Properties

Label 819.2.ew.a.176.14
Level $819$
Weight $2$
Character 819.176
Analytic conductor $6.540$
Analytic rank $0$
Dimension $336$
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] = [819,2,Mod(176,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.176");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.ew (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(84\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 176.14
Character \(\chi\) \(=\) 819.176
Dual form 819.2.ew.a.470.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.45048 + 1.45048i) q^{2} +(-0.883457 + 1.48980i) q^{3} -2.20781i q^{4} +(0.260529 + 0.972306i) q^{5} +(-0.879492 - 3.44237i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.301429 + 0.301429i) q^{8} +(-1.43901 - 2.63235i) q^{9} +O(q^{10})\) \(q+(-1.45048 + 1.45048i) q^{2} +(-0.883457 + 1.48980i) q^{3} -2.20781i q^{4} +(0.260529 + 0.972306i) q^{5} +(-0.879492 - 3.44237i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.301429 + 0.301429i) q^{8} +(-1.43901 - 2.63235i) q^{9} +(-1.78821 - 1.03242i) q^{10} +(-1.42941 - 1.42941i) q^{11} +(3.28920 + 1.95051i) q^{12} +(3.42411 + 1.12937i) q^{13} +(1.77647 + 1.02565i) q^{14} +(-1.67871 - 0.470855i) q^{15} +3.54119 q^{16} +(-3.04373 - 5.27189i) q^{17} +(5.90544 + 1.73092i) q^{18} +(-0.568478 + 2.12159i) q^{19} +(2.14667 - 0.575199i) q^{20} +(1.66769 + 0.467765i) q^{21} +4.14669 q^{22} +(0.726528 + 1.25838i) q^{23} +(-0.715369 + 0.182770i) q^{24} +(3.45262 - 1.99337i) q^{25} +(-6.60476 + 3.32848i) q^{26} +(5.19297 + 0.181731i) q^{27} +(-2.13258 + 0.571424i) q^{28} -0.669681i q^{29} +(3.11791 - 1.75197i) q^{30} +(7.78343 - 2.08556i) q^{31} +(-5.73930 + 5.73930i) q^{32} +(3.39237 - 0.866716i) q^{33} +(12.0617 + 3.23192i) q^{34} +(0.871746 - 0.503303i) q^{35} +(-5.81173 + 3.17706i) q^{36} +(-1.67263 - 6.24232i) q^{37} +(-2.25276 - 3.90190i) q^{38} +(-4.70759 + 4.10348i) q^{39} +(-0.214551 + 0.371613i) q^{40} +(7.98626 + 2.13991i) q^{41} +(-3.09745 + 1.74048i) q^{42} +(-3.20979 - 1.85317i) q^{43} +(-3.15588 + 3.15588i) q^{44} +(2.18455 - 2.08496i) q^{45} +(-2.87909 - 0.771449i) q^{46} +(-0.873330 + 3.25931i) q^{47} +(-3.12849 + 5.27566i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-2.11662 + 7.89933i) q^{50} +(10.5431 + 0.122942i) q^{51} +(2.49344 - 7.55979i) q^{52} -2.67409i q^{53} +(-7.79593 + 7.26873i) q^{54} +(1.01743 - 1.76223i) q^{55} +(0.213143 - 0.369174i) q^{56} +(-2.65852 - 2.72125i) q^{57} +(0.971363 + 0.971363i) q^{58} +(-5.30924 - 5.30924i) q^{59} +(-1.03956 + 3.70627i) q^{60} +(4.43396 - 7.67984i) q^{61} +(-8.26466 + 14.3148i) q^{62} +(-2.17021 + 2.07128i) q^{63} -9.56716i q^{64} +(-0.206018 + 3.62352i) q^{65} +(-3.66342 + 6.17774i) q^{66} +(-1.64704 + 6.14685i) q^{67} +(-11.6394 + 6.71999i) q^{68} +(-2.51660 - 0.0293459i) q^{69} +(-0.534421 + 1.99449i) q^{70} +(9.37428 + 2.51183i) q^{71} +(0.359707 - 1.22723i) q^{72} +(-11.1112 + 11.1112i) q^{73} +(11.4805 + 6.62828i) q^{74} +(-0.0805163 + 6.90478i) q^{75} +(4.68407 + 1.25509i) q^{76} +(-1.01075 + 1.75067i) q^{77} +(0.876249 - 12.7803i) q^{78} +(0.958551 + 1.66026i) q^{79} +(0.922581 + 3.44312i) q^{80} +(-4.85851 + 7.57594i) q^{81} +(-14.6879 + 8.48004i) q^{82} +(3.21806 + 0.862278i) q^{83} +(1.03274 - 3.68195i) q^{84} +(4.33292 - 4.33292i) q^{85} +(7.34374 - 1.96775i) q^{86} +(0.997691 + 0.591634i) q^{87} -0.861735i q^{88} +(5.61492 - 1.50451i) q^{89} +(-0.144449 + 6.19285i) q^{90} +(0.204666 - 3.59974i) q^{91} +(2.77828 - 1.60404i) q^{92} +(-3.76925 + 13.4383i) q^{93} +(-3.46083 - 5.99434i) q^{94} -2.21094 q^{95} +(-3.47998 - 13.6208i) q^{96} +(11.5320 - 3.08999i) q^{97} +(0.530914 - 1.98140i) q^{98} +(-1.70578 + 5.81965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q + 24 q^{6} - 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 336 q + 24 q^{6} - 36 q^{8} + 16 q^{15} - 336 q^{16} + 20 q^{18} + 8 q^{21} + 8 q^{24} + 96 q^{26} + 24 q^{27} - 96 q^{30} - 72 q^{32} - 36 q^{33} - 12 q^{36} - 72 q^{38} - 16 q^{39} - 48 q^{41} - 28 q^{45} + 60 q^{47} - 48 q^{48} + 132 q^{50} - 36 q^{52} - 108 q^{54} + 68 q^{57} - 72 q^{58} - 44 q^{60} - 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 72 q^{69} + 48 q^{71} - 104 q^{72} + 12 q^{74} + 104 q^{78} - 12 q^{79} + 96 q^{80} - 68 q^{81} - 120 q^{83} - 12 q^{84} + 36 q^{85} + 48 q^{86} - 24 q^{87} - 60 q^{89} - 72 q^{92} - 172 q^{93} - 48 q^{94} - 152 q^{96} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45048 + 1.45048i −1.02565 + 1.02565i −0.0259854 + 0.999662i \(0.508272\pi\)
−0.999662 + 0.0259854i \(0.991728\pi\)
\(3\) −0.883457 + 1.48980i −0.510064 + 0.860136i
\(4\) 2.20781i 1.10391i
\(5\) 0.260529 + 0.972306i 0.116512 + 0.434829i 0.999396 0.0347633i \(-0.0110677\pi\)
−0.882884 + 0.469592i \(0.844401\pi\)
\(6\) −0.879492 3.44237i −0.359051 1.40534i
\(7\) −0.258819 0.965926i −0.0978244 0.365086i
\(8\) 0.301429 + 0.301429i 0.106571 + 0.106571i
\(9\) −1.43901 2.63235i −0.479669 0.877449i
\(10\) −1.78821 1.03242i −0.565481 0.326481i
\(11\) −1.42941 1.42941i −0.430985 0.430985i 0.457979 0.888963i \(-0.348574\pi\)
−0.888963 + 0.457979i \(0.848574\pi\)
\(12\) 3.28920 + 1.95051i 0.949510 + 0.563063i
\(13\) 3.42411 + 1.12937i 0.949677 + 0.313232i
\(14\) 1.77647 + 1.02565i 0.474783 + 0.274116i
\(15\) −1.67871 0.470855i −0.433440 0.121574i
\(16\) 3.54119 0.885297
\(17\) −3.04373 5.27189i −0.738213 1.27862i −0.953299 0.302027i \(-0.902337\pi\)
0.215086 0.976595i \(-0.430997\pi\)
\(18\) 5.90544 + 1.73092i 1.39193 + 0.407982i
\(19\) −0.568478 + 2.12159i −0.130418 + 0.486726i −0.999975 0.00710689i \(-0.997738\pi\)
0.869557 + 0.493833i \(0.164404\pi\)
\(20\) 2.14667 0.575199i 0.480010 0.128618i
\(21\) 1.66769 + 0.467765i 0.363920 + 0.102075i
\(22\) 4.14669 0.884077
\(23\) 0.726528 + 1.25838i 0.151492 + 0.262391i 0.931776 0.363034i \(-0.118259\pi\)
−0.780284 + 0.625425i \(0.784926\pi\)
\(24\) −0.715369 + 0.182770i −0.146024 + 0.0373077i
\(25\) 3.45262 1.99337i 0.690525 0.398675i
\(26\) −6.60476 + 3.32848i −1.29530 + 0.652768i
\(27\) 5.19297 + 0.181731i 0.999388 + 0.0349742i
\(28\) −2.13258 + 0.571424i −0.403020 + 0.107989i
\(29\) 0.669681i 0.124357i −0.998065 0.0621783i \(-0.980195\pi\)
0.998065 0.0621783i \(-0.0198048\pi\)
\(30\) 3.11791 1.75197i 0.569250 0.319865i
\(31\) 7.78343 2.08556i 1.39794 0.374578i 0.520338 0.853960i \(-0.325806\pi\)
0.877606 + 0.479382i \(0.159139\pi\)
\(32\) −5.73930 + 5.73930i −1.01457 + 1.01457i
\(33\) 3.39237 0.866716i 0.590535 0.150876i
\(34\) 12.0617 + 3.23192i 2.06856 + 0.554270i
\(35\) 0.871746 0.503303i 0.147352 0.0850737i
\(36\) −5.81173 + 3.17706i −0.968622 + 0.529510i
\(37\) −1.67263 6.24232i −0.274978 1.02623i −0.955856 0.293835i \(-0.905068\pi\)
0.680878 0.732397i \(-0.261598\pi\)
\(38\) −2.25276 3.90190i −0.365446 0.632972i
\(39\) −4.70759 + 4.10348i −0.753818 + 0.657083i
\(40\) −0.214551 + 0.371613i −0.0339234 + 0.0587571i
\(41\) 7.98626 + 2.13991i 1.24724 + 0.334198i 0.821271 0.570538i \(-0.193265\pi\)
0.425973 + 0.904736i \(0.359932\pi\)
\(42\) −3.09745 + 1.74048i −0.477947 + 0.268561i
\(43\) −3.20979 1.85317i −0.489488 0.282606i 0.234874 0.972026i \(-0.424532\pi\)
−0.724362 + 0.689420i \(0.757866\pi\)
\(44\) −3.15588 + 3.15588i −0.475767 + 0.475767i
\(45\) 2.18455 2.08496i 0.325653 0.310807i
\(46\) −2.87909 0.771449i −0.424498 0.113744i
\(47\) −0.873330 + 3.25931i −0.127388 + 0.475420i −0.999914 0.0131494i \(-0.995814\pi\)
0.872525 + 0.488569i \(0.162481\pi\)
\(48\) −3.12849 + 5.27566i −0.451558 + 0.761476i
\(49\) −0.866025 + 0.500000i −0.123718 + 0.0714286i
\(50\) −2.11662 + 7.89933i −0.299335 + 1.11713i
\(51\) 10.5431 + 0.122942i 1.47633 + 0.0172154i
\(52\) 2.49344 7.55979i 0.345778 1.04835i
\(53\) 2.67409i 0.367315i −0.982990 0.183657i \(-0.941206\pi\)
0.982990 0.183657i \(-0.0587937\pi\)
