Properties

Label 847.2.f.v.323.2
Level $847$
Weight $2$
Character 847.323
Analytic conductor $6.763$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} - 1175 x^{7} + 2135 x^{6} - 2300 x^{5} + 1850 x^{4} - 925 x^{3} + 700 x^{2} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 323.2
Root \(0.435488 + 1.34029i\) of defining polynomial
Character \(\chi\) \(=\) 847.323
Dual form 847.2.f.v.729.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.14012 - 0.828347i) q^{2} +(-0.668522 + 2.05750i) q^{3} +(-0.00431527 - 0.0132810i) q^{4} +(1.48162 - 1.07646i) q^{5} +(2.46652 - 1.79203i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.877057 + 2.69930i) q^{8} +(-1.35932 - 0.987607i) q^{9} +O(q^{10})\) \(q+(-1.14012 - 0.828347i) q^{2} +(-0.668522 + 2.05750i) q^{3} +(-0.00431527 - 0.0132810i) q^{4} +(1.48162 - 1.07646i) q^{5} +(2.46652 - 1.79203i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.877057 + 2.69930i) q^{8} +(-1.35932 - 0.987607i) q^{9} -2.58091 q^{10} +0.0302106 q^{12} +(-3.75955 - 2.73147i) q^{13} +(-0.435488 + 1.34029i) q^{14} +(1.22432 + 3.76807i) q^{15} +(3.21332 - 2.33461i) q^{16} +(-4.42550 + 3.21531i) q^{17} +(0.731714 + 2.25198i) q^{18} +(1.79266 - 5.51725i) q^{19} +(-0.0206901 - 0.0150323i) q^{20} +2.16338 q^{21} -0.719682 q^{23} +(-4.96748 - 3.60908i) q^{24} +(-0.508649 + 1.56546i) q^{25} +(2.02374 + 6.22842i) q^{26} +(-2.30990 + 1.67824i) q^{27} +(-0.0112975 + 0.00820814i) q^{28} +(0.362314 + 1.11509i) q^{29} +(1.72540 - 5.31022i) q^{30} +(1.05809 + 0.768744i) q^{31} +0.0789938 q^{32} +7.70900 q^{34} +(-1.48162 - 1.07646i) q^{35} +(-0.00725060 + 0.0223150i) q^{36} +(0.647310 + 1.99221i) q^{37} +(-6.61405 + 4.80539i) q^{38} +(8.13333 - 5.90921i) q^{39} +(1.60623 + 4.94347i) q^{40} +(0.283259 - 0.871781i) q^{41} +(-2.46652 - 1.79203i) q^{42} -8.02379 q^{43} -3.07713 q^{45} +(0.820525 + 0.596147i) q^{46} +(1.84663 - 5.68336i) q^{47} +(2.65528 + 8.17213i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.87667 - 1.36348i) q^{50} +(-3.65696 - 11.2550i) q^{51} +(-0.0200533 + 0.0617178i) q^{52} +(-8.20742 - 5.96304i) q^{53} +4.02373 q^{54} +2.83822 q^{56} +(10.1533 + 7.37680i) q^{57} +(0.510598 - 1.57146i) q^{58} +(-2.37350 - 7.30488i) q^{59} +(0.0447607 - 0.0325205i) q^{60} +(-5.07749 + 3.68901i) q^{61} +(-0.569559 - 1.75292i) q^{62} +(-0.519216 + 1.59798i) q^{63} +(-6.51669 - 4.73465i) q^{64} -8.51056 q^{65} -15.4673 q^{67} +(0.0617999 + 0.0449003i) q^{68} +(0.481123 - 1.48075i) q^{69} +(0.797546 + 2.45459i) q^{70} +(-11.2469 + 8.17134i) q^{71} +(3.85806 - 2.80304i) q^{72} +(-1.85862 - 5.72025i) q^{73} +(0.912233 - 2.80756i) q^{74} +(-2.88089 - 2.09309i) q^{75} -0.0810106 q^{76} -14.1679 q^{78} +(-12.6538 - 9.19351i) q^{79} +(2.24780 - 6.91802i) q^{80} +(-3.46640 - 10.6685i) q^{81} +(-1.04509 + 0.759300i) q^{82} +(-3.54004 + 2.57199i) q^{83} +(-0.00933558 - 0.0287320i) q^{84} +(-3.09576 + 9.52776i) q^{85} +(9.14810 + 6.64648i) q^{86} -2.53651 q^{87} +15.3437 q^{89} +(3.50830 + 2.54893i) q^{90} +(-1.43602 + 4.41961i) q^{91} +(0.00310563 + 0.00955813i) q^{92} +(-2.28904 + 1.66309i) q^{93} +(-6.81318 + 4.95006i) q^{94} +(-3.28306 - 10.1042i) q^{95} +(-0.0528090 + 0.162530i) q^{96} +(-1.95073 - 1.41729i) q^{97} +1.40927 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.14012 0.828347i −0.806188 0.585730i 0.106535 0.994309i \(-0.466024\pi\)
−0.912723 + 0.408579i \(0.866024\pi\)
\(3\) −0.668522 + 2.05750i −0.385971 + 1.18790i 0.549802 + 0.835295i \(0.314703\pi\)
−0.935773 + 0.352602i \(0.885297\pi\)
\(4\) −0.00431527 0.0132810i −0.00215764 0.00664052i
\(5\) 1.48162 1.07646i 0.662602 0.481408i −0.204939 0.978775i \(-0.565700\pi\)
0.867541 + 0.497366i \(0.165700\pi\)
\(6\) 2.46652 1.79203i 1.00695 0.731593i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) −0.877057 + 2.69930i −0.310086 + 0.954348i
\(9\) −1.35932 0.987607i −0.453108 0.329202i
\(10\) −2.58091 −0.816157
\(11\) 0 0
\(12\) 0.0302106 0.00872104
\(13\) −3.75955 2.73147i −1.04271 0.757574i −0.0718980 0.997412i \(-0.522906\pi\)
−0.970813 + 0.239838i \(0.922906\pi\)
\(14\) −0.435488 + 1.34029i −0.116389 + 0.358208i
\(15\) 1.22432 + 3.76807i 0.316118 + 0.972912i
\(16\) 3.21332 2.33461i 0.803329 0.583653i
\(17\) −4.42550 + 3.21531i −1.07334 + 0.779827i −0.976510 0.215473i \(-0.930871\pi\)
−0.0968307 + 0.995301i \(0.530871\pi\)
\(18\) 0.731714 + 2.25198i 0.172467 + 0.530798i
\(19\) 1.79266 5.51725i 0.411265 1.26574i −0.504285 0.863538i \(-0.668244\pi\)
0.915549 0.402206i \(-0.131756\pi\)
\(20\) −0.0206901 0.0150323i −0.00462646 0.00336132i
\(21\) 2.16338 0.472088
\(22\) 0 0
\(23\) −0.719682 −0.150064 −0.0750321 0.997181i \(-0.523906\pi\)
−0.0750321 + 0.997181i \(0.523906\pi\)
\(24\) −4.96748 3.60908i −1.01398 0.736701i
\(25\) −0.508649 + 1.56546i −0.101730 + 0.313092i
\(26\) 2.02374 + 6.22842i 0.396887 + 1.22149i
\(27\) −2.30990 + 1.67824i −0.444540 + 0.322977i
\(28\) −0.0112975 + 0.00820814i −0.00213503 + 0.00155119i
\(29\) 0.362314 + 1.11509i 0.0672801 + 0.207067i 0.979044 0.203647i \(-0.0652795\pi\)
−0.911764 + 0.410714i \(0.865280\pi\)
\(30\) 1.72540 5.31022i 0.315013 0.969510i
\(31\) 1.05809 + 0.768744i 0.190038 + 0.138070i 0.678736 0.734382i \(-0.262528\pi\)
−0.488698 + 0.872453i \(0.662528\pi\)
\(32\) 0.0789938 0.0139643
\(33\) 0 0
\(34\) 7.70900 1.32208
\(35\) −1.48162 1.07646i −0.250440 0.181955i
\(36\) −0.00725060 + 0.0223150i −0.00120843 + 0.00371917i
\(37\) 0.647310 + 1.99221i 0.106417 + 0.327518i 0.990060 0.140643i \(-0.0449168\pi\)
−0.883643 + 0.468161i \(0.844917\pi\)
\(38\) −6.61405 + 4.80539i −1.07294 + 0.779536i
\(39\) 8.13333 5.90921i 1.30238 0.946231i
\(40\) 1.60623 + 4.94347i 0.253967 + 0.781631i
\(41\) 0.283259 0.871781i 0.0442376 0.136149i −0.926498 0.376299i \(-0.877197\pi\)
0.970736 + 0.240150i \(0.0771965\pi\)
\(42\) −2.46652 1.79203i −0.380592 0.276516i
\(43\) −8.02379 −1.22362 −0.611808 0.791006i \(-0.709558\pi\)
−0.611808 + 0.791006i \(0.709558\pi\)
\(44\) 0 0
\(45\) −3.07713 −0.458711
\(46\) 0.820525 + 0.596147i 0.120980 + 0.0878970i
\(47\) 1.84663 5.68336i 0.269359 0.829003i −0.721298 0.692625i \(-0.756454\pi\)
0.990657 0.136378i \(-0.0435460\pi\)
\(48\) 2.65528 + 8.17213i 0.383257 + 1.17954i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 1.87667 1.36348i 0.265401 0.192825i
\(51\) −3.65696 11.2550i −0.512076 1.57601i
\(52\) −0.0200533 + 0.0617178i −0.00278089 + 0.00855871i
\(53\) −8.20742 5.96304i −1.12738 0.819087i −0.142065 0.989857i \(-0.545374\pi\)
−0.985311 + 0.170771i \(0.945374\pi\)
\(54\) 4.02373 0.547560
\(55\) 0 0
\(56\) 2.83822 0.379272
\(57\) 10.1533 + 7.37680i 1.34484 + 0.977080i
\(58\) 0.510598 1.57146i 0.0670448 0.206343i
\(59\) −2.37350 7.30488i −0.309003 0.951014i −0.978153 0.207887i \(-0.933341\pi\)
0.669150 0.743128i \(-0.266659\pi\)
\(60\) 0.0447607 0.0325205i 0.00577858 0.00419838i
\(61\) −5.07749 + 3.68901i −0.650106 + 0.472330i −0.863307 0.504679i \(-0.831611\pi\)
0.213201 + 0.977008i \(0.431611\pi\)
\(62\) −0.569559 1.75292i −0.0723341 0.222621i
\(63\) −0.519216 + 1.59798i −0.0654151 + 0.201327i
\(64\) −6.51669 4.73465i −0.814587 0.591832i
\(65\) −8.51056 −1.05560
\(66\) 0 0
\(67\) −15.4673 −1.88963 −0.944814 0.327608i \(-0.893758\pi\)
−0.944814 + 0.327608i \(0.893758\pi\)
\(68\) 0.0617999 + 0.0449003i 0.00749434 + 0.00544496i
\(69\) 0.481123 1.48075i 0.0579204 0.178261i
\(70\) 0.797546 + 2.45459i 0.0953250 + 0.293380i
