\) −7.21885 22.2173i −0.232866 0.716688i
\(962\) 49.5967 36.0341i 1.59906 1.16179i
\(963\) 4.76393 3.46120i 0.153516 0.111536i
\(964\) 12.1672 + 37.4467i 0.391879 + 1.20608i
\(965\) 7.34752 22.6134i 0.236525 0.727950i
\(966\) 5.52786 + 4.01623i 0.177856 + 0.129220i
\(967\) 13.8885 0.446625 0.223313 0.974747i \(-0.428313\pi\)
0.223313 + 0.974747i \(0.428313\pi\)
\(968\) 0 0
\(969\) 25.8885 0.831660
\(970\) −63.0132 45.7817i −2.02323 1.46996i
\(971\) 3.43769 10.5801i 0.110321 0.339533i −0.880622 0.473820i \(-0.842875\pi\)
0.990942 + 0.134288i \(0.0428746\pi\)
\(972\) −12.6049 38.7938i −0.404302 1.24431i
\(973\) 1.23607 0.898056i 0.0396265 0.0287904i
\(974\) −65.7771 + 47.7899i −2.10763 + 1.53129i
\(975\) −1.23607 3.80423i −0.0395859 0.121833i
\(976\) −2.23607 + 6.88191i −0.0715748 + 0.220285i
\(977\) −18.5623 13.4863i −0.593861 0.431465i 0.249834 0.968289i \(-0.419624\pi\)
−0.843694 + 0.536824i \(0.819624\pi\)
\(978\) −9.44272 −0.301945
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) 5.32624 + 3.86974i 0.170054 + 0.123551i
\(982\) 0 0
\(983\) 6.74265 + 20.7517i 0.215057 + 0.661877i 0.999150 + 0.0412335i \(0.0131287\pi\)
−0.784093 + 0.620644i \(0.786871\pi\)
\(984\) −25.1246 + 18.2541i −0.800943 + 0.581919i
\(985\) 3.23607 2.35114i 0.103110 0.0749136i
\(986\) 18.9443 + 58.3045i 0.603309 + 1.85679i
\(987\) 1.05573 3.24920i 0.0336042 0.103423i
\(988\) −50.8328 36.9322i −1.61721 1.17497i
\(989\) −19.7771 −0.628875
\(990\) 0 0
\(991\) 54.2492 1.72328 0.861642 0.507517i \(-0.169437\pi\)
0.861642 + 0.507517i \(0.169437\pi\)
\(992\) 15.0000 + 10.8981i 0.476250 + 0.346016i
\(993\) 5.30495 16.3270i 0.168348 0.518120i
\(994\) −7.23607 22.2703i −0.229514 0.706372i
\(995\) −3.52786 + 2.56314i −0.111841 + 0.0812571i
\(996\) 34.2492 24.8835i 1.08523 0.788464i
\(997\) −0.416408 1.28157i −0.0131878 0.0405878i 0.944246 0.329241i \(-0.106793\pi\)
−0.957434 + 0.288653i \(0.906793\pi\)
\(998\) −1.05573 + 3.24920i −0.0334185 + 0.102852i
\(999\) 37.8885 + 27.5276i 1.19874 + 0.870936i
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 847.2.f.m.323.1 4
11.2 odd 10 847.2.f.n.148.1 4
11.3 even 5 inner 847.2.f.m.729.1 4
11.4 even 5 847.2.f.b.372.1 4
11.5 even 5 847.2.a.f.1.1 2
11.6 odd 10 77.2.a.d.1.2 2
11.7 odd 10 847.2.f.n.372.1 4
11.8 odd 10 847.2.f.a.729.1 4
11.9 even 5 847.2.f.b.148.1 4
11.10 odd 2 847.2.f.a.323.1 4
33.5 odd 10 7623.2.a.bl.1.2 2
33.17 even 10 693.2.a.h.1.1 2
44.39 even 10 1232.2.a.m.1.2 2
55.17 even 20 1925.2.b.h.1849.3 4
55.28 even 20 1925.2.b.h.1849.2 4
55.39 odd 10 1925.2.a.r.1.1 2
77.6 even 10 539.2.a.f.1.2 2
77.17 even 30 539.2.e.j.177.1 4
77.27 odd 10 5929.2.a.m.1.1 2
77.39 odd 30 539.2.e.i.177.1 4
77.61 even 30 539.2.e.j.67.1 4
77.72 odd 30 539.2.e.i.67.1 4
88.61 odd 10 4928.2.a.bm.1.2 2
88.83 even 10 4928.2.a.bv.1.1 2
231.83 odd 10 4851.2.a.y.1.1 2
308.83 odd 10 8624.2.a.ce.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.a.d.1.2 2 11.6 odd 10
539.2.a.f.1.2 2 77.6 even 10
539.2.e.i.67.1 4 77.72 odd 30
539.2.e.i.177.1 4 77.39 odd 30
539.2.e.j.67.1 4 77.61 even 30
539.2.e.j.177.1 4 77.17 even 30
693.2.a.h.1.1 2 33.17 even 10
847.2.a.f.1.1 2 11.5 even 5
847.2.f.a.323.1 4 11.10 odd 2
847.2.f.a.729.1 4 11.8 odd 10
847.2.f.b.148.1 4 11.9 even 5
847.2.f.b.372.1 4 11.4 even 5
847.2.f.m.323.1 4 1.1 even 1 trivial
847.2.f.m.729.1 4 11.3 even 5 inner
847.2.f.n.148.1 4 11.2 odd 10
847.2.f.n.372.1 4 11.7 odd 10
1232.2.a.m.1.2 2 44.39 even 10
1925.2.a.r.1.1 2 55.39 odd 10
1925.2.b.h.1849.2 4 55.28 even 20
1925.2.b.h.1849.3 4 55.17 even 20
4851.2.a.y.1.1 2 231.83 odd 10
4928.2.a.bm.1.2 2 88.61 odd 10
4928.2.a.bv.1.1 2 88.83 even 10
5929.2.a.m.1.1 2 77.27 odd 10
7623.2.a.bl.1.2 2 33.5 odd 10
8624.2.a.ce.1.1 2 308.83 odd 10