\(54\) −7.79593 + 7.26873i −1.06089 + 0.989149i
\(55\) 1.01743 1.76223i 0.137190 0.237619i
\(56\) 0.213143 0.369174i 0.0284824 0.0493329i
\(57\) −2.65852 2.72125i −0.352129 0.360438i
\(58\) 0.971363 + 0.971363i 0.127546 + 0.127546i
\(59\) −5.30924 5.30924i −0.691204 0.691204i 0.271293 0.962497i \(-0.412549\pi\)
−0.962497 + 0.271293i \(0.912549\pi\)
\(60\) −1.03956 + 3.70627i −0.134207 + 0.478478i
\(61\) 4.43396 7.67984i 0.567710 0.983303i −0.429081 0.903266i \(-0.641163\pi\)
0.996792 0.0800374i \(-0.0255040\pi\)
\(62\) −8.26466 + 14.3148i −1.04961 + 1.81798i
\(63\) −2.17021 + 2.07128i −0.273421 + 0.260956i
\(64\) 9.56716i 1.19589i
\(65\) −0.206018 + 3.62352i −0.0255534 + 0.449442i
\(66\) −3.66342 + 6.17774i −0.450936 + 0.760427i
\(67\) −1.64704 + 6.14685i −0.201219 + 0.750958i 0.789350 + 0.613943i \(0.210417\pi\)
−0.990569 + 0.137015i \(0.956249\pi\)
\(68\) −11.6394 + 6.71999i −1.41148 + 0.814918i
\(69\) −2.51660 0.0293459i −0.302963 0.00353284i
\(70\) −0.534421 + 1.99449i −0.0638756 + 0.238387i
\(71\) 9.37428 + 2.51183i 1.11252 + 0.298099i 0.767854 0.640625i \(-0.221325\pi\)
0.344668 + 0.938725i \(0.387991\pi\)
\(72\) 0.359707 1.22723i 0.0423919 0.144630i
\(73\) −11.1112 + 11.1112i −1.30047 + 1.30047i −0.372401 + 0.928072i \(0.621465\pi\)
−0.928072 + 0.372401i \(0.878535\pi\)
\(74\) 11.4805 + 6.62828i 1.33458 + 0.770522i
\(75\) −0.0805163 + 6.90478i −0.00929722 + 0.797295i
\(76\) 4.68407 + 1.25509i 0.537300 + 0.143969i
\(77\) −1.01075 + 1.75067i −0.115185 + 0.199507i
\(78\) 0.876249 12.7803i 0.0992156 1.44709i
\(79\) 0.958551 + 1.66026i 0.107845 + 0.186794i 0.914897 0.403687i \(-0.132272\pi\)
−0.807052 + 0.590481i \(0.798938\pi\)
\(80\) 0.922581 + 3.44312i 0.103148 + 0.384952i
\(81\) −4.85851 + 7.57594i −0.539835 + 0.841771i
\(82\) −14.6879 + 8.48004i −1.62200 + 0.936464i
\(83\) 3.21806 + 0.862278i 0.353228 + 0.0946473i 0.431070 0.902318i \(-0.358136\pi\)
−0.0778416 + 0.996966i \(0.524803\pi\)
\(84\) 1.03274 3.68195i 0.112681 0.401734i
\(85\) 4.33292 4.33292i 0.469971 0.469971i
\(86\) 7.34374 1.96775i 0.791896 0.212188i
\(87\) 0.997691 + 0.591634i 0.106964 + 0.0634299i
\(88\) 0.861735i 0.0918612i
\(89\) 5.61492 1.50451i 0.595180 0.159478i 0.0513604 0.998680i \(-0.483644\pi\)
0.543819 + 0.839202i \(0.316978\pi\)
\(90\) −0.144449 + 6.19285i −0.0152262 + 0.652784i
\(91\) 0.204666 3.59974i 0.0214548 0.377355i
\(92\) 2.77828 1.60404i 0.289655 0.167233i
\(93\) −3.76925 + 13.4383i −0.390853 + 1.39348i
\(94\) −3.46083 5.99434i −0.356958 0.618269i
\(95\) −2.21094 −0.226838
\(96\) −3.47998 13.6208i −0.355174 1.39017i
\(97\) 11.5320 3.08999i 1.17090 0.313741i 0.379587 0.925156i \(-0.376066\pi\)
0.791310 + 0.611415i \(0.209399\pi\)
\(98\) 0.530914 1.98140i 0.0536304 0.200152i
\(99\) −1.70578 + 5.81965i −0.171437 + 0.584897i
\(100\) −4.40099 7.62274i −0.440099 0.762274i
\(101\) −5.51900 −0.549161 −0.274581 0.961564i \(-0.588539\pi\)
−0.274581 + 0.961564i \(0.588539\pi\)
\(102\) −15.4709 + 15.1142i −1.53185 + 1.49653i
\(103\) 2.09947 + 1.21213i 0.206867 + 0.119435i 0.599855 0.800109i \(-0.295225\pi\)
−0.392987 + 0.919544i \(0.628558\pi\)
\(104\) 0.691700 + 1.37255i 0.0678268 + 0.134590i
\(105\) −0.0203294 + 1.74337i −0.00198395 + 0.170136i
\(106\) 3.87873 + 3.87873i 0.376735 + 0.376735i
\(107\) 0.00641718 + 0.00370496i 0.000620373 + 0.000358172i 0.500310 0.865846i \(-0.333219\pi\)
−0.499690 + 0.866204i \(0.666553\pi\)
\(108\) 0.401228 11.4651i 0.0386082 1.10323i
\(109\) −8.84853 8.84853i −0.847536 0.847536i 0.142289 0.989825i \(-0.454554\pi\)
−0.989825 + 0.142289i \(0.954554\pi\)
\(110\) 1.08033 + 4.03185i 0.103006 + 0.384422i
\(111\) 10.7775 + 3.02295i 1.02296 + 0.286925i
\(112\) −0.916527 3.42053i −0.0866037 0.323209i
\(113\) 5.44594i 0.512311i 0.966636 + 0.256155i \(0.0824559\pi\)
−0.966636 + 0.256155i \(0.917544\pi\)
\(114\) 7.80327 + 0.0909936i 0.730843 + 0.00852233i
\(115\) −1.03425 + 1.03425i −0.0964446 + 0.0964446i
\(116\) −1.47853 −0.137278
\(117\) −1.95442 10.6386i −0.180686 0.983541i
\(118\) 15.4020 1.41786
\(119\) −4.30448 + 4.30448i −0.394591 + 0.394591i
\(120\) −0.364082 0.647941i −0.0332360 0.0591487i
\(121\) 6.91355i 0.628504i
\(122\) 4.70811 + 17.5709i 0.426252 + 1.59079i
\(123\) −10.2436 + 10.0074i −0.923631 + 0.902338i
\(124\) −4.60453 17.1843i −0.413499 1.54320i
\(125\) 6.39656 + 6.39656i 0.572126 + 0.572126i
\(126\) 0.143501 6.15221i 0.0127841 0.548083i
\(127\) −2.51670 1.45302i −0.223321 0.128934i 0.384166 0.923264i \(-0.374489\pi\)
−0.607487 + 0.794330i \(0.707822\pi\)
\(128\) 2.39842 + 2.39842i 0.211992 + 0.211992i
\(129\) 5.59656 3.14474i 0.492750 0.276879i
\(130\) −4.95703 5.55468i −0.434760 0.487178i
\(131\) −3.19001 1.84176i −0.278713 0.160915i 0.354128 0.935197i \(-0.384778\pi\)
−0.632841 + 0.774282i \(0.718111\pi\)
\(132\) −1.91355 7.48971i −0.166553 0.651896i
\(133\) 2.19643 0.190455
\(134\) −6.52690 11.3049i −0.563839 0.976597i
\(135\) 1.17622 + 5.09651i 0.101233 + 0.438637i
\(136\) 0.671634 2.50657i 0.0575921 0.214937i
\(137\) −9.91272 + 2.65611i −0.846901 + 0.226926i −0.656073 0.754697i \(-0.727784\pi\)
−0.190828 + 0.981624i \(0.561117\pi\)
\(138\) 3.69285 3.60772i 0.314356 0.307110i
\(139\) 21.1780 1.79629 0.898146 0.439697i \(-0.144914\pi\)
0.898146 + 0.439697i \(0.144914\pi\)
\(140\) −1.11120 1.92465i −0.0939134 0.162663i
\(141\) −4.08418 4.18055i −0.343950 0.352066i
\(142\) −17.2406 + 9.95387i −1.44680 + 0.835311i
\(143\) −3.28013 6.50881i −0.274298 0.544294i
\(144\) −5.09580 9.32164i −0.424650 0.776803i
\(145\) 0.651135 0.174471i 0.0540738 0.0144890i
\(146\) 32.2334i 2.66765i
\(147\) 0.0201960 1.73193i 0.00166574 0.142847i
\(148\) −13.7819 + 3.69284i −1.13286 + 0.303550i
\(149\) 9.49436 9.49436i 0.777808 0.777808i −0.201649 0.979458i \(-0.564630\pi\)
0.979458 + 0.201649i \(0.0646302\pi\)
\(150\) −9.89849 10.1321i −0.808208 0.827279i
\(151\) −2.97827 0.798024i −0.242368 0.0649423i 0.135590 0.990765i \(-0.456707\pi\)
−0.377958 + 0.925823i \(0.623374\pi\)
\(152\) −0.810865 + 0.468153i −0.0657698 + 0.0379722i
\(153\) −9.49751 + 15.5985i −0.767828 + 1.26106i
\(154\) −1.07324 4.00539i −0.0864843 0.322764i
\(155\) 4.05561 + 7.02452i 0.325755 + 0.564223i
\(156\) 9.05972 + 10.3935i 0.725358 + 0.832144i
\(157\) 6.37713 11.0455i 0.508950 0.881528i −0.490996 0.871162i \(-0.663367\pi\)
0.999946 0.0103662i \(-0.00329971\pi\)
\(158\) −3.79854 1.01782i −0.302196 0.0809731i
\(159\) 3.98386 + 2.36244i 0.315941 + 0.187354i
\(160\) −7.07561 4.08510i −0.559376 0.322956i
\(161\) 1.02747 1.02747i 0.0809757 0.0809757i
\(162\) −3.94159 18.0360i −0.309681 1.41704i
\(163\) 12.1654 + 3.25972i 0.952871 + 0.255321i 0.701580 0.712591i \(-0.252478\pi\)
0.251291 + 0.967912i \(0.419145\pi\)
\(164\) 4.72453 17.6322i 0.368923 1.37684i
\(165\) 1.72652 + 3.07262i 0.134410 + 0.239203i
\(166\) −5.91847 + 3.41703i −0.459363 + 0.265213i
\(167\) 2.21374 8.26178i 0.171304 0.639316i −0.825848 0.563893i \(-0.809303\pi\)
0.997152 0.0754223i \(-0.0240305\pi\)
\(168\) 0.361693 + 0.643689i 0.0279052 + 0.0496617i
\(169\) 10.4490 + 7.73419i 0.803772 + 0.594938i
\(170\) 12.5697i 0.964049i
\(171\) 6.40280 1.55655i 0.489635 0.119032i
\(172\) −4.09145 + 7.08661i −0.311970 + 0.540349i
\(173\) 11.6024 20.0959i 0.882113 1.52786i 0.0331253 0.999451i \(-0.489454\pi\)
0.848987 0.528413i \(-0.177213\pi\)
\(174\) −2.30529 + 0.588979i −0.174764 + 0.0446504i
\(175\) −2.81905 2.81905i −0.213100 0.213100i
\(176\) −5.06183 5.06183i −0.381549 0.381549i
\(177\) 12.6002 3.21922i 0.947089 0.241972i
\(178\) −5.96208 + 10.3266i −0.446877 + 0.774013i
\(179\) 7.73849 13.4035i 0.578402 1.00182i −0.417261 0.908787i \(-0.637010\pi\)
0.995663 0.0930346i \(-0.0296567\pi\)
\(180\) −4.60320 4.82307i −0.343102 0.359490i
\(181\) 25.6408i 1.90586i −0.303185 0.952932i \(-0.598050\pi\)
0.303185 0.952932i \(-0.401950\pi\)
\(182\) 4.92450 + 5.51823i 0.365028 + 0.409038i