\(71\) −11.2469 + 8.17134i −1.33476 + 0.969759i −0.335140 + 0.942168i \(0.608784\pi\)
−0.999619 + 0.0275910i \(0.991216\pi\)
\(72\) 3.85806 2.80304i 0.454676 0.330342i
\(73\) −1.85862 5.72025i −0.217535 0.669504i −0.998964 0.0455099i \(-0.985509\pi\)
0.781429 0.623994i \(-0.214491\pi\)
\(74\) 0.912233 2.80756i 0.106045 0.326373i
\(75\) −2.88089 2.09309i −0.332657 0.241689i
\(76\) −0.0810106 −0.00929255
\(77\) 0 0
\(78\) −14.1679 −1.60420
\(79\) −12.6538 9.19351i −1.42366 1.03435i −0.991153 0.132722i \(-0.957628\pi\)
−0.432509 0.901630i \(-0.642372\pi\)
\(80\) 2.24780 6.91802i 0.251312 0.773458i
\(81\) −3.46640 10.6685i −0.385156 1.18539i
\(82\) −1.04509 + 0.759300i −0.115411 + 0.0838507i
\(83\) −3.54004 + 2.57199i −0.388570 + 0.282313i −0.764869 0.644186i \(-0.777196\pi\)
0.376299 + 0.926498i \(0.377196\pi\)
\(84\) −0.00933558 0.0287320i −0.00101860 0.00313491i
\(85\) −3.09576 + 9.52776i −0.335782 + 1.03343i
\(86\) 9.14810 + 6.64648i 0.986465 + 0.716708i
\(87\) −2.53651 −0.271942
\(88\) 0 0
\(89\) 15.3437 1.62643 0.813215 0.581963i \(-0.197715\pi\)
0.813215 + 0.581963i \(0.197715\pi\)
\(90\) 3.50830 + 2.54893i 0.369807 + 0.268681i
\(91\) −1.43602 + 4.41961i −0.150536 + 0.463301i
\(92\) 0.00310563 + 0.00955813i 0.000323784 + 0.000996504i
\(93\) −2.28904 + 1.66309i −0.237363 + 0.172454i
\(94\) −6.81318 + 4.95006i −0.702726 + 0.510560i
\(95\) −3.28306 10.1042i −0.336835 1.03667i
\(96\) −0.0528090 + 0.162530i −0.00538980 + 0.0165881i
\(97\) −1.95073 1.41729i −0.198067 0.143904i 0.484331 0.874885i \(-0.339063\pi\)
−0.682398 + 0.730981i \(0.739063\pi\)
\(98\) 1.40927 0.142358
\(99\) 0 0
\(100\) 0.0229859 0.00229859
\(101\) 9.62396 + 6.99222i 0.957620 + 0.695752i 0.952597 0.304236i \(-0.0984011\pi\)
0.00502316 + 0.999987i \(0.498401\pi\)
\(102\) −5.15363 + 15.8612i −0.510285 + 1.57050i
\(103\) 0.122468 + 0.376917i 0.0120671 + 0.0371387i 0.956909 0.290389i \(-0.0937846\pi\)
−0.944842 + 0.327527i \(0.893785\pi\)
\(104\) 10.6704 7.75250i 1.04632 0.760195i
\(105\) 3.20531 2.32880i 0.312807 0.227267i
\(106\) 4.41799 + 13.5972i 0.429113 + 1.32068i
\(107\) 1.01029 3.10934i 0.0976680 0.300591i −0.890272 0.455430i \(-0.849486\pi\)
0.987940 + 0.154838i \(0.0494857\pi\)
\(108\) 0.0322566 + 0.0234358i 0.00310389 + 0.00225511i
\(109\) 2.84638 0.272634 0.136317 0.990665i \(-0.456473\pi\)
0.136317 + 0.990665i \(0.456473\pi\)
\(110\) 0 0
\(111\) −4.53172 −0.430132
\(112\) −3.21332 2.33461i −0.303630 0.220600i
\(113\) 4.49451 13.8327i 0.422807 1.30127i −0.482271 0.876022i \(-0.660188\pi\)
0.905078 0.425245i \(-0.139812\pi\)
\(114\) −5.46544 16.8209i −0.511885 1.57542i
\(115\) −1.06630 + 0.774711i −0.0994328 + 0.0722421i
\(116\) 0.0132461 0.00962382i 0.00122987 0.000893550i
\(117\) 2.41283 + 7.42591i 0.223066 + 0.686526i
\(118\) −3.34490 + 10.2945i −0.307923 + 0.947688i
\(119\) 4.42550 + 3.21531i 0.405685 + 0.294747i
\(120\) −11.2450 −1.02652
\(121\) 0 0
\(122\) 8.84474 0.800765
\(123\) 1.60432 + 1.16561i 0.144657 + 0.105099i
\(124\) 0.00564379 0.0173698i 0.000506828 0.00155986i
\(125\) 3.76118 + 11.5757i 0.336410 + 1.03536i
\(126\) 1.91565 1.39180i 0.170660 0.123992i
\(127\) 4.07168 2.95825i 0.361303 0.262502i −0.392292 0.919841i \(-0.628318\pi\)
0.753595 + 0.657339i \(0.228318\pi\)
\(128\) 3.45907 + 10.6459i 0.305741 + 0.940974i
\(129\) 5.36408 16.5089i 0.472281 1.45353i
\(130\) 9.70307 + 7.04969i 0.851015 + 0.618299i
\(131\) 0.180053 0.0157313 0.00786565 0.999969i \(-0.497496\pi\)
0.00786565 + 0.999969i \(0.497496\pi\)
\(132\) 0 0
\(133\) −5.80118 −0.503026
\(134\) 17.6346 + 12.8123i 1.52339 + 1.10681i
\(135\) −1.61584 + 4.97304i −0.139069 + 0.428011i
\(136\) −4.79769 14.7658i −0.411398 1.26615i
\(137\) −6.73422 + 4.89270i −0.575343 + 0.418011i −0.837042 0.547138i \(-0.815717\pi\)
0.261699 + 0.965150i \(0.415717\pi\)
\(138\) −1.77511 + 1.28969i −0.151107 + 0.109786i
\(139\) 2.15113 + 6.62049i 0.182456 + 0.561543i 0.999895 0.0144726i \(-0.00460693\pi\)
−0.817439 + 0.576015i \(0.804607\pi\)
\(140\) −0.00790293 + 0.0243227i −0.000667920 + 0.00205565i
\(141\) 10.4590 + 7.59889i 0.880805 + 0.639942i
\(142\) 19.5915 1.64408
\(143\) 0 0
\(144\) −6.67362 −0.556135
\(145\) 1.73716 + 1.26212i 0.144264 + 0.104814i
\(146\) −2.61929 + 8.06136i −0.216774 + 0.667163i
\(147\) −0.668522 2.05750i −0.0551387 0.169700i
\(148\) 0.0236654 0.0171939i 0.00194528 0.00141333i
\(149\) −2.60043 + 1.88933i −0.213036 + 0.154780i −0.689186 0.724584i \(-0.742032\pi\)
0.476150 + 0.879364i \(0.342032\pi\)
\(150\) 1.55076 + 4.77275i 0.126619 + 0.389694i
\(151\) −6.88088 + 21.1772i −0.559958 + 1.72337i 0.122517 + 0.992466i \(0.460903\pi\)
−0.682476 + 0.730908i \(0.739097\pi\)
\(152\) 13.3205 + 9.67788i 1.08043 + 0.784979i
\(153\) 9.19115 0.743061
\(154\) 0 0
\(155\) 2.39521 0.192388
\(156\) −0.113578 0.0825193i −0.00909352 0.00660683i
\(157\) 4.09595 12.6060i 0.326892 1.00607i −0.643687 0.765289i \(-0.722596\pi\)
0.970579 0.240782i \(-0.0774040\pi\)
\(158\) 6.81144 + 20.9634i 0.541889 + 1.66776i
\(159\) 17.7558 12.9003i 1.40813 1.02306i
\(160\) 0.117039 0.0850338i 0.00925274 0.00672251i
\(161\) 0.222394 + 0.684459i 0.0175271 + 0.0539429i
\(162\) −4.88509 + 15.0348i −0.383809 + 1.18124i
\(163\) −11.0984 8.06344i −0.869292 0.631577i 0.0611050 0.998131i \(-0.480538\pi\)
−0.930397 + 0.366554i \(0.880538\pi\)
\(164\) −0.0128005 −0.000999552
\(165\) 0 0
\(166\) 6.16657 0.478619
\(167\) 7.53081 + 5.47146i 0.582752 + 0.423394i 0.839715 0.543027i \(-0.182722\pi\)
−0.256963 + 0.966421i \(0.582722\pi\)
\(168\) −1.89741 + 5.83962i −0.146388 + 0.450537i
\(169\) 2.65604 + 8.17446i 0.204311 + 0.628804i
\(170\) 11.4218 8.29844i 0.876014 0.636461i
\(171\) −7.88568 + 5.72928i −0.603033 + 0.438129i
\(172\) 0.0346248 + 0.106564i 0.00264012 + 0.00812545i
\(173\) −3.24643 + 9.99149i −0.246822 + 0.759639i 0.748510 + 0.663124i \(0.230770\pi\)
−0.995331 + 0.0965154i \(0.969230\pi\)
\(174\) 2.89193 + 2.10111i 0.219236 + 0.159285i
\(175\) 1.64602 0.124428
\(176\) 0 0
\(177\) 16.6165 1.24897
\(178\) −17.4937 12.7099i −1.31121 0.952648i
\(179\) −2.57204 + 7.91594i −0.192244 + 0.591665i 0.807754 + 0.589520i \(0.200683\pi\)
−0.999998 + 0.00214538i \(0.999317\pi\)
\(180\) 0.0132786 + 0.0408675i 0.000989732 + 0.00304608i
\(181\) 11.9758 8.70096i 0.890158 0.646738i −0.0457613 0.998952i \(-0.514571\pi\)
0.935919 + 0.352215i \(0.114571\pi\)
\(182\) 5.29821 3.84937i 0.392729 0.285335i
\(183\) −4.19572 12.9131i −0.310157 0.954565i
\(184\) 0.631202 1.94264i 0.0465329 0.143213i
\(185\) 3.10361 + 2.25491i 0.228182 + 0.165784i
\(186\) 3.98740 0.292370
\(187\) 0 0
\(188\) −0.0834496 −0.00608619
\(189\) 2.30990 + 1.67824i 0.168020 + 0.122074i
\(190\) −4.62671 + 14.2395i −0.335657 + 1.03304i
\(191\) −2.96865 9.13657i −0.214804 0.661099i −0.999167 0.0407974i \(-0.987010\pi\)
0.784363 0.620302i \(-0.212990\pi\)
\(192\) 14.0981 10.2429i 1.01744 0.739215i
\(193\) −1.20366 + 0.874512i −0.0866415 + 0.0629487i −0.630263 0.776382i \(-0.717053\pi\)
0.543621 + 0.839331i \(0.317053\pi\)
\(194\) 1.05007 + 3.23177i 0.0753903 + 0.232027i
\(195\) 5.68949 17.5104i 0.407433 1.25395i
\(196\) 0.0112975 + 0.00820814i 0.000806966 + 0.000586295i
\(197\) 14.0434 1.00055 0.500274 0.865867i \(-0.333233\pi\)
0.500274 + 0.865867i \(0.333233\pi\)
\(198\) 0 0
\(199\) −4.28729 −0.303918 −0.151959 0.988387i \(-0.548558\pi\)
−0.151959 + 0.988387i \(0.548558\pi\)