\(183\) 7.52422 + 13.3905i 0.556206 + 0.989856i
\(184\) −0.160317 + 0.598311i −0.0118187 + 0.0441080i
\(185\) 5.63368 3.25261i 0.414197 0.239137i
\(186\) −14.0247 24.9592i −1.02834 1.83010i
\(187\) −3.18497 + 11.8865i −0.232908 + 0.869225i
\(188\) 7.19595 + 1.92815i 0.524819 + 0.140625i
\(189\) −1.16850 5.06306i −0.0849960 0.368284i
\(190\) 3.20693 3.20693i 0.232655 0.232655i
\(191\) 20.3786 + 11.7656i 1.47454 + 0.851328i 0.999589 0.0286821i \(-0.00913104\pi\)
0.474955 + 0.880010i \(0.342464\pi\)
\(192\) 14.2531 + 8.45217i 1.02863 + 0.609983i
\(193\) 14.8353 + 3.97510i 1.06787 + 0.286134i 0.749616 0.661873i \(-0.230238\pi\)
0.318250 + 0.948007i \(0.396905\pi\)
\(194\) −12.2450 + 21.2090i −0.879140 + 1.52272i
\(195\) −5.21631 3.50815i −0.373547 0.251224i
\(196\) 1.10391 + 1.91202i 0.0788505 + 0.136573i
\(197\) 4.15096 + 15.4916i 0.295744 + 1.10373i 0.940625 + 0.339447i \(0.110240\pi\)
−0.644881 + 0.764283i \(0.723093\pi\)
\(198\) −5.96712 10.9155i −0.424065 0.775733i
\(199\) −6.49788 + 3.75155i −0.460622 + 0.265940i −0.712306 0.701869i \(-0.752349\pi\)
0.251684 + 0.967810i \(0.419016\pi\)
\(200\) 1.64158 + 0.439861i 0.116077 + 0.0311028i
\(201\) −7.70249 7.88425i −0.543292 0.556112i
\(202\) 8.00523 8.00523i 0.563246 0.563246i
\(203\) −0.646862 + 0.173326i −0.0454008 + 0.0121651i
\(204\) 0.271434 23.2771i 0.0190042 1.62973i
\(205\) 8.32260i 0.581276i
\(206\) −4.80344 + 1.28708i −0.334671 + 0.0896749i
\(207\) 2.26702 3.72330i 0.157569 0.258787i
\(208\) 12.1254 + 3.99932i 0.840746 + 0.277303i
\(209\) 3.84522 2.22004i 0.265979 0.153563i
\(210\) −2.49925 2.55822i −0.172465 0.176534i
\(211\) −2.95097 5.11124i −0.203153 0.351872i 0.746389 0.665509i \(-0.231786\pi\)
−0.949543 + 0.313637i \(0.898452\pi\)
\(212\) −5.90389 −0.405481
\(213\) −12.0239 + 11.7467i −0.823863 + 0.804871i
\(214\) −0.0146820 + 0.00393404i −0.00100364 + 0.000268925i
\(215\) 0.965608 3.60370i 0.0658539 0.245770i
\(216\) 1.51054 + 1.62009i 0.102779 + 0.110233i
\(217\) −4.02900 6.97843i −0.273506 0.473727i
\(218\) 25.6693 1.73855
\(219\) −6.73723 26.3698i −0.455260 1.78191i
\(220\) −3.89068 2.24628i −0.262309 0.151444i
\(221\) −4.46812 21.4890i −0.300559 1.44551i
\(222\) −20.0173 + 11.2479i −1.34348 + 0.754908i
\(223\) 5.60717 + 5.60717i 0.375484 + 0.375484i 0.869470 0.493986i \(-0.164461\pi\)
−0.493986 + 0.869470i \(0.664461\pi\)
\(224\) 7.02918 + 4.05830i 0.469657 + 0.271156i
\(225\) −10.2156 6.22002i −0.681040 0.414668i
\(226\) −7.89925 7.89925i −0.525451 0.525451i
\(227\) −3.81177 14.2257i −0.252996 0.944194i −0.969194 0.246297i \(-0.920786\pi\)
0.716198 0.697897i \(-0.245881\pi\)
\(228\) −6.00801 + 5.86951i −0.397890 + 0.388718i
\(229\) −6.09427 22.7441i −0.402721 1.50297i −0.808221 0.588879i \(-0.799569\pi\)
0.405500 0.914095i \(-0.367097\pi\)
\(230\) 3.00034i 0.197836i
\(231\) −1.71519 3.05245i −0.112851 0.200837i
\(232\) 0.201862 0.201862i 0.0132529 0.0132529i
\(233\) −1.58340 −0.103732 −0.0518660 0.998654i \(-0.516517\pi\)
−0.0518660 + 0.998654i \(0.516517\pi\)
\(234\) 18.2660 + 12.5963i 1.19409 + 0.823446i
\(235\) −3.39658 −0.221568
\(236\) −11.7218 + 11.7218i −0.763025 + 0.763025i
\(237\) −3.32029 0.0387178i −0.215676 0.00251499i
\(238\) 12.4872i 0.809424i
\(239\) 1.93336 + 7.21541i 0.125059 + 0.466726i 0.999842 0.0177890i \(-0.00566273\pi\)
−0.874783 + 0.484515i \(0.838996\pi\)
\(240\) −5.94462 1.66739i −0.383724 0.107629i
\(241\) 7.56726 + 28.2414i 0.487450 + 1.81919i 0.568764 + 0.822501i \(0.307422\pi\)
−0.0813134 + 0.996689i \(0.525911\pi\)
\(242\) 10.0280 + 10.0280i 0.644624 + 0.644624i
\(243\) −6.99435 13.9312i −0.448688 0.893689i
\(244\) −16.9557 9.78935i −1.08547 0.626699i
\(245\) −0.711778 0.711778i −0.0454738 0.0454738i
\(246\) 0.342526 29.3737i 0.0218387 1.87280i
\(247\) −4.34259 + 6.62252i −0.276313 + 0.421381i
\(248\) 2.97480 + 1.71750i 0.188900 + 0.109062i
\(249\) −4.12764 + 4.03249i −0.261579 + 0.255548i
\(250\) −18.5562 −1.17360
\(251\) −11.4061 19.7559i −0.719944 1.24698i −0.961022 0.276473i \(-0.910834\pi\)
0.241078 0.970506i \(-0.422499\pi\)
\(252\) 4.57299 + 4.79142i 0.288071 + 0.301831i
\(253\) 0.760242 2.83726i 0.0477960 0.178377i
\(254\) 5.75802 1.54286i 0.361290 0.0968074i
\(255\) 2.62724 + 10.2831i 0.164524 + 0.643954i
\(256\) 12.1766 0.761036
\(257\) −4.64508 8.04551i −0.289752 0.501865i 0.683999 0.729483i \(-0.260239\pi\)
−0.973750 + 0.227618i \(0.926906\pi\)
\(258\) −3.55633 + 12.6791i −0.221407 + 0.789368i
\(259\) −5.59671 + 3.23126i −0.347763 + 0.200781i
\(260\) 8.00004 + 0.454849i 0.496142 + 0.0282086i
\(261\) −1.76283 + 0.963677i −0.109117 + 0.0596501i
\(262\) 7.29851 1.95563i 0.450903 0.120819i
\(263\) 7.10480i 0.438100i 0.975714 + 0.219050i \(0.0702959\pi\)
−0.975714 + 0.219050i \(0.929704\pi\)
\(264\) 1.28381 + 0.761305i 0.0790132 + 0.0468551i
\(265\) 2.60004 0.696678i 0.159719 0.0427966i
\(266\) −3.18589 + 3.18589i −0.195339 + 0.195339i
\(267\) −2.71911 + 9.69427i −0.166407 + 0.593280i
\(268\) 13.5711 + 3.63637i 0.828987 + 0.222126i
\(269\) 9.58584 5.53439i 0.584459 0.337437i −0.178445 0.983950i \(-0.557107\pi\)
0.762903 + 0.646513i \(0.223773\pi\)
\(270\) −9.09850 5.68632i −0.553717 0.346058i
\(271\) 7.52953 + 28.1006i 0.457387 + 1.70699i 0.680975 + 0.732306i \(0.261556\pi\)
−0.223589 + 0.974684i \(0.571777\pi\)
\(272\) −10.7784 18.6688i −0.653538 1.13196i
\(273\) 5.18208 + 3.48512i 0.313633 + 0.210929i
\(274\) 10.5256 18.2309i 0.635876 1.10137i
\(275\) −7.78458 2.08587i −0.469428 0.125783i
\(276\) −0.0647903 + 5.55617i −0.00389992 + 0.334442i
\(277\) −11.4834 6.62995i −0.689972 0.398355i 0.113630 0.993523i \(-0.463752\pi\)
−0.803601 + 0.595168i \(0.797086\pi\)
\(278\) −30.7183 + 30.7183i −1.84236 + 1.84236i
\(279\) −16.6903 17.4875i −0.999224 1.04695i
\(280\) 0.414480 + 0.111060i 0.0247699 + 0.00663708i
\(281\) −6.33638 + 23.6477i −0.377996 + 1.41070i 0.470920 + 0.882176i \(0.343922\pi\)
−0.848917 + 0.528526i \(0.822745\pi\)
\(282\) 11.9879 + 0.139790i 0.713867 + 0.00832437i
\(283\) 4.57484 2.64129i 0.271946 0.157008i −0.357826 0.933788i \(-0.616482\pi\)
0.629772 + 0.776780i \(0.283148\pi\)
\(284\) 5.54565 20.6966i 0.329074 1.22812i
\(285\) 1.95327 3.29386i 0.115702 0.195111i
\(286\) 14.1987 + 4.68316i 0.839587 + 0.276921i
\(287\) 8.26799i 0.488044i
\(288\) 23.3667 + 6.84893i 1.37690 + 0.403577i
\(289\) −10.0286 + 17.3700i −0.589917 + 1.02177i
\(290\) −0.691394 + 1.19753i −0.0406001 + 0.0703214i
\(291\) −5.58455 + 19.9102i −0.327372 + 1.16716i
\(292\) 24.5315 + 24.5315i 1.43560 + 1.43560i
\(293\) −6.07416 6.07416i −0.354856 0.354856i 0.507057 0.861913i \(-0.330734\pi\)
−0.861913 + 0.507057i \(0.830734\pi\)
\(294\) 2.48285 + 2.54144i 0.144803 + 0.148220i
\(295\) 3.77900 6.54542i 0.220022 0.381089i
\(296\) 1.37744 2.38580i 0.0800621 0.138672i
\(297\) −7.16314 7.68268i −0.415648 0.445794i
\(298\) 27.5429i 1.59551i
\(299\) 1.06653 + 5.12936i 0.0616788 + 0.296639i
\(300\) 15.2445 + 0.177765i 0.880139 + 0.0102633i
\(301\) −0.959272 + 3.58005i −0.0552915 + 0.206351i
\(302\) 5.47745 3.16241i 0.315192 0.181976i
\(303\) 4.87580 8.22221i 0.280107 0.472354i
\(304\) −2.01309 + 7.51294i −0.115458 + 0.430897i
\(305\) 8.62233 + 2.31035i 0.493713 + 0.132290i
\(306\) −8.84933 36.4013i −0.505883 2.08092i
\(307\) −23.6669 + 23.6669i −1.35074 + 1.35074i −0.465908 + 0.884833i \(0.654272\pi\)
−0.884833 + 0.465908i \(0.845728\pi\)
\(308\) 3.86515 + 2.23154i 0.220237 + 0.127154i
\(309\) −3.66063 + 2.05693i −0.208246 + 0.117015i
\(310\) −16.0716 4.30636i −0.912804 0.244585i
\(311\) 6.74808 11.6880i 0.382649 0.662767i −0.608791 0.793330i \(-0.708345\pi\)
0.991440 + 0.130563i \(0.0416786\pi\)
\(312\) −2.65592 0.182096i −0.150362 0.0103091i
\(313\) −3.50547 6.07166i −0.198141 0.343190i 0.749785 0.661682i \(-0.230157\pi\)
−0.947926 + 0.318492i \(0.896824\pi\)
\(314\) 6.77142 + 25.2713i 0.382133 + 1.42614i
\(315\) −2.57932 1.57048i −0.145328 0.0884866i
\(316\) 3.66554 2.11630i 0.206203 0.119051i
\(317\) 33.4872 + 8.97287i 1.88083 + 0.503966i 0.999505 + 0.0314522i \(0.0100132\pi\)
0.881323 + 0.472514i \(0.156653\pi\)
\(318\) −9.20522 + 2.35184i −0.516203 + 0.131885i
\(319\) −0.957252 + 0.957252i −0.0535958 + 0.0535958i
\(320\) 9.30221 2.49252i 0.520009 0.139336i
\(321\) −0.0111890 + 0.00628715i −0.000624507 + 0.000350914i
\(322\) 2.98065i 0.166105i
\(323\) 12.9151 3.46059i 0.718614 0.192552i
\(324\) 16.7263 + 10.7267i 0.929237 + 0.595927i
\(325\) 14.0734 2.92622i 0.780653 0.162318i
\(326\) −22.3740 + 12.9176i −1.23918 + 0.715440i
\(327\) 20.9998 5.36525i 1.16129 0.296699i
\(328\) 1.76226 + 3.05233i 0.0973046 + 0.168536i
\(329\) 3.37429 0.186031
\(330\) −6.96108 1.95249i −0.383195 0.107481i
\(331\) −21.4693 + 5.75269i −1.18006 + 0.316196i −0.794950 0.606674i \(-0.792503\pi\)
−0.385110 + 0.922871i \(0.625836\pi\)
\(332\) 1.90375 7.10488i 0.104482 0.389931i
\(333\) −14.0250 + 13.3857i −0.768568 + 0.733531i
\(334\) 8.77259 + 15.1946i 0.480015 + 0.831410i
\(335\) −6.40573 −0.349982
\(336\) 5.90561 + 1.65644i 0.322177 + 0.0903664i
\(337\) −11.1799 6.45470i −0.609007 0.351610i 0.163570 0.986532i \(-0.447699\pi\)
−0.772577 + 0.634922i \(0.781032\pi\)
\(338\) −26.3745 + 3.93784i −1.43458 + 0.214190i
\(339\) −8.11336 4.81125i −0.440657 0.261311i
\(340\) −9.56627 9.56627i −0.518804 0.518804i
\(341\) −14.1069 8.14461i −0.763930 0.441055i
\(342\) −7.02941 + 11.5449i −0.380107 + 0.624278i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −0.408924 1.52612i −0.0220477 0.0822831i
\(345\) −0.627112 2.45455i −0.0337626 0.132148i
\(346\) 12.3197 + 45.9779i 0.662313 + 2.47179i
\(347\) 32.3228i 1.73518i 0.497283 + 0.867588i \(0.334331\pi\)
−0.497283 + 0.867588i \(0.665669\pi\)
\(348\) 1.30622 2.20272i 0.0700206 0.118078i
\(349\) 21.8914 21.8914i 1.17182 1.17182i 0.190047 0.981775i \(-0.439136\pi\)
0.981775 0.190047i \(-0.0608642\pi\)
\(350\) 8.17799 0.437132
\(351\) 17.5761 + 6.48707i 0.938141 + 0.346254i
\(352\) 16.4077 0.874532
\(353\) 15.9215 15.9215i 0.847417 0.847417i −0.142393 0.989810i \(-0.545480\pi\)
0.989810 + 0.142393i \(0.0454797\pi\)
\(354\) −13.6070 + 22.9458i −0.723202 + 1.21956i
\(355\) 9.76907i 0.518488i
\(356\) −3.32168 12.3967i −0.176049 0.657023i
\(357\) −2.60999 10.2156i −0.138136 0.540669i
\(358\) 8.21695 + 30.6661i 0.434279 + 1.62075i
\(359\) −6.29529 6.29529i −0.332253 0.332253i 0.521189 0.853441i \(-0.325489\pi\)
−0.853441 + 0.521189i \(0.825489\pi\)
\(360\) 1.28695 + 0.0300183i 0.0678284 + 0.00158210i
\(361\) 12.2765 + 7.08785i 0.646132 + 0.373045i
\(362\) 37.1915 + 37.1915i 1.95474 + 1.95474i
\(363\) 10.2998 + 6.10782i 0.540600 + 0.320578i
\(364\) −7.94755 0.451865i −0.416565 0.0236841i
\(365\) −13.6983 7.90873i −0.717003 0.413962i
\(366\) −30.3365 8.50899i −1.58572 0.444772i
\(367\) −19.9709 −1.04247 −0.521235 0.853413i \(-0.674529\pi\)
−0.521235 + 0.853413i \(0.674529\pi\)
\(368\) 2.57277 + 4.45617i 0.134115 + 0.232294i
\(369\) −5.85930 24.1020i −0.305023 1.25470i
\(370\) −3.45371 + 12.8894i −0.179550 + 0.670090i
\(371\) −2.58297 + 0.692106i −0.134101 + 0.0359323i
\(372\) 29.6691 + 8.32180i 1.53827 + 0.431465i
\(373\) −5.09103 −0.263604 −0.131802 0.991276i \(-0.542076\pi\)
−0.131802 + 0.991276i \(0.542076\pi\)
\(374\) −12.6214 21.8609i −0.652637 1.13040i
\(375\) −15.1807 + 3.87851i −0.783927 + 0.200286i
\(376\) −1.24570 + 0.719205i −0.0642421 + 0.0370902i
\(377\) 0.756320 2.29306i 0.0389525 0.118099i
\(378\) 9.03879 + 5.64900i 0.464905 + 0.290553i
\(379\) −21.4781 + 5.75503i −1.10325 + 0.295616i −0.764089 0.645110i \(-0.776811\pi\)
−0.339165 + 0.940727i \(0.610145\pi\)
\(380\) 4.88134i 0.250407i
\(381\) 4.38810 2.46570i 0.224809 0.126322i
\(382\) −46.6247 + 12.4930i −2.38552 + 0.639199i
\(383\) −13.8766 + 13.8766i −0.709062 + 0.709062i −0.966338 0.257276i \(-0.917175\pi\)
0.257276 + 0.966338i \(0.417175\pi\)
\(384\) −5.69206 + 1.45426i −0.290472 + 0.0742126i
\(385\) −1.96551 0.526658i −0.100172 0.0268410i
\(386\) −27.2841 + 15.7525i −1.38873 + 0.801782i
\(387\) −0.259282 + 11.1160i −0.0131800 + 0.565058i
\(388\) −6.82212 25.4605i −0.346341 1.29256i
\(389\) −9.13346 15.8196i −0.463085 0.802087i 0.536028 0.844200i \(-0.319924\pi\)
−0.999113 + 0.0421136i \(0.986591\pi\)
\(390\) 12.6547 2.47766i 0.640795 0.125461i
\(391\) 4.42271 7.66036i 0.223666 0.387401i
\(392\) −0.411760 0.110331i −0.0207970 0.00557255i
\(393\) 5.56209 3.12537i 0.280570 0.157654i
\(394\) −28.4912 16.4494i −1.43537 0.828709i
\(395\) −1.36455 + 1.36455i −0.0686579 + 0.0686579i
\(396\) 12.8487 + 3.76604i 0.645672 + 0.189250i
\(397\) −12.4408 3.33352i −0.624388 0.167304i −0.0672664 0.997735i \(-0.521428\pi\)
−0.557122 + 0.830431i \(0.688094\pi\)
\(398\) 3.98351 14.8666i 0.199675 0.745198i
\(399\) −1.94045 + 3.27224i −0.0971440 + 0.163817i
\(400\) 12.2264 7.05891i 0.611319 0.352945i
\(401\) 7.29917 27.2409i 0.364503 1.36034i −0.503590 0.863943i \(-0.667988\pi\)
0.868093 0.496401i \(-0.165346\pi\)
\(402\) 22.6083 + 0.263635i 1.12760 + 0.0131489i
\(403\) 29.0067 + 1.64920i 1.44493 + 0.0821525i
\(404\) 12.1849i 0.606223i
\(405\) −8.63192 2.75021i −0.428923 0.136659i
\(406\) 0.686857 1.18967i 0.0340881 0.0590424i
\(407\) −6.53199 + 11.3137i −0.323779 + 0.560801i
\(408\) 3.14093 + 3.21505i 0.155499 + 0.159169i
\(409\) 6.41648 + 6.41648i 0.317274 + 0.317274i 0.847719 0.530445i \(-0.177975\pi\)
−0.530445 + 0.847719i \(0.677975\pi\)
\(410\) −12.0718 12.0718i −0.596184 0.596184i
\(411\) 4.80040 17.1145i 0.236786 0.844198i
\(412\) 2.67616 4.63525i 0.131845 0.228362i
\(413\) −3.75420 + 6.50247i −0.184732 + 0.319965i
\(414\) 2.11231 + 8.68887i 0.103814 + 0.427035i
\(415\) 3.35359i 0.164621i
\(416\) −26.1338 + 13.1702i −1.28131 + 0.645721i
\(417\) −18.7098 + 31.5509i −0.916224 + 1.54506i
\(418\) −2.35730 + 8.79756i −0.115299 + 0.430303i
\(419\) 17.6415 10.1853i 0.861844 0.497586i −0.00278531 0.999996i \(-0.500887\pi\)
0.864629 + 0.502410i \(0.167553\pi\)
\(420\) 3.84904 + 0.0448835i 0.187814 + 0.00219009i
\(421\) −5.58891 + 20.8581i −0.272387 + 1.01656i 0.685185 + 0.728369i \(0.259721\pi\)
−0.957572 + 0.288193i \(0.906946\pi\)
\(422\) 11.6941 + 3.13343i 0.569260 + 0.152533i
\(423\) 9.83638 2.39127i 0.478261 0.116267i
\(424\) 0.806049 0.806049i 0.0391452 0.0391452i
\(425\) −21.0177 12.1346i −1.01951 0.588613i
\(426\) 0.402057 34.4789i 0.0194797 1.67051i
\(427\) −8.56575 2.29519i −0.414526 0.111072i
\(428\) 0.00817986 0.0141679i 0.000395389 0.000684833i
\(429\) 12.5947 + 0.863520i 0.608077 + 0.0416911i
\(430\) 3.82651 + 6.62771i 0.184531 + 0.319617i
\(431\) 3.13362 + 11.6948i 0.150941 + 0.563319i 0.999419 + 0.0340884i \(0.0108528\pi\)
−0.848478 + 0.529231i \(0.822481\pi\)
\(432\) 18.3893 + 0.643544i 0.884755 + 0.0309625i
\(433\) −15.1668 + 8.75658i −0.728872 + 0.420814i −0.818009 0.575205i \(-0.804922\pi\)
0.0891375 + 0.996019i \(0.471589\pi\)
\(434\) 15.9661 + 4.27810i 0.766398 + 0.205356i
\(435\) −0.315323 + 1.12420i −0.0151186 + 0.0539012i
\(436\) −19.5359 + 19.5359i −0.935600 + 0.935600i
\(437\) −3.08279 + 0.826031i −0.147470 + 0.0395144i
\(438\) 48.0213 + 28.4768i 2.29455 + 1.36067i
\(439\) 1.45876i 0.0696229i 0.999394 + 0.0348114i \(0.0110831\pi\)
−0.999394 + 0.0348114i \(0.988917\pi\)
\(440\) 0.837870 0.224507i 0.0399439 0.0107029i
\(441\) 2.56239 + 1.56018i 0.122019 + 0.0742941i
\(442\) 37.6505 + 24.6886i 1.79085 + 1.17432i
\(443\) 16.5122 9.53330i 0.784516 0.452941i −0.0535122 0.998567i \(-0.517042\pi\)
0.838028 + 0.545626i \(0.183708\pi\)
\(444\) 6.67410 23.7947i 0.316739 1.12925i
\(445\) 2.92569 + 5.06745i 0.138691 + 0.240220i
\(446\) −16.2662 −0.770229
\(447\) 5.75684 + 22.5326i 0.272289 + 1.06575i
\(448\) −9.24116 + 2.47616i −0.436604 + 0.116988i