\(200\) −3.77954 2.74600i −0.267254 0.194171i
\(201\) 10.3402 31.8239i 0.729342 2.24468i
\(202\) −5.18050 15.9440i −0.364499 1.12181i
\(203\) 0.948551 0.689163i 0.0665753 0.0483698i
\(204\) −0.133697 + 0.0971364i −0.00936064 + 0.00680091i
\(205\) −0.518757 1.59657i −0.0362315 0.111509i
\(206\) 0.172590 0.531177i 0.0120249 0.0370088i
\(207\) 0.978282 + 0.710764i 0.0679953 + 0.0494015i
\(208\) −18.4575 −1.27980
\(209\) 0 0
\(210\) −5.58350 −0.385298
\(211\) −1.17734 0.855387i −0.0810514 0.0588873i 0.546522 0.837445i \(-0.315952\pi\)
−0.627573 + 0.778558i \(0.715952\pi\)
\(212\) −0.0437781 + 0.134735i −0.00300670 + 0.00925366i
\(213\) −9.29373 28.6031i −0.636796 1.95986i
\(214\) −3.72746 + 2.70816i −0.254804 + 0.185126i
\(215\) −11.8882 + 8.63730i −0.810771 + 0.589059i
\(216\) −2.50416 7.70703i −0.170387 0.524397i
\(217\) 0.404153 1.24385i 0.0274357 0.0844383i
\(218\) −3.24522 2.35779i −0.219794 0.159690i
\(219\) 13.0119 0.879264
\(220\) 0 0
\(221\) 25.4204 1.70996
\(222\) 5.16671 + 3.75383i 0.346767 + 0.251941i
\(223\) −1.50072 + 4.61873i −0.100495 + 0.309293i −0.988647 0.150258i \(-0.951990\pi\)
0.888151 + 0.459551i \(0.151990\pi\)
\(224\) −0.0244104 0.0751275i −0.00163099 0.00501967i
\(225\) 2.23748 1.62563i 0.149165 0.108375i
\(226\) −16.5825 + 12.0479i −1.10305 + 0.801415i
\(227\) −0.122724 0.377706i −0.00814549 0.0250692i 0.946901 0.321525i \(-0.104195\pi\)
−0.955047 + 0.296456i \(0.904195\pi\)
\(228\) 0.0541573 0.166679i 0.00358666 0.0110386i
\(229\) −1.77145 1.28703i −0.117061 0.0850496i 0.527715 0.849422i \(-0.323049\pi\)
−0.644775 + 0.764372i \(0.723049\pi\)
\(230\) 1.85744 0.122476
\(231\) 0 0
\(232\) −3.32773 −0.218476
\(233\) −1.01949 0.740701i −0.0667888 0.0485249i 0.553890 0.832590i \(-0.313143\pi\)
−0.620679 + 0.784065i \(0.713143\pi\)
\(234\) 3.40032 10.4651i 0.222286 0.684125i
\(235\) −3.38190 10.4084i −0.220611 0.678971i
\(236\) −0.0867741 + 0.0630451i −0.00564851 + 0.00410389i
\(237\) 27.3750 19.8891i 1.77820 1.29193i
\(238\) −2.38221 7.33169i −0.154416 0.475243i
\(239\) 3.44914 10.6154i 0.223106 0.686651i −0.775372 0.631505i \(-0.782438\pi\)
0.998478 0.0551459i \(-0.0175624\pi\)
\(240\) 12.7311 + 9.24969i 0.821790 + 0.597065i
\(241\) 21.4843 1.38392 0.691962 0.721934i \(-0.256746\pi\)
0.691962 + 0.721934i \(0.256746\pi\)
\(242\) 0 0
\(243\) 15.7022 1.00730
\(244\) 0.0709047 + 0.0515153i 0.00453921 + 0.00329793i
\(245\) −0.565930 + 1.74175i −0.0361559 + 0.111276i
\(246\) −0.863595 2.65787i −0.0550608 0.169460i
\(247\) −21.8098 + 15.8457i −1.38772 + 1.00824i
\(248\) −3.00307 + 2.18186i −0.190695 + 0.138548i
\(249\) −2.92527 9.00305i −0.185381 0.570545i
\(250\) 5.30051 16.3133i 0.335234 1.03174i
\(251\) 0.342877 + 0.249115i 0.0216422 + 0.0157240i 0.598554 0.801083i \(-0.295742\pi\)
−0.576912 + 0.816807i \(0.695742\pi\)
\(252\) 0.0234634 0.00147806
\(253\) 0 0
\(254\) −7.09267 −0.445033
\(255\) −17.5338 12.7390i −1.09801 0.797748i
\(256\) −0.103561 + 0.318729i −0.00647259 + 0.0199206i
\(257\) 5.38928 + 16.5865i 0.336174 + 1.03464i 0.966141 + 0.258015i \(0.0830684\pi\)
−0.629967 + 0.776622i \(0.716932\pi\)
\(258\) −19.7908 + 14.3789i −1.23212 + 0.895189i
\(259\) 1.69468 1.23126i 0.105302 0.0765066i
\(260\) 0.0367254 + 0.113029i 0.00227761 + 0.00700976i
\(261\) 0.608767 1.87359i 0.0376817 0.115972i
\(262\) −0.205282 0.149146i −0.0126824 0.00921429i
\(263\) −1.51519 −0.0934307 −0.0467153 0.998908i \(-0.514875\pi\)
−0.0467153 + 0.998908i \(0.514875\pi\)
\(264\) 0 0
\(265\) −18.5793 −1.14132
\(266\) 6.61405 + 4.80539i 0.405533 + 0.294637i
\(267\) −10.2576 + 31.5697i −0.627755 + 1.93203i
\(268\) 0.0667455 + 0.205421i 0.00407713 + 0.0125481i
\(269\) 1.64314 1.19381i 0.100184 0.0727878i −0.536566 0.843859i \(-0.680279\pi\)
0.636749 + 0.771071i \(0.280279\pi\)
\(270\) 5.96165 4.33139i 0.362814 0.263600i
\(271\) −2.34990 7.23225i −0.142746 0.439328i 0.853968 0.520326i \(-0.174189\pi\)
−0.996714 + 0.0809976i \(0.974189\pi\)
\(272\) −6.71402 + 20.6636i −0.407097 + 1.25292i
\(273\) −8.13333 5.90921i −0.492252 0.357642i
\(274\) 11.7307 0.708676
\(275\) 0 0
\(276\) −0.0217420 −0.00130872
\(277\) 11.6715 + 8.47987i 0.701274 + 0.509506i 0.880347 0.474330i \(-0.157310\pi\)
−0.179073 + 0.983836i \(0.557310\pi\)
\(278\) 3.03151 9.33004i 0.181818 0.559579i
\(279\) −0.679064 2.08995i −0.0406545 0.125122i
\(280\) 4.20516 3.05523i 0.251307 0.182585i
\(281\) 14.3598 10.4330i 0.856632 0.622379i −0.0703347 0.997523i \(-0.522407\pi\)
0.926967 + 0.375144i \(0.122407\pi\)
\(282\) −5.62999 17.3273i −0.335261 1.03183i
\(283\) 9.62160 29.6122i 0.571945 1.76026i −0.0744107 0.997228i \(-0.523708\pi\)
0.646355 0.763037i \(-0.276292\pi\)
\(284\) 0.157057 + 0.114109i 0.00931963 + 0.00677111i
\(285\) 22.9842 1.36147
\(286\) 0 0
\(287\) −0.916645 −0.0541079
\(288\) −0.107378 0.0780148i −0.00632732 0.00459707i
\(289\) 3.99350 12.2907i 0.234912 0.722984i
\(290\) −0.935102 2.87795i −0.0549111 0.168999i
\(291\) 4.22018 3.06614i 0.247391 0.179740i
\(292\) −0.0679504 + 0.0493689i −0.00397650 + 0.00288909i
\(293\) 7.42577 + 22.8542i 0.433818 + 1.33515i 0.894293 + 0.447482i \(0.147679\pi\)
−0.460475 + 0.887673i \(0.652321\pi\)
\(294\) −0.942126 + 2.89957i −0.0549459 + 0.169106i
\(295\) −11.3801 8.26809i −0.662572 0.481387i
\(296\) −5.94532 −0.345565
\(297\) 0 0
\(298\) 4.52983 0.262406
\(299\) 2.70568 + 1.96579i 0.156474 + 0.113685i
\(300\) −0.0153666 + 0.0472935i −0.000887190 + 0.00273049i
\(301\) 2.47949 + 7.63108i 0.142915 + 0.439848i
\(302\) 25.3871 18.4448i 1.46086 1.06138i
\(303\) −20.8203 + 15.1268i −1.19609 + 0.869014i
\(304\) −7.12023 21.9138i −0.408373 1.25684i
\(305\) −3.55184 + 10.9315i −0.203378 + 0.625933i
\(306\) −10.4790 7.61346i −0.599046 0.435233i
\(307\) 5.46298 0.311789 0.155894 0.987774i \(-0.450174\pi\)
0.155894 + 0.987774i \(0.450174\pi\)
\(308\) 0 0
\(309\) −0.857378 −0.0487745
\(310\) −2.73083 1.98406i −0.155101 0.112687i
\(311\) 4.29176 13.2087i 0.243364 0.748996i −0.752538 0.658549i \(-0.771170\pi\)
0.995901 0.0904468i \(-0.0288295\pi\)
\(312\) 8.81736 + 27.1371i 0.499185 + 1.53633i
\(313\) −22.2064 + 16.1339i −1.25518 + 0.911940i −0.998510 0.0545602i \(-0.982624\pi\)
−0.256667 + 0.966500i \(0.582624\pi\)
\(314\) −15.1121 + 10.9796i −0.852823 + 0.619612i
\(315\) 0.950885 + 2.92652i 0.0535763 + 0.164891i
\(316\) −0.0674949 + 0.207728i −0.00379689 + 0.0116856i
\(317\) −6.33113 4.59983i −0.355592 0.258352i 0.395619 0.918415i \(-0.370530\pi\)
−0.751211 + 0.660062i \(0.770530\pi\)
\(318\) −30.9297 −1.73445
\(319\) 0 0
\(320\) −14.7520 −0.824659
\(321\) 5.72206 + 4.15732i 0.319374 + 0.232039i
\(322\) 0.313413 0.964586i 0.0174658 0.0537543i
\(323\) 9.80624 + 30.1805i 0.545634 + 1.67929i
\(324\) −0.126730 + 0.0920749i −0.00704057 + 0.00511527i
\(325\) 6.18831 4.49607i 0.343265 0.249397i
\(326\) 5.97417 + 18.3866i 0.330879 + 1.01834i
\(327\) −1.90287 + 5.85643i −0.105229 + 0.323861i
\(328\) 2.10477 + 1.52920i 0.116216 + 0.0844361i
\(329\) −5.97584 −0.329458
\(330\) 0 0
\(331\) −28.1462 −1.54705 −0.773527 0.633764i \(-0.781509\pi\)
−0.773527 + 0.633764i \(0.781509\pi\)
\(332\) 0.0494349 + 0.0359166i 0.00271309 + 0.00197118i
\(333\) 1.08762 3.34736i 0.0596013 0.183434i
\(334\) −4.05378 12.4762i −0.221813 0.682670i
\(335\) −22.9167 + 16.6499i −1.25207 + 0.909683i
\(336\) 6.95163 5.05065i 0.379242 0.275536i
\(337\) 7.71892 + 23.7564i 0.420476 + 1.29409i 0.907260 + 0.420570i \(0.138170\pi\)