\(449\) 4.69320 17.5153i 0.221486 0.826596i −0.762296 0.647228i \(-0.775928\pi\)
0.983782 0.179368i \(-0.0574052\pi\)
\(450\) 23.8396 5.79553i 1.12381 0.273204i
\(451\) −8.35686 14.4745i −0.393509 0.681578i
\(452\) 12.0236 0.565543
\(453\) 3.82007 3.73200i 0.179482 0.175345i
\(454\) 26.1631 + 15.1053i 1.22790 + 0.708926i
\(455\) 3.55337 0.738837i 0.166585 0.0346372i
\(456\) 0.0189096 1.62162i 0.000885525 0.0759393i
\(457\) −18.8399 18.8399i −0.881294 0.881294i 0.112372 0.993666i \(-0.464155\pi\)
−0.993666 + 0.112372i \(0.964155\pi\)
\(458\) 41.8297 + 24.1504i 1.95457 + 1.12847i
\(459\) −14.8479 27.9300i −0.693043 1.30366i
\(460\) 2.28344 + 2.28344i 0.106466 + 0.106466i
\(461\) −7.11986 26.5717i −0.331605 1.23757i −0.907503 0.420045i \(-0.862014\pi\)
0.575898 0.817522i \(-0.304653\pi\)
\(462\) 6.91540 + 1.93968i 0.321733 + 0.0902419i
\(463\) 3.64236 + 13.5935i 0.169275 + 0.631743i 0.997456 + 0.0712825i \(0.0227092\pi\)
−0.828181 + 0.560461i \(0.810624\pi\)
\(464\) 2.37147i 0.110093i
\(465\) −14.0481 0.163814i −0.651465 0.00759670i
\(466\) 2.29670 2.29670i 0.106392 0.106392i
\(467\) −3.14733 −0.145641 −0.0728206 0.997345i \(-0.523200\pi\)
−0.0728206 + 0.997345i \(0.523200\pi\)
\(468\) −23.4881 + 4.31499i −1.08574 + 0.199460i
\(469\) 6.36369 0.293848
\(470\) 4.92669 4.92669i 0.227251 0.227251i
\(471\) 10.8217 + 19.2589i 0.498637 + 0.887403i
\(472\) 3.20072i 0.147325i
\(473\) 1.93917 + 7.23706i 0.0891629 + 0.332761i
\(474\) 4.87219 4.75987i 0.223787 0.218628i
\(475\) 2.26638 + 8.45823i 0.103988 + 0.388090i
\(476\) 9.50350 + 9.50350i 0.435592 + 0.435592i
\(477\) −7.03914 + 3.84804i −0.322300 + 0.176190i
\(478\) −13.2702 7.66153i −0.606963 0.350430i
\(479\) 14.7886 + 14.7886i 0.675709 + 0.675709i 0.959026 0.283317i \(-0.0914349\pi\)
−0.283317 + 0.959026i \(0.591435\pi\)
\(480\) 12.3370 6.93223i 0.563104 0.316411i
\(481\) 1.32266 23.2634i 0.0603082 1.06072i
\(482\) −51.9399 29.9875i −2.36580 1.36590i
\(483\) 0.622997 + 2.43844i 0.0283474 + 0.110953i
\(484\) −15.2638 −0.693810
\(485\) 6.00883 + 10.4076i 0.272847 + 0.472585i
\(486\) 30.3522 + 10.0618i 1.37681 + 0.456414i
\(487\) 1.38867 5.18261i 0.0629269 0.234846i −0.927299 0.374323i \(-0.877875\pi\)
0.990225 + 0.139476i \(0.0445419\pi\)
\(488\) 3.65145 0.978404i 0.165294 0.0442903i
\(489\) −15.6040 + 15.2442i −0.705636 + 0.689369i
\(490\) 2.06485 0.0932802
\(491\) 19.0607 + 33.0140i 0.860195 + 1.48990i 0.871740 + 0.489969i \(0.162992\pi\)
−0.0115444 + 0.999933i \(0.503675\pi\)
\(492\) 22.0945 + 22.6159i 0.996097 + 1.01960i
\(493\) −3.53049 + 2.03833i −0.159005 + 0.0918017i
\(494\) −3.30700 15.9047i −0.148789 0.715588i
\(495\) −6.10289 0.142350i −0.274305 0.00639818i
\(496\) 27.5626 7.38537i 1.23760 0.331613i
\(497\) 9.70496i 0.435327i
\(498\) 0.138021 11.8361i 0.00618486 0.530390i
\(499\) −39.7756 + 10.6578i −1.78060 + 0.477110i −0.990693 0.136118i \(-0.956537\pi\)
−0.789906 + 0.613228i \(0.789871\pi\)
\(500\) 14.1224 14.1224i 0.631574 0.631574i
\(501\) 10.3527 + 10.5970i 0.462523 + 0.473437i
\(502\) 45.1999 + 12.1113i 2.01737 + 0.540552i
\(503\) −21.3989 + 12.3546i −0.954128 + 0.550866i −0.894361 0.447346i \(-0.852369\pi\)
−0.0597674 + 0.998212i \(0.519036\pi\)
\(504\) −1.27851 0.0298213i −0.0569493 0.00132835i
\(505\) −1.43786 5.36616i −0.0639839 0.238791i
\(506\) 3.01269 + 5.21813i 0.133930 + 0.231974i
\(507\) −20.7537 + 8.73415i −0.921703 + 0.387897i
\(508\) −3.20799 + 5.55640i −0.142332 + 0.246526i
\(509\) 14.2404 + 3.81572i 0.631197 + 0.169129i 0.560213 0.828349i \(-0.310719\pi\)
0.0709840 + 0.997477i \(0.477386\pi\)
\(510\) −18.7263 11.1048i −0.829214 0.491727i
\(511\) 13.6084 + 7.85684i 0.602002 + 0.347566i
\(512\) −22.4588 + 22.4588i −0.992547 + 0.992547i
\(513\) −3.33765 + 10.9140i −0.147361 + 0.481867i
\(514\) 18.4075 + 4.93227i 0.811920 + 0.217553i
\(515\) −0.631590 + 2.35713i −0.0278312 + 0.103867i
\(516\) −6.94300 12.3562i −0.305649 0.543950i
\(517\) 5.90726 3.41056i 0.259801 0.149996i
\(518\) 3.43105 12.8048i 0.150752 0.562613i
\(519\) 19.6887 + 35.0391i 0.864238 + 1.53805i
\(520\) −1.15433 + 1.03013i −0.0506209 + 0.0451744i
\(521\) 12.1754i 0.533416i −0.963777 0.266708i \(-0.914064\pi\)
0.963777 0.266708i \(-0.0859359\pi\)
\(522\) 1.15917 3.95476i 0.0507353 0.173095i
\(523\) 14.6667 25.4035i 0.641331 1.11082i −0.343805 0.939041i \(-0.611716\pi\)
0.985136 0.171777i \(-0.0549509\pi\)
\(524\) −4.06625 + 7.04295i −0.177635 + 0.307673i
\(525\) 6.69034 1.70931i 0.291990 0.0746006i
\(526\) −10.3054 10.3054i −0.449337 0.449337i
\(527\) −34.6855 34.6855i −1.51092 1.51092i
\(528\) 12.0130 3.06920i 0.522799 0.133570i
\(529\) 10.4443 18.0901i 0.454101 0.786525i
\(530\) −2.76079 + 4.78183i −0.119921 + 0.207710i
\(531\) −6.33573 + 21.6158i −0.274947 + 0.938046i
\(532\) 4.84931i 0.210244i
\(533\) 24.9291 + 16.3468i 1.07980 + 0.708057i
\(534\) −10.1174 18.0054i −0.437821 0.779171i
\(535\) −0.00193050 + 0.00720472i −8.34627e−5 + 0.000311487i
\(536\) −2.34931 + 1.35637i −0.101475 + 0.0585864i
\(537\) 13.1318 + 23.3702i 0.566681 + 1.00850i
\(538\) −5.87657 + 21.9317i −0.253357 + 0.945541i
\(539\) 1.95262 + 0.523202i 0.0841051 + 0.0225359i
\(540\) 11.2521 2.59687i 0.484215 0.111752i
\(541\) 3.73205 3.73205i 0.160453 0.160453i −0.622314 0.782768i \(-0.713807\pi\)
0.782768 + 0.622314i \(0.213807\pi\)
\(542\) −51.6810 29.8380i −2.21989 1.28165i
\(543\) 38.1996 + 22.6525i 1.63930 + 0.972112i
\(544\) 47.7259 + 12.7881i 2.04623 + 0.548285i
\(545\) 6.29819 10.9088i 0.269785 0.467281i
\(546\) −12.5716 + 2.46140i −0.538017 + 0.105338i
\(547\) −9.45122 16.3700i −0.404105 0.699930i 0.590112 0.807321i \(-0.299084\pi\)
−0.994217 + 0.107391i \(0.965750\pi\)
\(548\) 5.86419 + 21.8854i 0.250506 + 0.934900i
\(549\) −26.5965 0.620366i −1.13511 0.0264766i
\(550\) 14.3169 8.26589i 0.610477 0.352459i
\(551\) 1.42079 + 0.380699i 0.0605276 + 0.0162183i
\(552\) −0.749730 0.767422i −0.0319106 0.0326636i
\(553\) 1.35560 1.35560i 0.0576458 0.0576458i
\(554\) 26.2732 7.03988i 1.11624 0.299096i
\(555\) −0.131379 + 11.2666i −0.00557674 + 0.478241i
\(556\) 46.7570i 1.98294i
\(557\) −9.55512 + 2.56029i −0.404864 + 0.108483i −0.455503 0.890234i \(-0.650541\pi\)
0.0506397 + 0.998717i \(0.483874\pi\)
\(558\) 49.5745 + 1.15633i 2.09866 + 0.0489513i
\(559\) −8.89773 9.97050i −0.376334 0.421707i
\(560\) 3.08702 1.78229i 0.130450 0.0753155i
\(561\) −14.8947 15.2462i −0.628854 0.643693i
\(562\) −25.1098 43.4914i −1.05919 1.83457i
\(563\) 35.0766 1.47830 0.739151 0.673540i \(-0.235227\pi\)
0.739151 + 0.673540i \(0.235227\pi\)
\(564\) −9.22987 + 9.01709i −0.388648 + 0.379688i
\(565\) −5.29512 + 1.41882i −0.222767 + 0.0596904i
\(566\) −2.80459 + 10.4669i −0.117886 + 0.439956i
\(567\) 8.57527 + 2.73216i 0.360128 + 0.114740i
\(568\) 2.06854 + 3.58282i 0.0867941 + 0.150332i
\(569\) −4.32255 −0.181211 −0.0906054 0.995887i \(-0.528880\pi\)
−0.0906054 + 0.995887i \(0.528880\pi\)
\(570\) 1.94450 + 7.61088i 0.0814462 + 0.318784i
\(571\) −7.96985 4.60140i −0.333528 0.192562i 0.323878 0.946099i \(-0.395013\pi\)
−0.657406 + 0.753536i \(0.728346\pi\)
\(572\) −14.3702 + 7.24191i −0.600850 + 0.302799i
\(573\) −35.5320 + 19.9656i −1.48437 + 0.834077i
\(574\) 11.9926 + 11.9926i 0.500561 + 0.500561i
\(575\) 5.01686 + 2.89648i 0.209217 + 0.120792i
\(576\) −25.1841 + 13.7672i −1.04934 + 0.573634i
\(577\) −18.0030 18.0030i −0.749474 0.749474i 0.224906 0.974380i \(-0.427792\pi\)
−0.974380 + 0.224906i \(0.927792\pi\)
\(578\) −10.6486 39.7413i −0.442925 1.65302i
\(579\) −19.0284 + 18.5898i −0.790794 + 0.772564i
\(580\) −0.385200 1.43758i −0.0159945 0.0596925i
\(581\) 3.33159i 0.138217i
\(582\) −20.7792 36.9798i −0.861325 1.53286i
\(583\) −3.82238 + 3.82238i −0.158307 + 0.158307i
\(584\) −6.69851 −0.277186
\(585\) 9.83482 4.67196i 0.406620 0.193162i
\(586\) 17.6210 0.727915
\(587\) 12.1523 12.1523i 0.501579 0.501579i −0.410349 0.911928i \(-0.634593\pi\)
0.911928 + 0.410349i \(0.134593\pi\)
\(588\) −3.82378 0.0445890i −0.157690 0.00183882i
\(589\) 17.6988i 0.729267i
\(590\) 4.01265 + 14.9754i 0.165198 + 0.616528i
\(591\) −26.7466 7.50205i −1.10021 0.308593i
\(592\) −5.92308 22.1052i −0.243437 0.908520i
\(593\) −10.4567 10.4567i −0.429406 0.429406i 0.459020 0.888426i \(-0.348201\pi\)
−0.888426 + 0.459020i \(0.848201\pi\)
\(594\) 21.5336 + 0.753582i 0.883536 + 0.0309198i
\(595\) −5.30672 3.06384i −0.217554 0.125605i
\(596\) −20.9618 20.9618i −0.858628 0.858628i
\(597\) 0.151533 12.9949i 0.00620182 0.531845i
\(598\) −8.98705 5.89308i −0.367508 0.240986i
\(599\) −11.0015 6.35175i −0.449511 0.259525i 0.258113 0.966115i \(-0.416899\pi\)
−0.707624 + 0.706590i \(0.750233\pi\)
\(600\) −2.10557 + 2.05703i −0.0859596 + 0.0839780i
\(601\) −8.99800 −0.367036 −0.183518 0.983016i \(-0.558749\pi\)
−0.183518 + 0.983016i \(0.558749\pi\)
\(602\) −3.80140 6.58422i −0.154934 0.268353i
\(603\) 18.5508 4.50978i 0.755446 0.183652i
\(604\) −1.76189 + 6.57545i −0.0716902 + 0.267551i
\(605\) 6.72209 1.80118i 0.273292 0.0732283i
\(606\) 4.85392 + 18.9985i 0.197177 + 0.771760i
\(607\) −34.7020 −1.40851 −0.704256 0.709946i \(-0.748719\pi\)
−0.704256 + 0.709946i \(0.748719\pi\)
\(608\) −8.91376 15.4391i −0.361501 0.626138i
\(609\) 0.313254 1.11682i 0.0126937 0.0452559i
\(610\) −15.8577 + 9.15544i −0.642059 + 0.370693i
\(611\) −6.67136 + 10.1739i −0.269894 + 0.411593i
\(612\) 34.4385 + 20.9687i 1.39209 + 0.847610i
\(613\) 3.53014 0.945898i 0.142581 0.0382045i −0.186823 0.982394i \(-0.559819\pi\)
0.329404 + 0.944189i \(0.393152\pi\)
\(614\) 68.6570i 2.77077i
\(615\) −12.3990 7.35266i −0.499976 0.296488i
\(616\) −0.832372 + 0.223033i −0.0335372 + 0.00898627i
\(617\) −11.5860 + 11.5860i −0.466435 + 0.466435i −0.900758 0.434322i \(-0.856988\pi\)
0.434322 + 0.900758i \(0.356988\pi\)
\(618\) 2.32614 8.29323i 0.0935711 0.333603i
\(619\) 2.34524 + 0.628405i 0.0942631 + 0.0252577i 0.305642 0.952146i \(-0.401129\pi\)
−0.211379 + 0.977404i \(0.567795\pi\)
\(620\) 15.5088 8.95403i 0.622850 0.359603i
\(621\) 3.54415 + 6.66679i 0.142222 + 0.267529i
\(622\) 7.16531 + 26.7413i 0.287303 + 1.07223i
\(623\) −2.90649 5.03420i −0.116446 0.201691i
\(624\) −16.6705 + 14.5312i −0.667353 + 0.581714i
\(625\) 5.41393 9.37721i 0.216557 0.375088i
\(626\) 13.8915 + 3.72221i 0.555216 + 0.148770i
\(627\) −0.0896718 + 7.68992i −0.00358115 + 0.307106i
\(628\) −24.3864 14.0795i −0.973125 0.561834i
\(629\) −27.8179 + 27.8179i −1.10917 + 1.10917i
\(630\) 6.01922 1.46330i 0.239812 0.0582993i
\(631\) −24.3582 6.52677i −0.969686 0.259827i −0.260991 0.965341i \(-0.584049\pi\)
−0.708695 + 0.705515i \(0.750716\pi\)
\(632\) −0.211515 + 0.789386i −0.00841362 + 0.0314001i
\(633\) 10.2218 + 0.119196i 0.406279 + 0.00473760i
\(634\) −61.5877 + 35.5577i −2.44596 + 1.41218i
\(635\) 0.757106 2.82556i 0.0300448 0.112129i
\(636\) 5.21583 8.79562i 0.206821 0.348769i
\(637\) −3.53005 + 0.733988i −0.139866 + 0.0290817i
\(638\) 2.77696i 0.109941i
\(639\) −6.87765 28.2909i −0.272076 1.11917i
\(640\) −1.70714 + 2.95685i −0.0674806 + 0.116880i
\(641\) 4.11186 7.12195i 0.162409 0.281300i −0.773323 0.634012i \(-0.781407\pi\)
0.935732 + 0.352712i \(0.114740\pi\)
\(642\) 0.00711000 0.0253488i 0.000280609 0.00100044i
\(643\) 25.0827 + 25.0827i 0.989164 + 0.989164i 0.999942 0.0107777i \(-0.00343070\pi\)
−0.0107777 + 0.999942i \(0.503431\pi\)
\(644\) −2.26845 2.26845i −0.0893896 0.0893896i
\(645\) 4.51572 + 4.62228i 0.177806 + 0.182002i
\(646\) −13.7136 + 23.7527i −0.539555 + 0.934536i
\(647\) 10.3865 17.9900i 0.408336 0.707259i −0.586367 0.810045i \(-0.699442\pi\)
0.994703 + 0.102786i \(0.0327758\pi\)
\(648\) −3.74811 + 0.819113i −0.147240 + 0.0321778i
\(649\) 15.1782i 0.595797i
\(650\) −16.1688 + 24.6577i −0.634194 + 0.967155i
\(651\) 13.9559 + 0.162739i 0.546975 + 0.00637826i
\(652\) 7.19685 26.8590i 0.281850 1.05188i
\(653\) −29.1286 + 16.8174i −1.13989 + 0.658116i −0.946404 0.322986i \(-0.895313\pi\)
−0.193487 + 0.981103i \(0.561980\pi\)
\(654\) −22.6777 + 38.2422i −0.886770 + 1.49539i
\(655\) 0.959660 3.58150i 0.0374970 0.139941i
\(656\) 28.2809 + 7.57783i 1.10418 + 0.295865i
\(657\) 45.2378 + 13.2595i 1.76490 + 0.517302i
\(658\) −4.89436 + 4.89436i −0.190802 + 0.190802i
\(659\) −31.7473 18.3293i −1.23670 0.714009i −0.268281 0.963341i \(-0.586456\pi\)
−0.968418 + 0.249332i \(0.919789\pi\)
\(660\) 6.78376 3.81184i 0.264058 0.148376i
\(661\) −24.5866 6.58797i −0.956309 0.256242i −0.253272 0.967395i \(-0.581507\pi\)
−0.703037 + 0.711153i \(0.748173\pi\)
\(662\) 22.7967 39.4851i 0.886020 1.53463i
\(663\) 35.9618 + 12.3280i 1.39664 + 0.478781i
\(664\) 0.710103 + 1.22993i 0.0275573 + 0.0477307i
\(665\) 0.572233 + 2.13560i 0.0221902 + 0.0828151i
\(666\) 0.927379 39.7588i 0.0359352 1.54062i
\(667\) 0.842716 0.486542i 0.0326301 0.0188390i
\(668\) −18.2405 4.88752i −0.705745 0.189104i
\(669\) −13.3073 + 3.39987i −0.514489 + 0.131447i
\(670\) 9.29141 9.29141i 0.358958 0.358958i
\(671\) −17.3156 + 4.63971i −0.668463 + 0.179114i
\(672\) −12.2560 + 6.88674i −0.472786 + 0.265662i
\(673\) 1.64858i 0.0635482i −0.999495 0.0317741i \(-0.989884\pi\)
0.999495 0.0317741i \(-0.0101157\pi\)
\(674\) 25.5787 6.85379i 0.985254 0.263998i
\(675\) 18.2916 9.72408i 0.704045 0.374280i
\(676\) 17.0756 23.0695i 0.656756 0.887289i
\(677\) −26.6492 + 15.3859i −1.02421 + 0.591330i −0.915322 0.402724i \(-0.868064\pi\)
−0.108892 + 0.994054i \(0.534730\pi\)
\(678\) 18.7470 4.78966i 0.719973 0.183946i
\(679\) −5.96940 10.3393i −0.229085 0.396786i
\(680\) 2.61214 0.100171
\(681\) 24.5610 + 6.88903i 0.941180 + 0.263988i
\(682\) 32.2754 8.64818i 1.23589 0.331156i
\(683\) 0.595756 2.22339i 0.0227960 0.0850758i −0.953591 0.301106i \(-0.902644\pi\)
0.976387 + 0.216030i \(0.0693109\pi\)
\(684\) −3.43657 14.1362i −0.131401 0.540511i
\(685\) −5.16510 8.94621i −0.197348 0.341817i
\(686\) −2.05130 −0.0783188
\(687\) 39.2682 + 11.0142i 1.49818 + 0.420218i
\(688\) −11.3665 6.56243i −0.433342 0.250190i
\(689\) 3.02005 9.15638i 0.115055 0.348830i
\(690\) 4.46990 + 2.65067i 0.170166 + 0.100909i
\(691\) 1.64500 + 1.64500i 0.0625788 + 0.0625788i 0.737704 0.675125i \(-0.235910\pi\)
−0.675125 + 0.737704i \(0.735910\pi\)
\(692\) −44.3680 25.6159i −1.68662 0.973770i
\(693\) 6.06284 + 0.141416i 0.230308 + 0.00537196i
\(694\) −46.8837 46.8837i −1.77968 1.77968i
\(695\) 5.51747 + 20.5915i 0.209290 + 0.781079i
\(696\) 0.122397 + 0.479069i 0.00463946 + 0.0181591i
\(697\) −13.0266 48.6160i −0.493419 1.84146i
\(698\) 63.5064i 2.40375i
\(699\) 1.39887 2.35895i 0.0529100 0.0892237i
\(700\) −6.22394 + 6.22394i −0.235243 + 0.235243i
\(701\) −38.8753 −1.46830 −0.734151 0.678986i \(-0.762420\pi\)
−0.734151 + 0.678986i \(0.762420\pi\)
\(702\) −34.9032 + 16.0844i −1.31734 + 0.607067i
\(703\) 14.1945 0.535355
\(704\) −13.6754 + 13.6754i −0.515412 + 0.515412i
\(705\) 3.00073 5.06022i 0.113014 0.190579i
\(706\) 46.1879i 1.73830i
\(707\) 1.42842 + 5.33095i 0.0537214 + 0.200491i
\(708\) −7.10744 27.8189i −0.267114 1.04550i
\(709\) 0.153288 + 0.572078i 0.00575685 + 0.0214848i 0.968745 0.248061i \(-0.0797932\pi\)
−0.962988 + 0.269545i \(0.913127\pi\)
\(710\) −14.1699 14.1699i −0.531786 0.531786i
\(711\) 2.99102 4.91236i 0.112172 0.184228i
\(712\) 2.14600 + 1.23900i 0.0804249 + 0.0464333i
\(713\) 8.27932 + 8.27932i 0.310063 + 0.310063i
\(714\) 18.6034 + 11.0319i 0.696215 + 0.412858i
\(715\) 5.47399 4.88502i 0.204716 0.182689i
\(716\) −29.5923 17.0851i −1.10592 0.638501i
\(717\) −12.4576 3.49418i −0.465236 0.130492i
\(718\) 18.2624 0.681548
\(719\) 3.23441 + 5.60216i 0.120623 + 0.208925i 0.920014 0.391887i \(-0.128177\pi\)
−0.799390 + 0.600812i \(0.794844\pi\)
\(720\) 7.73589 7.38323i 0.288299 0.275157i
\(721\) 0.627446 2.34166i 0.0233673 0.0872080i