−0.486784 + 0.873523i \(0.661830\pi\)
\(338\) 3.74308 11.5200i 0.203596 0.626605i
\(339\) 25.4560 + 18.4949i 1.38258 + 1.00450i
\(340\) 0.139898 0.00758701
\(341\) 0 0
\(342\) 13.7365 0.742783
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) 7.03732 21.6586i 0.379427 1.16776i
\(345\) −0.881123 2.71182i −0.0474380 0.145999i
\(346\) 11.9778 8.70235i 0.643928 0.467841i
\(347\) 16.7056 12.1373i 0.896802 0.651565i −0.0408403 0.999166i \(-0.513003\pi\)
0.937643 + 0.347601i \(0.113003\pi\)
\(348\) 0.0109457 + 0.0336875i 0.000586752 + 0.00180584i
\(349\) 1.85324 5.70369i 0.0992017 0.305311i −0.889124 0.457666i \(-0.848686\pi\)
0.988326 + 0.152355i \(0.0486856\pi\)
\(350\) −1.87667 1.36348i −0.100312 0.0728810i
\(351\) 13.2682 0.708206
\(352\) 0 0
\(353\) 24.0382 1.27942 0.639712 0.768615i \(-0.279054\pi\)
0.639712 + 0.768615i \(0.279054\pi\)
\(354\) −18.9448 13.7642i −1.00691 0.731561i
\(355\) −7.86750 + 24.2137i −0.417564 + 1.28513i
\(356\) −0.0662123 0.203780i −0.00350924 0.0108003i
\(357\) −9.57403 + 6.95594i −0.506712 + 0.368148i
\(358\) 9.48958 6.89459i 0.501540 0.364390i
\(359\) 3.38377 + 10.4142i 0.178589 + 0.549640i 0.999779 0.0210147i \(-0.00668966\pi\)
−0.821190 + 0.570654i \(0.806690\pi\)
\(360\) 2.69882 8.30610i 0.142240 0.437770i
\(361\) −11.8550 8.61319i −0.623950 0.453326i
\(362\) −20.8613 −1.09645
\(363\) 0 0
\(364\) 0.0648939 0.00340136
\(365\) −8.91140 6.47451i −0.466444 0.338892i
\(366\) −5.91290 + 18.1980i −0.309072 + 0.951226i
\(367\) 3.28107 + 10.0981i 0.171270 + 0.527116i 0.999444 0.0333563i \(-0.0106196\pi\)
−0.828173 + 0.560472i \(0.810620\pi\)
\(368\) −2.31257 + 1.68018i −0.120551 + 0.0875853i
\(369\) −1.24602 + 0.905286i −0.0648651 + 0.0471273i
\(370\) −1.67065 5.14173i −0.0868530 0.267306i
\(371\) −3.13496 + 9.64840i −0.162759 + 0.500920i
\(372\) 0.0319654 + 0.0232242i 0.00165733 + 0.00120412i
\(373\) −36.6036 −1.89526 −0.947631 0.319367i \(-0.896530\pi\)
−0.947631 + 0.319367i \(0.896530\pi\)
\(374\) 0 0
\(375\) −26.3315 −1.35975
\(376\) 13.7215 + 9.96925i 0.707632 + 0.514125i
\(377\) 1.68370 5.18188i 0.0867147 0.266880i
\(378\) −1.24340 3.82679i −0.0639536 0.196829i
\(379\) 10.2404 7.44005i 0.526012 0.382170i −0.292852 0.956158i \(-0.594604\pi\)
0.818864 + 0.573988i \(0.194604\pi\)
\(380\) −0.120027 + 0.0872048i −0.00615726 + 0.00447351i
\(381\) 3.36458 + 10.3551i 0.172373 + 0.530509i
\(382\) −4.18363 + 12.8759i −0.214053 + 0.658787i
\(383\) 12.5138 + 9.09179i 0.639424 + 0.464569i 0.859652 0.510879i \(-0.170680\pi\)
−0.220228 + 0.975448i \(0.570680\pi\)
\(384\) −24.2164 −1.23579
\(385\) 0 0
\(386\) 2.09672 0.106720
\(387\) 10.9069 + 7.92435i 0.554431 + 0.402818i
\(388\) −0.0104052 + 0.0320238i −0.000528242 + 0.00162576i
\(389\) −3.92852 12.0907i −0.199184 0.613025i −0.999902 0.0139838i \(-0.995549\pi\)
0.800718 0.599041i \(-0.204451\pi\)
\(390\) −20.9914 + 15.2512i −1.06294 + 0.772273i
\(391\) 3.18495 2.31400i 0.161070 0.117024i
\(392\) −0.877057 2.69930i −0.0442981 0.136335i
\(393\) −0.120369 + 0.370459i −0.00607183 + 0.0186872i
\(394\) −16.0111 11.6328i −0.806630 0.586051i
\(395\) −28.6446 −1.44127
\(396\) 0 0
\(397\) −18.9574 −0.951445 −0.475722 0.879596i \(-0.657813\pi\)
−0.475722 + 0.879596i \(0.657813\pi\)
\(398\) 4.88803 + 3.55136i 0.245015 + 0.178014i
\(399\) 3.87821 11.9359i 0.194153 0.597543i
\(400\) 2.02029 + 6.21782i 0.101015 + 0.310891i
\(401\) 7.02395 5.10320i 0.350759 0.254842i −0.398428 0.917200i \(-0.630444\pi\)
0.749188 + 0.662358i \(0.230444\pi\)
\(402\) −38.1503 + 27.7178i −1.90276 + 1.38244i
\(403\) −1.87812 5.78026i −0.0935558 0.287935i
\(404\) 0.0513339 0.157990i 0.00255396 0.00786027i
\(405\) −16.6201 12.0752i −0.825861 0.600023i
\(406\) −1.65233 −0.0820037
\(407\) 0 0
\(408\) 33.5879 1.66285
\(409\) 4.62277 + 3.35864i 0.228581 + 0.166074i 0.696181 0.717866i \(-0.254881\pi\)
−0.467600 + 0.883940i \(0.654881\pi\)
\(410\) −0.731067 + 2.24999i −0.0361048 + 0.111119i
\(411\) −5.56474 17.1265i −0.274489 0.844789i
\(412\) 0.00447737 0.00325300i 0.000220584 0.000160264i
\(413\) −6.21390 + 4.51466i −0.305766 + 0.222152i
\(414\) −0.526602 1.62071i −0.0258811 0.0796537i
\(415\) −2.47635 + 7.62144i −0.121559 + 0.374122i
\(416\) −0.296981 0.215769i −0.0145607 0.0105790i
\(417\) −15.0597 −0.737477
\(418\) 0 0
\(419\) −27.1909 −1.32836 −0.664181 0.747571i \(-0.731220\pi\)
−0.664181 + 0.747571i \(0.731220\pi\)
\(420\) −0.0447607 0.0325205i −0.00218410 0.00158684i
\(421\) −7.40561 + 22.7921i −0.360928 + 1.11082i 0.591565 + 0.806258i \(0.298510\pi\)
−0.952492 + 0.304563i \(0.901490\pi\)
\(422\) 0.633753 + 1.95049i 0.0308506 + 0.0949484i
\(423\) −8.12310 + 5.90178i −0.394959 + 0.286954i
\(424\) 23.2944 16.9244i 1.13128 0.821921i
\(425\) −2.78242 8.56341i −0.134967 0.415386i
\(426\) −13.0973 + 40.3095i −0.634569 + 1.95300i
\(427\) 5.07749 + 3.68901i 0.245717 + 0.178524i
\(428\) −0.0456549 −0.00220681
\(429\) 0 0
\(430\) 20.7087 0.998663
\(431\) 13.3271 + 9.68268i 0.641942 + 0.466398i 0.860517 0.509422i \(-0.170141\pi\)
−0.218575 + 0.975820i \(0.570141\pi\)
\(432\) −3.50440 + 10.7854i −0.168605 + 0.518914i
\(433\) 6.20844 + 19.1076i 0.298359 + 0.918253i 0.982073 + 0.188503i \(0.0603636\pi\)
−0.683714 + 0.729750i \(0.739636\pi\)
\(434\) −1.49113 + 1.08337i −0.0715763 + 0.0520032i
\(435\) −3.75815 + 2.73045i −0.180189 + 0.130915i
\(436\) −0.0122829 0.0378030i −0.000588245 0.00181043i
\(437\) −1.29015 + 3.97067i −0.0617161 + 0.189943i
\(438\) −14.8352 10.7784i −0.708852 0.515011i
\(439\) −26.7682 −1.27758 −0.638788 0.769383i \(-0.720564\pi\)
−0.638788 + 0.769383i \(0.720564\pi\)
\(440\) 0 0
\(441\) 1.68022 0.0800104
\(442\) −28.9823 21.0569i −1.37855 1.00157i
\(443\) 8.10098 24.9323i 0.384889 1.18457i −0.551671 0.834062i \(-0.686010\pi\)
0.936561 0.350506i \(-0.113990\pi\)
\(444\) 0.0195556 + 0.0601859i 0.000928068 + 0.00285630i
\(445\) 22.7336 16.5169i 1.07768 0.782977i
\(446\) 5.53691 4.02280i 0.262180 0.190485i
\(447\) −2.14884 6.61344i −0.101637 0.312805i
\(448\) −2.48916 + 7.66083i −0.117602 + 0.361940i
\(449\) −7.88582 5.72938i −0.372155 0.270386i 0.385949 0.922520i \(-0.373874\pi\)
−0.758104 + 0.652134i \(0.773874\pi\)
\(450\) −3.89758 −0.183734
\(451\) 0 0
\(452\) −0.203107 −0.00955336
\(453\) −38.9720 28.3148i −1.83106 1.33035i
\(454\) −0.172951 + 0.532289i −0.00811700 + 0.0249816i
\(455\) 2.62991 + 8.09402i 0.123292 + 0.379453i
\(456\) −28.8172 + 20.9369i −1.34949 + 0.980462i
\(457\) 9.61541 6.98601i 0.449790 0.326792i −0.339723 0.940526i \(-0.610333\pi\)
0.789513 + 0.613734i \(0.210333\pi\)
\(458\) 0.953558 + 2.93475i 0.0445568 + 0.137132i
\(459\) 4.82638 14.8541i 0.225276 0.693329i
\(460\) 0.0148903 + 0.0108185i 0.000694265 + 0.000504413i
\(461\) −9.14737 −0.426035 −0.213018 0.977048i \(-0.568329\pi\)
−0.213018 + 0.977048i \(0.568329\pi\)
\(462\) 0 0
\(463\) 38.9342 1.80943 0.904713 0.426021i \(-0.140085\pi\)
0.904713 + 0.426021i \(0.140085\pi\)
\(464\) 3.76753 + 2.73727i 0.174903 + 0.127075i
\(465\) −1.60125 + 4.92813i −0.0742561 + 0.228537i
\(466\) 0.548782 + 1.68898i 0.0254218 + 0.0782404i
\(467\) 16.8141 12.2162i 0.778066 0.565298i −0.126332 0.991988i \(-0.540320\pi\)
0.904398 + 0.426690i \(0.140320\pi\)
\(468\) 0.0882119 0.0640897i 0.00407760 0.00296255i
\(469\) 4.77965 + 14.7102i 0.220704 + 0.679256i
\(470\) −4.76600 + 14.6683i −0.219839 + 0.676596i
\(471\) 23.1987 + 16.8548i 1.06894 + 0.776629i