\(722\) −28.0877 + 7.52608i −1.04532 + 0.280092i
\(723\) −48.7594 13.6764i −1.81338 0.508629i
\(724\) −56.6100 −2.10389
\(725\) −1.33492 2.31216i −0.0495778 0.0858713i
\(726\) −23.7990 + 6.08041i −0.883264 + 0.225665i
\(727\) 25.4332 14.6839i 0.943265 0.544594i 0.0522826 0.998632i \(-0.483350\pi\)
0.890982 + 0.454038i \(0.150017\pi\)
\(728\) 1.14676 1.02337i 0.0425017 0.0379288i
\(729\) 26.9339 + 1.88745i 0.997554 + 0.0699055i
\(730\) 31.3407 8.39772i 1.15997 0.310814i
\(731\) 22.5622i 0.834493i
\(732\) 29.5638 16.6121i 1.09271 0.614000i
\(733\) −11.6436 + 3.11989i −0.430066 + 0.115236i −0.467357 0.884069i \(-0.654794\pi\)
0.0372911 + 0.999304i \(0.488127\pi\)
\(734\) 28.9674 28.9674i 1.06921 1.06921i
\(735\) 1.68923 0.431582i 0.0623082 0.0159191i
\(736\) −11.3920 3.05248i −0.419915 0.112516i
\(737\) 11.1407 6.43209i 0.410373 0.236929i
\(738\) 43.4584 + 26.4607i 1.59972 + 0.974032i
\(739\) −3.41778 12.7553i −0.125725 0.469212i 0.874139 0.485675i \(-0.161426\pi\)
−0.999864 + 0.0164628i \(0.994759\pi\)
\(740\) −7.18115 12.4381i −0.263984 0.457234i
\(741\) −6.02974 12.3203i −0.221508 0.452598i
\(742\) 2.74268 4.75045i 0.100687 0.174395i
\(743\) −7.71215 2.06646i −0.282931 0.0758112i 0.114563 0.993416i \(-0.463453\pi\)
−0.397494 + 0.917605i \(0.630120\pi\)
\(744\) −5.18684 + 2.91452i −0.190159 + 0.106852i
\(745\) 11.7050 + 6.75787i 0.428837 + 0.247589i
\(746\) 7.38446 7.38446i 0.270364 0.270364i
\(747\) −2.36101 9.71189i −0.0863847 0.355339i
\(748\) 26.2431 + 7.03182i 0.959543 + 0.257109i
\(749\) 0.00191783 0.00715744i 7.00760e−5 0.000261527i
\(750\) 16.3936 27.6451i 0.598611 1.00946i
\(751\) 6.76052 3.90319i 0.246695 0.142429i −0.371555 0.928411i \(-0.621175\pi\)
0.618250 + 0.785982i \(0.287842\pi\)
\(752\) −3.09263 + 11.5418i −0.112777 + 0.420888i
\(753\) 39.5090 + 0.460713i 1.43979 + 0.0167893i
\(754\) 2.22902 + 4.42308i 0.0811761 + 0.161079i
\(755\) 3.10370i 0.112955i
\(756\) −11.1783 + 2.57983i −0.406551 + 0.0938276i
\(757\) −19.7889 + 34.2755i −0.719241 + 1.24576i 0.242059 + 0.970261i \(0.422177\pi\)
−0.961301 + 0.275501i \(0.911156\pi\)
\(758\) 22.8060 39.5012i 0.828353 1.43475i
\(759\) 3.55531 + 3.63921i 0.129050 + 0.132095i
\(760\) −0.666442 0.666442i −0.0241744 0.0241744i
\(761\) 15.1478 + 15.1478i 0.549106 + 0.549106i 0.926182 0.377076i \(-0.123071\pi\)
−0.377076 + 0.926182i \(0.623071\pi\)
\(762\) −2.78841 + 9.94134i −0.101014 + 0.360137i
\(763\) −6.25686 + 10.8372i −0.226513 + 0.392333i
\(764\) 25.9762 44.9921i 0.939786 1.62776i
\(765\) −17.6409 5.17064i −0.637806 0.186945i
\(766\) 40.2557i 1.45450i
\(767\) −12.1833 24.1755i −0.439914 0.872928i
\(768\) −10.7575 + 18.1407i −0.388177 + 0.654595i
\(769\) 1.51250 5.64473i 0.0545422 0.203554i −0.933278 0.359155i \(-0.883065\pi\)
0.987820 + 0.155601i \(0.0497315\pi\)
\(770\) 3.61486 2.08704i 0.130270 0.0752117i
\(771\) 16.0899 + 0.187624i 0.579464 + 0.00675711i
\(772\) 8.77627 32.7535i 0.315865 1.17882i
\(773\) 6.25771 + 1.67675i 0.225074 + 0.0603085i 0.369594 0.929194i \(-0.379497\pi\)
−0.144519 + 0.989502i \(0.546164\pi\)
\(774\) −15.7475 16.4997i −0.566032 0.593069i
\(775\) 22.7159 22.7159i 0.815980 0.815980i
\(776\) 4.40749 + 2.54467i 0.158220 + 0.0913483i
\(777\) 0.130517 11.1927i 0.00468228 0.401535i
\(778\) 36.1941 + 9.69817i 1.29762 + 0.347696i
\(779\) −9.08003 + 15.7271i −0.325326 + 0.563481i
\(780\) −7.74533 + 11.5166i −0.277327 + 0.412361i
\(781\) −9.80928 16.9902i −0.351004 0.607956i
\(782\) 4.69616 + 17.5263i 0.167934 + 0.626740i
\(783\) 0.121702 3.47764i 0.00434927 0.124281i
\(784\) −3.06676 + 1.77059i −0.109527 + 0.0632355i
\(785\) 12.4011 + 3.32285i 0.442612 + 0.118598i
\(786\) −3.53442 + 12.6010i −0.126069 + 0.449464i
\(787\) 8.54630 8.54630i 0.304643 0.304643i −0.538184 0.842827i \(-0.680890\pi\)
0.842827 + 0.538184i \(0.180890\pi\)
\(788\) 34.2025 9.16454i 1.21841 0.326473i
\(789\) −10.5847 6.27678i −0.376826 0.223459i
\(790\) 3.95852i 0.140838i
\(791\) 5.26037 1.40951i 0.187037 0.0501165i
\(792\) −2.26839 + 1.24004i −0.0806036 + 0.0440630i
\(793\) 23.8558 21.2890i 0.847143 0.755995i
\(794\) 22.8805 13.2100i 0.811998 0.468807i
\(795\) −1.25911 + 4.48902i −0.0446560 + 0.159209i
\(796\) 8.28272 + 14.3461i 0.293573 + 0.508484i
\(797\) 8.34235 0.295501 0.147751 0.989025i \(-0.452797\pi\)
0.147751 + 0.989025i \(0.452797\pi\)
\(798\) −1.93174 7.56093i −0.0683829 0.267654i
\(799\) 19.8409 5.31636i 0.701922 0.188079i
\(800\) −8.37507 + 31.2562i −0.296104 + 1.10507i
\(801\) −12.0403 12.6154i −0.425423 0.445743i
\(802\) 28.9251 + 50.0998i 1.02138 + 1.76909i
\(803\) 31.7651 1.12097
\(804\) −17.4069 + 17.0057i −0.613895 + 0.599743i
\(805\) 1.26670 + 0.731327i 0.0446452 + 0.0257759i
\(806\) −44.4659 + 39.6816i −1.56624 + 1.39772i
\(807\) −0.223545 + 19.1704i −0.00786915 + 0.674829i
\(808\) −1.66359 1.66359i −0.0585249 0.0585249i
\(809\) −10.1847 5.88016i −0.358076 0.206735i 0.310160 0.950684i \(-0.399617\pi\)
−0.668236 + 0.743949i \(0.732951\pi\)
\(810\) 16.5096 8.53132i 0.580088 0.299760i
\(811\) −8.83907 8.83907i −0.310382 0.310382i 0.534676 0.845057i \(-0.320434\pi\)
−0.845057 + 0.534676i \(0.820434\pi\)
\(812\) 0.382672 + 1.42815i 0.0134292 + 0.0501183i
\(813\) −48.5163 13.6082i −1.70154 0.477259i
\(814\) −6.93586 25.8850i −0.243102 0.907268i
\(815\) 12.6778i 0.444083i
\(816\) 37.3350 + 0.435362i 1.30699 + 0.0152407i
\(817\) 5.75636 5.75636i 0.201389 0.201389i
\(818\) −18.6140 −0.650823
\(819\) −9.77028 + 4.64130i −0.341401 + 0.162180i
\(820\) 18.3747 0.641674
\(821\) −22.3161 + 22.3161i −0.778838 + 0.778838i −0.979633 0.200795i \(-0.935648\pi\)
0.200795 + 0.979633i \(0.435648\pi\)
\(822\) 17.8615 + 31.7873i 0.622990 + 1.10871i
\(823\) 22.7870i 0.794304i 0.917753 + 0.397152i \(0.130001\pi\)
−0.917753 + 0.397152i \(0.869999\pi\)
\(824\) 0.267471 + 0.998215i 0.00931779 + 0.0347745i
\(825\) 9.98488 9.75469i 0.347629 0.339615i
\(826\) −3.98632 14.8771i −0.138702 0.517642i
\(827\) −35.6472 35.6472i −1.23957 1.23957i −0.960176 0.279397i \(-0.909865\pi\)
−0.279397 0.960176i \(-0.590135\pi\)
\(828\) −8.22035 5.00516i −0.285677 0.173941i
\(829\) 14.6884 + 8.48038i 0.510151 + 0.294536i 0.732896 0.680341i \(-0.238168\pi\)
−0.222745 + 0.974877i \(0.571502\pi\)
\(830\) −4.86434 4.86434i −0.168844 0.168844i
\(831\) 20.0224 11.2507i 0.694570 0.390283i
\(832\) 10.8049 32.7590i 0.374592 1.13571i
\(833\) 5.27189 + 3.04373i 0.182660 + 0.105459i
\(834\) −18.6258 72.9025i −0.644960 2.52441i
\(835\) 8.60972 0.297952
\(836\) −4.90143 8.48952i −0.169519 0.293616i
\(837\) 40.7981 9.41578i 1.41019 0.325457i
\(838\) −10.8151 + 40.3624i −0.373601 + 1.39430i
\(839\) 31.5834 8.46274i 1.09038 0.292166i 0.331538 0.943442i \(-0.392432\pi\)
0.758841 + 0.651275i \(0.225766\pi\)
\(840\) −0.531632 + 0.519376i −0.0183430 + 0.0179202i
\(841\) 28.5515 0.984535
\(842\) −22.1477 38.3610i −0.763261 1.32201i
\(843\) −29.6324 30.3316i −1.02059 1.04468i
\(844\) −11.2847 + 6.51520i −0.388434 + 0.224262i
\(845\) −4.79773 + 12.1746i −0.165047 + 0.418820i
\(846\) −10.7990 + 17.7360i −0.371278 + 0.609777i
\(847\) −6.67798 + 1.78936i −0.229458 + 0.0614831i
\(848\) 9.46946i 0.325183i
\(849\) −0.106687 + 9.14907i −0.00366148 + 0.313995i
\(850\) 48.0869 12.8848i 1.64937 0.441946i
\(851\) 6.64003 6.64003i 0.227617 0.227617i
\(852\) 25.9345 + 26.5465i 0.888502 + 0.909468i
\(853\) −8.79481 2.35656i −0.301129 0.0806871i 0.105091 0.994463i \(-0.466487\pi\)
−0.406220 + 0.913775i \(0.633153\pi\)
\(854\) 15.7536 9.09536i 0.539078 0.311237i
\(855\) 3.18156 + 5.81996i 0.108807 + 0.199038i
\(856\) 0.000817543 0.00305111i 2.79430e−5 0.000104285i
\(857\) 15.9654 + 27.6529i 0.545368 + 0.944604i 0.998584 + 0.0532037i \(0.0169433\pi\)
−0.453216 + 0.891401i \(0.649723\pi\)
\(858\) −19.5209 + 17.0159i −0.666433 + 0.580912i