\(472\) 21.7998 1.00342
\(473\) 0 0
\(474\) −47.6858 −2.19028
\(475\) 7.72520 + 5.61269i 0.354457 + 0.257528i
\(476\) 0.0236055 0.0726501i 0.00108195 0.00332991i
\(477\) 5.26741 + 16.2114i 0.241178 + 0.742270i
\(478\) −12.7256 + 9.24572i −0.582057 + 0.422889i
\(479\) −19.8503 + 14.4221i −0.906983 + 0.658962i −0.940250 0.340485i \(-0.889409\pi\)
0.0332672 + 0.999446i \(0.489409\pi\)
\(480\) 0.0967138 + 0.297654i 0.00441436 + 0.0135860i
\(481\) 3.00809 9.25794i 0.137157 0.422126i
\(482\) −24.4947 17.7964i −1.11570 0.810606i
\(483\) −1.55695 −0.0708436
\(484\) 0 0
\(485\) −4.41591 −0.200516
\(486\) −17.9024 13.0069i −0.812070 0.590003i
\(487\) −3.82295 + 11.7658i −0.173234 + 0.533160i −0.999548 0.0300493i \(-0.990434\pi\)
0.826314 + 0.563209i \(0.190434\pi\)
\(488\) −5.50452 16.9412i −0.249178 0.766890i
\(489\) 24.0100 17.4443i 1.08577 0.788858i
\(490\) 2.08800 1.51702i 0.0943264 0.0685321i
\(491\) −5.10653 15.7163i −0.230454 0.709266i −0.997692 0.0679027i \(-0.978369\pi\)
0.767238 0.641363i \(-0.221631\pi\)
\(492\) 0.00855741 0.0263370i 0.000385798 0.00118736i
\(493\) −5.18878 3.76987i −0.233691 0.169786i
\(494\) 37.9916 1.70932
\(495\) 0 0
\(496\) 5.19468 0.233248
\(497\) 11.2469 + 8.17134i 0.504492 + 0.366535i
\(498\) −4.12249 + 12.6877i −0.184733 + 0.568550i
\(499\) −4.24619 13.0684i −0.190085 0.585023i 0.809913 0.586549i \(-0.199514\pi\)
−0.999999 + 0.00152665i \(0.999514\pi\)
\(500\) 0.137507 0.0999048i 0.00614951 0.00446788i
\(501\) −16.2920 + 11.8368i −0.727874 + 0.528831i
\(502\) −0.184568 0.568043i −0.00823769 0.0253530i
\(503\) 6.98278 21.4908i 0.311347 0.958227i −0.665885 0.746054i \(-0.731946\pi\)
0.977232 0.212173i \(-0.0680541\pi\)
\(504\) −3.85806 2.80304i −0.171851 0.124857i
\(505\) 21.7859 0.969461
\(506\) 0 0
\(507\) −18.5946 −0.825813
\(508\) −0.0568590 0.0413105i −0.00252271 0.00183286i
\(509\) −6.63262 + 20.4131i −0.293986 + 0.904795i 0.689575 + 0.724215i \(0.257798\pi\)
−0.983560 + 0.180580i \(0.942202\pi\)
\(510\) 9.43829 + 29.0481i 0.417934 + 1.28627i
\(511\) −4.86593 + 3.53531i −0.215256 + 0.156393i
\(512\) 18.4940 13.4367i 0.817327 0.593823i
\(513\) 5.11839 + 15.7528i 0.225983 + 0.695503i
\(514\) 7.59493 23.3748i 0.334998 1.03102i
\(515\) 0.587188 + 0.426617i 0.0258746 + 0.0187990i
\(516\) −0.242403 −0.0106712
\(517\) 0 0
\(518\) −2.95205 −0.129706
\(519\) −18.3872 13.3591i −0.807107 0.586398i
\(520\) 7.46424 22.9726i 0.327329 1.00741i
\(521\) 10.7265 + 33.0127i 0.469935 + 1.44631i 0.852669 + 0.522452i \(0.174983\pi\)
−0.382734 + 0.923859i \(0.625017\pi\)
\(522\) −2.24605 + 1.63185i −0.0983071 + 0.0714243i
\(523\) 15.9604 11.5959i 0.697900 0.507054i −0.181348 0.983419i \(-0.558046\pi\)
0.879247 + 0.476365i \(0.158046\pi\)
\(524\) −0.000776978 0.00239129i −3.39424e−5 0.000104464i
\(525\) −1.10040 + 3.38669i −0.0480255 + 0.147807i
\(526\) 1.72750 + 1.25510i 0.0753227 + 0.0547251i
\(527\) −7.15430 −0.311646
\(528\) 0 0
\(529\) −22.4821 −0.977481
\(530\) 21.1826 + 15.3901i 0.920115 + 0.668503i
\(531\) −3.98800 + 12.2738i −0.173064 + 0.532637i
\(532\) 0.0250337 + 0.0770457i 0.00108535 + 0.00334035i
\(533\) −3.44617 + 2.50379i −0.149270 + 0.108451i
\(534\) 37.8455 27.4964i 1.63774 1.18989i
\(535\) −1.85022 5.69440i −0.0799921 0.246190i
\(536\) 13.5657 41.7508i 0.585948 1.80336i
\(537\) −14.5676 10.5839i −0.628636 0.456731i
\(538\) −2.86226 −0.123401
\(539\) 0 0
\(540\) 0.0730199 0.00314227
\(541\) −4.48958 3.26187i −0.193022 0.140239i 0.487077 0.873359i \(-0.338063\pi\)
−0.680099 + 0.733120i \(0.738063\pi\)
\(542\) −3.31164 + 10.1922i −0.142247 + 0.437792i
\(543\) 9.89610 + 30.4571i 0.424682 + 1.30704i
\(544\) −0.349587 + 0.253990i −0.0149884 + 0.0108897i
\(545\) 4.21727 3.06402i 0.180648 0.131248i
\(546\) 4.37811 + 13.4744i 0.187366 + 0.576653i
\(547\) 2.61018 8.03330i 0.111603 0.343479i −0.879620 0.475677i \(-0.842203\pi\)
0.991223 + 0.132197i \(0.0422033\pi\)
\(548\) 0.0940401 + 0.0683241i 0.00401719 + 0.00291866i
\(549\) 10.5453 0.450061
\(550\) 0 0
\(551\) 6.80173 0.289763
\(552\) 3.57501 + 2.59739i 0.152162 + 0.110552i
\(553\) −4.83332 + 14.8754i −0.205534 + 0.632567i
\(554\) −6.28270 19.3362i −0.266926 0.821514i
\(555\) −6.71430 + 4.87822i −0.285006 + 0.207069i
\(556\) 0.0786443 0.0571384i 0.00333526 0.00242321i
\(557\) 3.76491 + 11.5872i 0.159524 + 0.490965i 0.998591 0.0530632i \(-0.0168985\pi\)
−0.839067 + 0.544028i \(0.816898\pi\)
\(558\) −0.956984 + 2.94529i −0.0405123 + 0.124684i
\(559\) 30.1658 + 21.9168i 1.27588 + 0.926980i
\(560\) −7.27404 −0.307384
\(561\) 0 0
\(562\) −25.0140 −1.05515
\(563\) −22.1295 16.0780i −0.932646 0.677607i 0.0139935 0.999902i \(-0.495546\pi\)
−0.946639 + 0.322295i \(0.895546\pi\)
\(564\) 0.0557879 0.171697i 0.00234909 0.00722977i
\(565\) −8.23118 25.3330i −0.346288 1.06577i
\(566\) −35.4990 + 25.7915i −1.49213 + 1.08410i
\(567\) −9.07517 + 6.59349i −0.381121 + 0.276901i
\(568\) −12.1928 37.5255i −0.511597 1.57453i
\(569\) −2.20491 + 6.78602i −0.0924346 + 0.284485i −0.986577 0.163299i \(-0.947786\pi\)
0.894142 + 0.447784i \(0.147786\pi\)
\(570\) −26.2048 19.0389i −1.09760 0.797451i
\(571\) −32.4839 −1.35941 −0.679705 0.733486i \(-0.737892\pi\)
−0.679705 + 0.733486i \(0.737892\pi\)
\(572\) 0 0
\(573\) 20.7831 0.868226
\(574\) 1.04509 + 0.759300i 0.0436211 + 0.0316926i
\(575\) 0.366066 1.12664i 0.0152660 0.0469839i
\(576\) 4.18232 + 12.8719i 0.174263 + 0.536328i
\(577\) −28.1391 + 20.4443i −1.17145 + 0.851107i −0.991182 0.132511i \(-0.957696\pi\)
−0.180266 + 0.983618i \(0.557696\pi\)
\(578\) −14.7341 + 10.7049i −0.612856 + 0.445266i
\(579\) −0.994632 3.06116i −0.0413355 0.127218i
\(580\) 0.00926598 0.0285178i 0.000384749 0.00118414i
\(581\) 3.54004 + 2.57199i 0.146866 + 0.106704i
\(582\) −7.35135 −0.304723
\(583\) 0 0
\(584\) 17.0708 0.706395
\(585\) 11.5686 + 8.40509i 0.478303 + 0.347508i
\(586\) 10.4649 32.2076i 0.432301 1.33049i
\(587\) −4.47300 13.7665i −0.184621 0.568204i 0.815321 0.579009i \(-0.196560\pi\)
−0.999942 + 0.0108054i \(0.996560\pi\)
\(588\) −0.0244409 + 0.0177573i −0.00100792 + 0.000732300i
\(589\) 6.13814 4.45962i 0.252918 0.183755i
\(590\) 6.12580 + 18.8533i 0.252195 + 0.776177i
\(591\) −9.38829 + 28.8942i −0.386183 + 1.18855i
\(592\) 6.73106 + 4.89040i 0.276645 + 0.200994i
\(593\) 15.0291 0.617169 0.308585 0.951197i \(-0.400145\pi\)
0.308585 + 0.951197i \(0.400145\pi\)
\(594\) 0 0
\(595\) 10.0181 0.410701
\(596\) 0.0363138 + 0.0263835i 0.00148747 + 0.00108071i
\(597\) 2.86614 8.82108i 0.117303 0.361023i
\(598\) −1.45645 4.48248i −0.0595586 0.183302i
\(599\) −1.42424 + 1.03477i −0.0581927 + 0.0422795i −0.616501 0.787354i \(-0.711451\pi\)
0.558309 + 0.829633i \(0.311451\pi\)
\(600\) 8.17659 5.94064i 0.333808 0.242526i
\(601\) −7.24227 22.2894i −0.295418 0.909204i −0.983081 0.183173i \(-0.941363\pi\)
0.687662 0.726031i \(-0.258637\pi\)
\(602\) 3.49426 10.7542i 0.142415 0.438310i
\(603\) 21.0250 + 15.2756i 0.856206 + 0.622070i
\(604\) 0.310948 0.0126523
\(605\) 0 0
\(606\) 36.2679 1.47328
\(607\) −20.4508 14.8583i −0.830070 0.603081i 0.0895088 0.995986i \(-0.471470\pi\)
−0.919579 + 0.392905i \(0.871470\pi\)
\(608\) 0.141609 0.435828i 0.00574301 0.0176752i
\(609\) 0.783824 + 2.41236i 0.0317622 + 0.0977539i
\(610\) 13.1046 9.52102i 0.530588 0.385495i
\(611\) −22.4664 + 16.3228i −0.908895 + 0.660351i
\(612\) −0.0396623 0.122068i −0.00160325 0.00493431i
\(613\) −0.358751 + 1.10412i −0.0144898 + 0.0445951i −0.958040 0.286635i \(-0.907463\pi\)
0.943550 + 0.331230i \(0.107463\pi\)
\(614\) −6.22846 4.52524i −0.251360 0.182624i
\(615\) 3.63174 0.146446
\(616\) 0 0
\(617\) 12.9711 0.522197 0.261098 0.965312i \(-0.415915\pi\)
0.261098 + 0.965312i \(0.415915\pi\)
\(618\) 0.977515 + 0.710206i 0.0393214 + 0.0285687i
\(619\) 14.1505 43.5507i 0.568756 1.75045i −0.0877618 0.996141i \(-0.527971\pi\)
0.656518 0.754310i \(-0.272029\pi\)
\(620\) −0.0103360 0.0318108i −0.000415102 0.00127755i
\(621\) 1.66239 1.20780i 0.0667095 0.0484673i
\(622\) −15.8345 + 11.5044i −0.634906 + 0.461286i
\(623\) −4.74147 14.5927i −0.189963 0.584646i
\(624\) 12.3393 37.9763i 0.493966 1.52027i
\(625\) 11.3752 + 8.26455i 0.455007 + 0.330582i
\(626\) 38.6824 1.54606
\(627\) 0 0
\(628\) −0.185097 −0.00738615
\(629\) −9.27026 6.73524i −0.369629 0.268551i
\(630\) 1.34005 4.12425i 0.0533889 0.164314i
\(631\) −3.90000 12.0030i −0.155257 0.477831i 0.842930 0.538023i \(-0.180829\pi\)
−0.998187 + 0.0601922i \(0.980829\pi\)
\(632\) 35.9142 26.0932i 1.42859 1.03793i
\(633\) 2.54703 1.85053i 0.101236 0.0735519i
\(634\) 3.40800 + 10.4887i 0.135349 + 0.416561i
\(635\) 2.84825 8.76602i 0.113029 0.347869i
\(636\) −0.247951 0.180147i −0.00983189 0.00714329i
\(637\) 4.64706 0.184123
\(638\) 0 0
\(639\) 23.3582 0.924038
\(640\) 16.5849 + 12.0497i 0.655577 + 0.476305i
\(641\) 8.63910 26.5884i 0.341224 1.05018i −0.622350 0.782739i \(-0.713822\pi\)
0.963574 0.267441i \(-0.0861780\pi\)
\(642\) −3.08014 9.47970i −0.121564 0.374134i
\(643\) 40.2066 29.2118i 1.58559 1.15200i 0.675684 0.737191i \(-0.263848\pi\)
0.909908 0.414809i \(-0.136152\pi\)
\(644\) 0.00813063 0.00590725i 0.000320392 0.000232778i
\(645\) −9.82370 30.2342i −0.386808 1.19047i
\(646\) 13.8196 42.5324i 0.543726 1.67342i
\(647\) 8.90460 + 6.46957i 0.350076 + 0.254345i 0.748901 0.662682i \(-0.230582\pi\)
−0.398825 + 0.917027i \(0.630582\pi\)
\(648\) 31.8377 1.25070
\(649\) 0 0
\(650\) −10.7797 −0.422816
\(651\) 2.28904 + 1.66309i 0.0897146 + 0.0651815i
\(652\) −0.0591984 + 0.182194i −0.00231839 + 0.00713526i
\(653\) 8.94184 + 27.5202i 0.349921 + 1.07695i 0.958896 + 0.283757i \(0.0915811\pi\)
−0.608975 + 0.793190i \(0.708419\pi\)
\(654\) 7.02066 5.10081i 0.274529 0.199457i
\(655\) 0.266771 0.193820i 0.0104236 0.00757318i
\(656\) −1.12507 3.46261i −0.0439266 0.135192i
\(657\) −3.12289 + 9.61126i −0.121835 + 0.374971i
\(658\) 6.81318 + 4.95006i 0.265605 + 0.192974i
\(659\) −10.8405 −0.422288 −0.211144 0.977455i \(-0.567719\pi\)
−0.211144 + 0.977455i \(0.567719\pi\)
\(660\) 0 0
\(661\) 20.3444 0.791305 0.395652 0.918400i \(-0.370519\pi\)
0.395652 + 0.918400i \(0.370519\pi\)
\(662\) 32.0901 + 23.3148i 1.24722 + 0.906155i
\(663\) −16.9941 + 52.3024i −0.659995 + 2.03126i
\(664\) −3.83776 11.8114i −0.148934 0.458372i
\(665\) −8.59515 + 6.24474i −0.333306 + 0.242161i
\(666\) −4.01279 + 2.91546i −0.155493 + 0.112972i
\(667\) −0.260751 0.802510i −0.0100963 0.0310733i
\(668\) 0.0401691 0.123628i 0.00155419 0.00478331i
\(669\) −8.49977 6.17545i −0.328620 0.238757i
\(670\) 39.9197 1.54223
\(671\) 0 0
\(672\) 0.170894 0.00659237
\(673\) −9.77196 7.09974i −0.376681 0.273675i 0.383295 0.923626i \(-0.374789\pi\)
−0.759976 + 0.649951i \(0.774789\pi\)
\(674\) 10.8780 33.4791i 0.419006 1.28957i
\(675\) −1.45229 4.46969i −0.0558987 0.172039i
\(676\) 0.0971038 0.0705500i 0.00373476 0.00271346i
\(677\) 2.74766 1.99629i 0.105601 0.0767238i −0.533731 0.845654i \(-0.679211\pi\)
0.639333 + 0.768930i \(0.279211\pi\)
\(678\) −13.7028 42.1728i −0.526252 1.61964i
\(679\) −0.745114 + 2.29323i −0.0285949 + 0.0880059i
\(680\) −23.0031 16.7128i −0.882130 0.640905i
\(681\) 0.859173 0.0329236
\(682\) 0 0
\(683\) −4.75643 −0.182000 −0.0909999 0.995851i \(-0.529006\pi\)
−0.0909999 + 0.995851i \(0.529006\pi\)
\(684\) 0.110120 + 0.0800067i 0.00421053 + 0.00305913i
\(685\) −4.71077 + 14.4983i −0.179989 + 0.553950i
\(686\) −0.435488 1.34029i −0.0166270 0.0511726i
\(687\) 3.83232 2.78434i 0.146212 0.106229i
\(688\) −25.7830 + 18.7324i −0.982966 + 0.714167i
\(689\) 14.5683 + 44.8367i 0.555009 + 1.70814i
\(690\) −1.24174 + 3.82168i −0.0472721 + 0.145489i
\(691\) −5.36692 3.89930i −0.204167 0.148336i 0.481003 0.876719i \(-0.340272\pi\)
−0.685171 + 0.728382i \(0.740272\pi\)
\(692\) 0.146707 0.00557695
\(693\) 0 0
\(694\) −29.1003 −1.10463
\(695\) 10.3139 + 7.49346i 0.391227 + 0.284243i
\(696\) 2.22466 6.84680i 0.0843256 0.259527i
\(697\) 1.54949 + 4.76883i 0.0586910 + 0.180632i
\(698\) −6.83755 + 4.96777i −0.258805 + 0.188033i
\(699\) 2.20554 1.60242i 0.0834212 0.0606090i
\(700\) −0.00710304 0.0218609i −0.000268470 0.000826265i
\(701\) −0.936330 + 2.88173i −0.0353647 + 0.108841i −0.967181 0.254090i \(-0.918224\pi\)
0.931816 + 0.362931i \(0.118224\pi\)
\(702\) −15.1274 10.9907i −0.570947 0.414817i
\(703\) 12.1519 0.458319
\(704\) 0 0
\(705\) 23.6762 0.891697
\(706\) −27.4065 19.9120i −1.03146 0.749396i
\(707\) 3.67603 11.3136i 0.138251 0.425493i
\(708\) −0.0717048 0.220685i −0.00269483 0.00829383i
\(709\) 11.0488 8.02741i 0.414946 0.301476i −0.360655 0.932699i \(-0.617447\pi\)
0.775601 + 0.631223i \(0.217447\pi\)
\(710\) 29.0272 21.0895i 1.08937 0.791475i
\(711\) 8.12103 + 24.9939i 0.304562 + 0.937346i
\(712\) −13.4573 + 41.4173i −0.504334 + 1.55218i
\(713\) −0.761485 0.553251i −0.0285178 0.0207194i
\(714\) 16.6775 0.624140
\(715\) 0 0
\(716\) 0.116231 0.00434376
\(717\) 19.5353 + 14.1932i 0.729558 + 0.530055i
\(718\) 4.76864 14.6764i 0.177964 0.547717i
\(719\) −0.587222 1.80728i −0.0218997 0.0674003i 0.939509 0.342523i \(-0.111281\pi\)
−0.961409 + 0.275123i \(0.911281\pi\)
\(720\) −9.88778 + 7.18390i −0.368496 + 0.267728i
\(721\) 0.320625 0.232947i 0.0119407 0.00867541i
\(722\) 6.38148 + 19.6402i 0.237494 + 0.730932i
\(723\) −14.3627 + 44.2039i −0.534155 + 1.64396i
\(724\) −0.167237 0.121505i −0.00621531 0.00451569i
\(725\) −1.92992 −0.0716754
\(726\) 0 0
\(727\) −13.8211 −0.512595 −0.256298 0.966598i \(-0.582503\pi\)
−0.256298 + 0.966598i \(0.582503\pi\)
\(728\) −10.6704 7.75250i −0.395472 0.287327i
\(729\) −0.0980447 + 0.301750i −0.00363128 + 0.0111759i
\(730\) 4.79694 + 14.7635i 0.177543 + 0.546420i
\(731\) 35.5092 25.7990i 1.31336 0.954210i
\(732\) −0.153394 + 0.111447i −0.00566960 + 0.00411921i
\(733\) −14.9485 46.0068i −0.552136 1.69930i −0.703391 0.710804i \(-0.748331\pi\)
0.151255 0.988495i \(-0.451669\pi\)
\(734\) 4.62390 14.2309i 0.170671 0.525273i
\(735\) −3.20531 2.32880i −0.118230 0.0858990i
\(736\) −0.0568504 −0.00209553
\(737\) 0 0
\(738\) 2.17050 0.0798973
\(739\) 18.7757 + 13.6414i 0.690677 + 0.501806i 0.876883 0.480705i \(-0.159619\pi\)
−0.186206 + 0.982511i \(0.559619\pi\)
\(740\) 0.0165546 0.0509497i 0.000608558 0.00187295i
\(741\) −18.0223 55.4668i −0.662064 2.03762i
\(742\) 11.5665 8.40352i 0.424618 0.308503i
\(743\) −36.2691 + 26.3511i −1.33059 + 0.966727i −0.330851 + 0.943683i \(0.607336\pi\)
−0.999734 + 0.0230437i \(0.992664\pi\)
\(744\) −2.48155 7.63744i −0.0909782 0.280002i
\(745\) −1.81907 + 5.59854i −0.0666457 + 0.205114i
\(746\) 41.7325 + 30.3205i 1.52794 + 1.11011i
\(747\) 7.35218 0.269002
\(748\) 0 0
\(749\) −3.26935 −0.119460
\(750\) 30.0211 + 21.8116i 1.09621 + 0.796446i
\(751\) −12.7271 + 39.1698i −0.464417 + 1.42933i 0.395298 + 0.918553i \(0.370641\pi\)
−0.859715 + 0.510775i \(0.829359\pi\)
\(752\) −7.33460 22.5736i −0.267465 0.823174i
\(753\) −0.741775 + 0.538931i −0.0270318 + 0.0196397i
\(754\) −6.21201 + 4.51329i −0.226228 + 0.164364i
\(755\) 12.6016 + 38.7836i 0.458618 + 1.41148i
\(756\) 0.0123209 0.0379199i 0.000448108 0.00137913i
\(757\) 17.7084 + 12.8659i 0.643623 + 0.467619i 0.861093 0.508448i \(-0.169781\pi\)
−0.217470 + 0.976067i \(0.569781\pi\)
\(758\) −17.8382 −0.647912
\(759\) 0 0
\(760\) 30.1537 1.09379
\(761\) −28.8943 20.9930i −1.04742 0.760994i −0.0756987 0.997131i \(-0.524119\pi\)
−0.971720 + 0.236137i \(0.924119\pi\)
\(762\) 4.74160 14.5931i 0.171770 0.528654i
\(763\) −0.879581 2.70707i −0.0318430 0.0980026i
\(764\) −0.108533 + 0.0788536i −0.00392657 + 0.00285282i
\(765\) 13.6178 9.89392i 0.492353 0.357716i
\(766\) −6.73607 20.7315i −0.243384 0.749060i
\(767\) −11.0298 + 33.9462i −0.398263 + 1.22573i
\(768\) −0.586552 0.426155i −0.0211654 0.0153775i
\(769\) −5.30246 −0.191212 −0.0956058 0.995419i \(-0.530479\pi\)
−0.0956058 + 0.995419i \(0.530479\pi\)
\(770\) 0 0
\(771\) −37.7295 −1.35880
\(772\) 0.0168086 + 0.0122121i 0.000604953 + 0.000439524i
\(773\) −15.4172 + 47.4494i −0.554519 + 1.70663i 0.142690 + 0.989767i \(0.454425\pi\)
−0.697209 + 0.716868i \(0.745575\pi\)
\(774\) −5.87112 18.0695i −0.211033 0.649493i
\(775\) −1.74163 + 1.26537i −0.0625613 + 0.0454535i
\(776\) 5.53660 4.02258i 0.198752 0.144402i
\(777\) 1.40038 + 4.30992i 0.0502383 + 0.154618i
\(778\) −5.53633 + 17.0391i −0.198487 + 0.610881i
\(779\) −4.30205 3.12562i −0.154137 0.111987i
\(780\) −0.257109 −0.00920597
\(781\) 0 0
\(782\) −5.54803 −0.198397
\(783\) −2.70830 1.96769i −0.0967866 0.0703196i
\(784\) −1.22738 + 3.77748i −0.0438349 + 0.134910i
\(785\) −7.50127 23.0865i −0.267732 0.823994i
\(786\) 0.444104 0.322660i 0.0158407 0.0115089i
\(787\) 29.0089 21.0762i 1.03406 0.751285i 0.0649388 0.997889i \(-0.479315\pi\)
0.969116 + 0.246604i \(0.0793148\pi\)
\(788\) −0.0606010 0.186511i −0.00215882 0.00664416i
\(789\) 1.01294 3.11750i 0.0360615 0.110986i
\(790\) 32.6583 + 23.7277i 1.16193 + 0.844193i
\(791\) −14.5445 −0.517144
\(792\) 0 0
\(793\) 29.1655 1.03570
\(794\) 21.6137 + 15.7033i 0.767043 + 0.557289i
\(795\) 12.4207 38.2268i 0.440515 1.35577i
\(796\) 0.0185008 + 0.0569396i 0.000655744 + 0.00201817i
\(797\) −11.9259 + 8.66470i −0.422438 + 0.306919i −0.778618 0.627498i \(-0.784079\pi\)
0.356180 + 0.934417i \(0.384079\pi\)
\(798\) −14.3087 + 10.3959i −0.506523 + 0.368010i
\(799\) 10.1015 + 31.0892i 0.357365 + 1.09986i
\(800\) −0.0401801 + 0.123662i −0.00142058 + 0.00437210i
\(801\) −20.8571 15.1536i −0.736949 0.535425i
\(802\) −12.2354 −0.432046
\(803\) 0 0
\(804\) −0.467275 −0.0164795
\(805\) 1.06630 + 0.774711i 0.0375821 + 0.0273050i
\(806\) −2.64677 + 8.14593i −0.0932286 + 0.286928i
\(807\) 1.35779 + 4.17883i 0.0477963 + 0.147102i
\(808\) −27.3149 + 19.8454i −0.960934 + 0.698159i
\(809\) −21.8239 + 15.8560i −0.767288 + 0.557467i −0.901137 0.433534i \(-0.857266\pi\)
0.133849 + 0.991002i \(0.457266\pi\)
\(810\) 8.94649 + 27.5345i 0.314348 + 0.967463i
\(811\) −0.452523 + 1.39272i −0.0158902 + 0.0489051i −0.958687 0.284462i \(-0.908185\pi\)
0.942797 + 0.333367i \(0.108185\pi\)
\(812\) −0.0132461 0.00962382i −0.000464846 0.000337730i
\(813\) 16.4513 0.576972
\(814\) 0 0
\(815\) −25.1236 −0.880041
\(816\) −38.0269 27.6281i −1.33121 0.967178i
\(817\) −14.3839 + 44.2692i −0.503230 + 1.54878i
\(818\) −2.48840 7.65852i −0.0870050 0.267774i
\(819\) 6.31686 4.58947i 0.220729 0.160369i
\(820\) −0.0189655 + 0.0137793i −0.000662305 + 0.000481193i
\(821\) −9.46478 29.1296i −0.330323 1.01663i −0.968980 0.247139i \(-0.920510\pi\)
0.638657 0.769492i \(-0.279490\pi\)
\(822\) −7.84221 + 24.1358i −0.273529 + 0.841834i
\(823\) 19.8483 + 14.4206i 0.691867 + 0.502671i 0.877273 0.479991i \(-0.159360\pi\)
−0.185406 + 0.982662i \(0.559360\pi\)
\(824\) −1.12482 −0.0391851
\(825\) 0 0
\(826\) 10.8243 0.376626
\(827\) −5.31270 3.85990i −0.184741 0.134222i 0.491571 0.870837i \(-0.336423\pi\)
−0.676312 + 0.736615i \(0.736423\pi\)
\(828\) 0.00521813 0.0160597i 0.000181342 0.000558115i
\(829\) −6.13221 18.8730i −0.212980 0.655486i −0.999291 0.0376547i \(-0.988011\pi\)
0.786310 0.617832i \(-0.211989\pi\)
\(830\) 9.13654 6.63808i 0.317134 0.230411i
\(831\) −25.2500 + 18.3452i −0.875912 + 0.636387i
\(832\) 11.5672 + 35.6003i 0.401022 + 1.23422i
\(833\) 1.69039 5.20248i 0.0585685 0.180255i
\(834\) 17.1699 + 12.4747i 0.594545 + 0.431962i
\(835\) 17.0476 0.589958
\(836\) 0 0
\(837\) −3.73421 −0.129073
\(838\) 31.0009 + 22.5235i 1.07091 + 0.778061i
\(839\) −2.45993 + 7.57090i −0.0849263 + 0.261376i −0.984498 0.175397i \(-0.943879\pi\)
0.899571 + 0.436774i \(0.143879\pi\)
\(840\) 3.47489 + 10.6946i 0.119895 + 0.368999i
\(841\) 22.3493 16.2377i 0.770667 0.559922i
\(842\) 27.3231 19.8514i 0.941616 0.684124i
\(843\) 11.8660 + 36.5199i 0.408687 + 1.25781i
\(844\) −0.00627989 + 0.0193275i −0.000216163 + 0.000665281i
\(845\) 12.7347 + 9.25233i 0.438089 + 0.318290i
\(846\) 14.1500 0.486489
\(847\) 0 0
\(848\) −40.2944 −1.38372
\(849\) 54.4949 + 39.5928i 1.87026 + 1.35882i
\(850\) −3.92118 + 12.0681i −0.134495 + 0.413934i
\(851\) −0.465858 1.43376i −0.0159694 0.0491487i
\(852\) −0.339775 + 0.246861i −0.0116405 + 0.00845731i
\(853\) 27.5658 20.0277i 0.943834 0.685736i −0.00550627 0.999985i \(-0.501753\pi\)
0.949341 + 0.314249i \(0.101753\pi\)
\(854\) −2.73317 8.41185i −0.0935273 0.287847i
\(855\) −5.51625 + 16.9773i −0.188652 + 0.580611i
\(856\) 7.50697 + 5.45413i 0.256583 + 0.186418i
\(857\) −24.8539 −0.848992 −0.424496 0.905430i \(-0.639549\pi\)
−0.424496 + 0.905430i \(0.639549\pi\)
\(858\) 0 0
\(859\) 2.05654 0.0701683 0.0350841 0.999384i \(-0.488830\pi\)
0.0350841 + 0.999384i \(0.488830\pi\)
\(860\) 0.166013 + 0.120616i 0.00566101 + 0.00411296i
\(861\) 0.612797 1.88600i 0.0208841 0.0642746i
\(862\) −7.17386 22.0789i −0.244343 0.752009i
\(863\) 0.209920 0.152516i 0.00714576 0.00519170i −0.584207 0.811605i \(-0.698594\pi\)
0.591352 + 0.806413i \(0.298594\pi\)
\(864\) −0.182468 + 0.132570i −0.00620767 + 0.00451014i
\(865\) 5.94547 + 18.2983i 0.202152 + 0.622160i
\(866\) 8.74936 26.9277i 0.297315 0.915042i
\(867\) 22.6184 + 16.4332i 0.768161 + 0.558102i
\(868\) −0.0182637 −0.000619910
\(869\) 0 0
\(870\) 6.54651 0.221947
\(871\) 58.1499 + 42.2484i 1.97034 + 1.43153i
\(872\) −2.49644 + 7.68326i −0.0845402 + 0.260188i
\(873\) 1.25195 + 3.85312i 0.0423722 + 0.130408i
\(874\) 4.76001 3.45835i 0.161010 0.116980i
\(875\) 9.84690 7.15419i 0.332886 0.241856i
\(876\) −0.0561500 0.172812i −0.00189713 0.00583877i
\(877\) −5.74555 + 17.6830i −0.194013 + 0.597112i 0.805973 + 0.591952i \(0.201642\pi\)
−0.999987 + 0.00515985i \(0.998358\pi\)
\(878\) 30.5190 + 22.1733i 1.02997 + 0.748314i
\(879\) −51.9867 −1.75347
\(880\) 0 0
\(881\) 6.45292 0.217404 0.108702 0.994074i \(-0.465330\pi\)
0.108702 + 0.994074i \(0.465330\pi\)
\(882\) −1.91565 1.39180i −0.0645034 0.0468645i
\(883\) −0.0860573 + 0.264857i −0.00289606 + 0.00891316i −0.952494 0.304557i \(-0.901492\pi\)
0.949598 + 0.313470i \(0.101492\pi\)
\(884\) −0.109696 0.337609i −0.00368947 0.0113550i
\(885\) 24.6194 17.8870i 0.827572 0.601266i
\(886\) −29.8887 + 21.7154i −1.00413 + 0.729543i
\(887\) −9.44262 29.0614i −0.317052 0.975787i −0.974901 0.222637i \(-0.928534\pi\)
0.657849 0.753150i \(-0.271466\pi\)
\(888\) 3.97457 12.2325i 0.133378 0.410495i
\(889\) −4.07168 2.95825i −0.136560 0.0992165i
\(890\) −39.6008 −1.32742
\(891\) 0 0
\(892\) 0.0678176 0.00227070
\(893\) −28.0461 20.3767i −0.938527 0.681879i
\(894\) −3.02829 + 9.32011i −0.101281 + 0.311711i
\(895\) 4.71041 + 14.4971i 0.157452 + 0.484586i
\(896\) 9.05595 6.57953i 0.302538 0.219807i
\(897\) −5.85342 + 4.25276i −0.195440 + 0.141995i
\(898\) 4.24487 + 13.0644i 0.141653 + 0.435964i
\(899\) −0.473858 + 1.45839i −0.0158041 + 0.0486399i
\(900\) −0.0312453 0.0227011i −0.00104151 0.000756702i
\(901\) 55.4949 1.84880
\(902\) 0 0
\(903\) −17.3585 −0.577655
\(904\) 33.3966 + 24.2641i 1.11076 + 0.807011i
\(905\) 8.37743 25.7831i 0.278475 0.857059i
\(906\) 20.9783 + 64.5646i 0.696958 + 2.14502i
\(907\) −25.8357 + 18.7707i −0.857860 + 0.623272i −0.927302 0.374314i \(-0.877878\pi\)
0.0694417 + 0.997586i \(0.477878\pi\)
\(908\) −0.00448674 + 0.00325981i −0.000148898 + 0.000108181i
\(909\) −6.17653 19.0094i −0.204862 0.630502i
\(910\) 3.70624 11.4066i 0.122861 0.378126i
\(911\) −2.26559 1.64605i −0.0750623 0.0545360i 0.549621 0.835414i \(-0.314772\pi\)
−0.624684 + 0.780878i \(0.714772\pi\)
\(912\) 49.8477 1.65062
\(913\) 0 0
\(914\) −16.7496 −0.554027
\(915\) −20.1170 14.6158i −0.665046 0.483184i
\(916\) −0.00944886 + 0.0290806i −0.000312199 + 0.000960850i
\(917\) −0.0556394 0.171241i −0.00183738 0.00565486i
\(918\) −17.8070 + 12.9375i −0.587718 + 0.427002i
\(919\) −12.8099 + 9.30691i −0.422559 + 0.307007i −0.778666 0.627438i \(-0.784104\pi\)
0.356108 + 0.934445i \(0.384104\pi\)
\(920\) −1.15598 3.55773i −0.0381114 0.117295i
\(921\) −3.65212 + 11.2401i −0.120341 + 0.370373i
\(922\) 10.4291 + 7.57719i 0.343464 + 0.249541i
\(923\) 64.6030 2.12643
\(924\) 0 0
\(925\) −3.44799 −0.113369
\(926\) −44.3897 32.2510i −1.45874 1.05983i
\(927\) 0.205772 0.633302i 0.00675845 0.0208004i
\(928\) 0.0286206 + 0.0880851i 0.000939517 + 0.00289153i
\(929\) 22.2345 16.1543i 0.729490 0.530006i −0.159912 0.987131i \(-0.551121\pi\)
0.889402 + 0.457126i \(0.151121\pi\)
\(930\) 5.90782 4.29228i 0.193725 0.140749i
\(931\) 1.79266 + 5.51725i 0.0587521 + 0.180820i
\(932\) −0.00543791 + 0.0167362i −0.000178125 + 0.000548212i
\(933\) 24.3077 + 17.6606i 0.795799 + 0.578182i
\(934\) −29.2894 −0.958379
\(935\) 0 0
\(936\) −22.1610 −0.724354
\(937\) −9.95789 7.23483i −0.325310 0.236352i 0.413128 0.910673i \(-0.364436\pi\)
−0.738438 + 0.674321i \(0.764436\pi\)
\(938\) 6.73581 20.7307i 0.219932 0.676881i
\(939\) −18.3500 56.4754i −0.598828 1.84300i
\(940\) −0.123641 + 0.0898304i −0.00403272 + 0.00292994i
\(941\) 1.18128 0.858248i 0.0385085 0.0279781i −0.568365 0.822777i \(-0.692424\pi\)
0.606873 + 0.794799i \(0.292424\pi\)
\(942\) −12.4877 38.4331i −0.406870 1.25222i
\(943\) −0.203857 + 0.627406i −0.00663848 + 0.0204311i
\(944\) −24.6808 17.9317i −0.803293 0.583627i
\(945\) 5.22896 0.170098
\(946\) 0 0
\(947\) 11.0714 0.359771 0.179885 0.983688i \(-0.442427\pi\)
0.179885 + 0.983688i \(0.442427\pi\)
\(948\) −0.382278 0.277741i −0.0124158 0.00902062i
\(949\) −8.63712 + 26.5823i −0.280373 + 0.862898i
\(950\) −4.15842 12.7983i −0.134917 0.415231i
\(951\) 13.6966 9.95119i 0.444144 0.322690i
\(952\) −12.5605 + 9.12574i −0.407088 + 0.295767i
\(953\) 4.58067 + 14.0979i 0.148383 + 0.456675i 0.997430 0.0716413i \(-0.0228237\pi\)
−0.849048 + 0.528316i \(0.822824\pi\)
\(954\) 7.42319 22.8462i 0.240335 0.739674i
\(955\) −14.2336 10.3413i −0.460588 0.334637i
\(956\) −0.155867 −0.00504110
\(957\) 0 0
\(958\) 34.5782 1.11717
\(959\) 6.73422 + 4.89270i 0.217459 + 0.157993i
\(960\) 9.86200 30.3521i 0.318295 0.979610i
\(961\) −9.05095 27.8560i −0.291966 0.898579i
\(962\) −11.0984 + 8.06343i −0.357826 + 0.259976i
\(963\) −4.44411 + 3.22884i −0.143210 + 0.104048i
\(964\) −0.0927105 0.285334i −0.00298601 0.00918998i
\(965\) −0.841995 + 2.59139i −0.0271048 + 0.0834199i
\(966\) 1.77511 + 1.28969i 0.0571132 + 0.0414952i
\(967\) −16.5193 −0.531224 −0.265612 0.964080i \(-0.585574\pi\)
−0.265612 + 0.964080i \(0.585574\pi\)
\(968\) 0 0
\(969\) −68.6520 −2.20542
\(970\) 5.03468 + 3.65791i 0.161654 + 0.117448i
\(971\) 12.6077 38.8025i 0.404600 1.24523i −0.516629 0.856209i \(-0.672813\pi\)
0.921229 0.389021i \(-0.127187\pi\)
\(972\) −0.0677593 0.208542i −0.00217338 0.00668897i
\(973\) 5.63172 4.09169i 0.180545 0.131173i
\(974\) 14.1048 10.2477i 0.451947 0.328359i
\(975\) 5.11363 + 15.7381i 0.163767 + 0.504024i
\(976\) −7.70317 + 23.7079i −0.246573 + 0.758872i
\(977\) −39.7345 28.8688i −1.27122 0.923594i −0.271967 0.962306i \(-0.587674\pi\)
−0.999250 + 0.0387127i \(0.987674\pi\)
\(978\) −41.8243 −1.33739
\(979\) 0 0
\(980\) 0.0255744 0.000816945
\(981\) −3.86916 2.81111i −0.123533 0.0897519i
\(982\) −7.19647 + 22.1484i −0.229648 + 0.706785i
\(983\) 0.342017 + 1.05262i 0.0109086 + 0.0335733i 0.956363 0.292182i \(-0.0943814\pi\)
−0.945454 + 0.325756i \(0.894381\pi\)
\(984\) −4.55342 + 3.30825i −0.145158 + 0.105463i
\(985\) 20.8070 15.1172i 0.662965 0.481672i
\(986\) 2.79308 + 8.59622i 0.0889498 + 0.273759i
\(987\) 3.99497 12.2953i 0.127161 0.391363i
\(988\) 0.304563 + 0.221278i 0.00968945 + 0.00703980i
\(989\) 5.77458 0.183621
\(990\) 0 0
\(991\) 41.7851 1.32735 0.663674 0.748022i \(-0.268996\pi\)
0.663674 + 0.748022i \(0.268996\pi\)
\(992\) 0.0835821 + 0.0607260i 0.00265374 + 0.00192805i
\(993\) 18.8163 57.9107i 0.597118 1.83774i
\(994\) −6.05411 18.6326i −0.192025 0.590991i
\(995\) −6.35214 + 4.61510i −0.201376 + 0.146308i
\(996\) −0.106947 + 0.0777013i −0.00338873 + 0.00246206i
\(997\) −13.6568 42.0314i −0.432517 1.33115i −0.895610 0.444840i \(-0.853261\pi\)
0.463094 0.886309i \(-0.346739\pi\)
\(998\) −5.98401 + 18.4169i −0.189421 + 0.582977i
\(999\) −4.83863 3.51547i −0.153088 0.111225i
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.v.323.2 16
11.2 odd 10 77.2.f.b.71.2 yes 16
11.3 even 5 inner 847.2.f.v.729.2 16
11.4 even 5 847.2.f.x.372.3 16
11.5 even 5 847.2.a.o.1.6 8
11.6 odd 10 847.2.a.p.1.3 8
11.7 odd 10 77.2.f.b.64.2 16
11.8 odd 10 847.2.f.w.729.3 16
11.9 even 5 847.2.f.x.148.3 16
11.10 odd 2 847.2.f.w.323.3 16
33.2 even 10 693.2.m.i.379.3 16
33.5 odd 10 7623.2.a.cw.1.3 8
33.17 even 10 7623.2.a.ct.1.6 8
33.29 even 10 693.2.m.i.64.3 16
77.2 odd 30 539.2.q.g.214.2 32
77.6 even 10 5929.2.a.bt.1.3 8
77.13 even 10 539.2.f.e.148.2 16
77.18 odd 30 539.2.q.g.471.2 32
77.24 even 30 539.2.q.f.324.3 32
77.27 odd 10 5929.2.a.bs.1.6 8
77.40 even 30 539.2.q.f.361.3 32
77.46 odd 30 539.2.q.g.324.3 32
77.51 odd 30 539.2.q.g.361.3 32
77.62 even 10 539.2.f.e.295.2 16
77.68 even 30 539.2.q.f.214.2 32
77.73 even 30 539.2.q.f.471.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.2 16 11.7 odd 10
77.2.f.b.71.2 yes 16 11.2 odd 10
539.2.f.e.148.2 16 77.13 even 10
539.2.f.e.295.2 16 77.62 even 10
539.2.q.f.214.2 32 77.68 even 30
539.2.q.f.324.3 32 77.24 even 30
539.2.q.f.361.3 32 77.40 even 30
539.2.q.f.471.2 32 77.73 even 30
539.2.q.g.214.2 32 77.2 odd 30
539.2.q.g.324.3 32 77.46 odd 30
539.2.q.g.361.3 32 77.51 odd 30
539.2.q.g.471.2 32 77.18 odd 30
693.2.m.i.64.3 16 33.29 even 10
693.2.m.i.379.3 16 33.2 even 10
847.2.a.o.1.6 8 11.5 even 5
847.2.a.p.1.3 8 11.6 odd 10
847.2.f.v.323.2 16 1.1 even 1 trivial
847.2.f.v.729.2 16 11.3 even 5 inner
847.2.f.w.323.3 16 11.10 odd 2
847.2.f.w.729.3 16 11.8 odd 10
847.2.f.x.148.3 16 11.9 even 5
847.2.f.x.372.3 16 11.4 even 5
5929.2.a.bs.1.6 8 77.27 odd 10
5929.2.a.bt.1.3 8 77.6 even 10
7623.2.a.ct.1.6 8 33.17 even 10
7623.2.a.cw.1.3 8 33.5 odd 10