\(859\) −8.63882 + 14.9629i −0.294753 + 0.510527i −0.974927 0.222523i \(-0.928571\pi\)
0.680175 + 0.733050i \(0.261904\pi\)
\(860\) −7.95629 2.13188i −0.271307 0.0726966i
\(861\) 12.3176 + 7.30441i 0.419784 + 0.248934i
\(862\) −21.5084 12.4179i −0.732579 0.422955i
\(863\) 22.0290 22.0290i 0.749874 0.749874i −0.224581 0.974455i \(-0.572101\pi\)
0.974455 + 0.224581i \(0.0721013\pi\)
\(864\) −30.8470 + 28.7610i −1.04944 + 0.978470i
\(865\) 22.5621 + 6.04551i 0.767136 + 0.205553i
\(866\) 9.29799 34.7006i 0.315958 1.17917i
\(867\) −17.0180 30.2862i −0.577963 1.02857i
\(868\) −15.4071 + 8.89527i −0.522950 + 0.301925i
\(869\) 1.00303 3.74336i 0.0340255 0.126985i
\(870\) −1.17326 2.08800i −0.0397773 0.0707900i
\(871\) −12.5817 + 19.1874i −0.426316 + 0.650139i
\(872\) 5.33441i 0.180646i
\(873\) −24.7286 25.9097i −0.836935 0.876911i
\(874\) 3.27339 5.66968i 0.110724 0.191780i
\(875\) 4.52305 7.83416i 0.152907 0.264843i
\(876\) −58.2197 + 14.8745i −1.96706 + 0.502564i
\(877\) 26.1315 + 26.1315i 0.882400 + 0.882400i 0.993778 0.111378i \(-0.0355266\pi\)
−0.111378 + 0.993778i \(0.535527\pi\)
\(878\) −2.11591 2.11591i −0.0714085 0.0714085i
\(879\) 14.4155 3.68303i 0.486224 0.124225i
\(880\) 3.60289 6.24040i 0.121454 0.210364i
\(881\) −21.1413 + 36.6179i −0.712270 + 1.23369i 0.251734 + 0.967797i \(0.418999\pi\)
−0.964003 + 0.265891i \(0.914334\pi\)
\(882\) −5.97972 + 1.45370i −0.201348 + 0.0489486i
\(883\) 41.8104i 1.40703i 0.710679 + 0.703517i \(0.248388\pi\)
−0.710679 + 0.703517i \(0.751612\pi\)
\(884\) −47.4438 + 9.86478i −1.59571 + 0.331789i
\(885\) 6.41278 + 11.4125i 0.215563 + 0.383629i
\(886\) −10.1227 + 37.7785i −0.340080 + 1.26919i
\(887\) −9.76881 + 5.64003i −0.328005 + 0.189374i −0.654955 0.755668i \(-0.727312\pi\)
0.326950 + 0.945042i \(0.393979\pi\)
\(888\) 2.33745 + 4.15986i 0.0784397 + 0.139596i
\(889\) −0.752137 + 2.80701i −0.0252259 + 0.0941442i
\(890\) −11.5939 3.10658i −0.388629 0.104133i
\(891\) 17.7740 3.88433i 0.595451 0.130130i
\(892\) 12.3796 12.3796i 0.414499 0.414499i
\(893\) −6.41845 3.70570i −0.214785 0.124006i
\(894\) −41.0333 24.3329i −1.37236 0.813815i
\(895\) 15.0484 + 4.03220i 0.503011 + 0.134781i
\(896\) 1.69594 2.93745i 0.0566573 0.0981333i
\(897\) −8.58396 2.94266i −0.286610 0.0982526i
\(898\) 18.5982 + 32.2130i 0.620630 + 1.07496i
\(899\) −1.39666 5.21241i −0.0465813 0.173844i
\(900\) −13.7326 + 22.5541i −0.457755 + 0.751805i
\(901\) −14.0975 + 8.13921i −0.469657 + 0.271156i
\(902\) 33.1165 + 8.87355i 1.10266 + 0.295457i
\(903\) −4.48609 4.59194i −0.149288 0.152810i
\(904\) −1.64157 + 1.64157i −0.0545977 + 0.0545977i
\(905\) 24.9307 6.68016i 0.828724 0.222056i
\(906\) −0.127736 + 10.9542i −0.00424374 + 0.363928i
\(907\) 40.8532i 1.35651i −0.734827 0.678254i \(-0.762737\pi\)
0.734827 0.678254i \(-0.237263\pi\)
\(908\) −31.4077 + 8.41568i −1.04230 + 0.279284i
\(909\) 7.94189 + 14.5279i 0.263416 + 0.481861i
\(910\) −4.08244 + 6.22578i −0.135331 + 0.206383i
\(911\) −26.6038 + 15.3597i −0.881423 + 0.508890i −0.871127 0.491057i \(-0.836611\pi\)
−0.0102955 + 0.999947i \(0.503277\pi\)
\(912\) −9.41431 9.63646i −0.311739 0.319095i
\(913\) −3.36740 5.83250i −0.111445 0.193028i
\(914\) 54.6540 1.80779
\(915\) −11.0594 + 10.8045i −0.365613 + 0.357184i
\(916\) −50.2148 + 13.4550i −1.65914 + 0.444566i
\(917\) −0.953363 + 3.55800i −0.0314828 + 0.117495i
\(918\) 62.0487 + 18.9753i 2.04791 + 0.626277i
\(919\) 5.47089 + 9.47586i 0.180468 + 0.312580i 0.942040 0.335501i \(-0.108905\pi\)
−0.761572 + 0.648080i \(0.775572\pi\)
\(920\) −0.623508 −0.0205565
\(921\) −14.3503 56.1676i −0.472857 1.85079i
\(922\) 48.8691 + 28.2146i 1.60942 + 0.929198i
\(923\) 29.2617 + 19.1878i 0.963162 + 0.631575i
\(924\) −6.73924 + 3.78682i −0.221705 + 0.124577i
\(925\) −18.2182 18.2182i −0.599011 0.599011i
\(926\) −25.0003 14.4340i −0.821562 0.474329i
\(927\) 0.169592 7.27082i 0.00557015 0.238805i
\(928\) 3.84350 + 3.84350i 0.126169 + 0.126169i
\(929\) −3.62244 13.5191i −0.118848 0.443548i 0.880698 0.473679i \(-0.157074\pi\)
−0.999546 + 0.0301308i \(0.990408\pi\)
\(930\) 20.6142 20.1389i 0.675965 0.660382i
\(931\) −0.568478 2.12159i −0.0186311 0.0695322i
\(932\) 3.49585i 0.114510i
\(933\) 11.4512 + 20.3792i 0.374895 + 0.667184i
\(934\) 4.56516 4.56516i 0.149377 0.149377i
\(935\) −12.3871 −0.405100
\(936\) 2.61767 3.79591i 0.0855613 0.124073i
\(937\) −17.2843 −0.564652 −0.282326 0.959318i \(-0.591106\pi\)
−0.282326 + 0.959318i \(0.591106\pi\)
\(938\) −9.23044 + 9.23044i −0.301384 + 0.301384i
\(939\) 12.1425 + 0.141593i 0.396255 + 0.00462072i
\(940\) 7.49901i 0.244591i
\(941\) 9.70158 + 36.2068i 0.316263 + 1.18031i 0.922808 + 0.385260i \(0.125888\pi\)
−0.606546 + 0.795049i \(0.707445\pi\)
\(942\) −43.6314 12.2380i −1.42159 0.398736i
\(943\) 3.10941 + 11.6045i 0.101256 + 0.377894i
\(944\) −18.8010 18.8010i −0.611921 0.611921i
\(945\) 4.61842 2.45521i 0.150237 0.0798681i
\(946\) −13.3100 7.68452i −0.432745 0.249845i
\(947\) 13.7547 + 13.7547i 0.446966 + 0.446966i 0.894345 0.447378i \(-0.147642\pi\)
−0.447378 + 0.894345i \(0.647642\pi\)
\(948\) −0.0854816 + 7.33058i −0.00277631 + 0.238086i
\(949\) −50.5948 + 25.4974i −1.64238 + 0.827679i
\(950\) −15.5559 8.98119i −0.504699 0.291388i
\(951\) −42.9523 + 41.9621i −1.39282 + 1.36071i
\(952\) −2.59499 −0.0841043
\(953\) −0.792189 1.37211i −0.0256615 0.0444471i 0.852909 0.522059i \(-0.174836\pi\)
−0.878571 + 0.477612i \(0.841503\pi\)
\(954\) 4.62864 15.7917i 0.149858 0.511275i
\(955\) −6.13055 + 22.8795i −0.198380 + 0.740364i
\(956\) 15.9303 4.26850i 0.515222 0.138053i
\(957\) −0.580423 2.27180i −0.0187624 0.0734370i
\(958\) −42.9013 −1.38608
\(959\) 5.13120 + 8.88750i 0.165695 + 0.286993i
\(960\) −4.50474 + 16.0605i −0.145390 + 0.518349i
\(961\) 29.3854 16.9656i 0.947915 0.547279i
\(962\) 31.8247 + 35.6617i 1.02607 + 1.14978i
\(963\) 0.000518371 0.0222237i 1.67043e−5 0.000716150i
\(964\) 62.3518 16.7071i 2.00821 0.538100i
\(965\) 15.4600i 0.497677i
\(966\) −4.44057 2.63327i −0.142873 0.0847242i
\(967\) −10.2105 + 2.73589i −0.328347 + 0.0879804i −0.419227 0.907881i \(-0.637699\pi\)
0.0908795 + 0.995862i \(0.471032\pi\)
\(968\) 2.08395 2.08395i 0.0669806 0.0669806i
\(969\) −6.25434 + 22.2982i −0.200918 + 0.716320i
\(970\) −23.8118 6.38035i −0.764550 0.204861i
\(971\) 16.4308 9.48631i 0.527288 0.304430i −0.212623 0.977134i \(-0.568201\pi\)
0.739912 + 0.672704i \(0.234867\pi\)
\(972\) −30.7575 + 15.4422i −0.986548 + 0.495309i
\(973\) −5.48126 20.4563i −0.175721 0.655800i
\(974\) 5.50304 + 9.53154i 0.176329 + 0.305410i
\(975\) −8.07376 + 23.5518i −0.258567 + 0.754260i
\(976\) 15.7015 27.1958i 0.502592 0.870515i
\(977\) 9.84485 + 2.63792i 0.314965 + 0.0843945i 0.412838 0.910804i \(-0.364537\pi\)
−0.0978738 + 0.995199i \(0.531204\pi\)
\(978\) 0.521768 44.7449i 0.0166843 1.43078i
\(979\) −10.1766 5.87547i −0.325246 0.187781i
\(980\) −1.57147 + 1.57147i −0.0501988 + 0.0501988i
\(981\) −10.5593 + 36.0255i −0.337133 + 1.15021i
\(982\) −75.5335 20.2392i −2.41037 0.645857i
\(983\) −10.7135 + 39.9832i −0.341707 + 1.27527i 0.554706 + 0.832047i \(0.312831\pi\)
−0.896412 + 0.443221i \(0.853836\pi\)
\(984\) −6.10424 0.0711812i −0.194596 0.00226918i
\(985\) −13.9811 + 8.07201i −0.445476 + 0.257196i
\(986\) 2.16436 8.07749i 0.0689271 0.257240i
\(987\) −2.98104 + 5.02702i −0.0948875 + 0.160012i
\(988\) 14.6213 + 9.58764i 0.465165 + 0.305023i
\(989\) 5.38552i 0.171250i
\(990\) 9.05863 8.64567i 0.287902 0.274778i
\(991\) −27.9330 + 48.3814i −0.887322 + 1.53689i −0.0442926 + 0.999019i \(0.514103\pi\)
−0.843029 + 0.537868i \(0.819230\pi\)
\(992\) −32.7017 + 56.6411i −1.03828 + 1.79836i
\(993\) 10.3969 37.0672i 0.329934 1.17629i
\(994\) 14.0769 + 14.0769i 0.446492 + 0.446492i
\(995\) −5.34054 5.34054i −0.169307 0.169307i
\(996\) 8.90298 + 9.11306i 0.282102 + 0.288758i
\(997\) −4.78988 + 8.29631i −0.151697 + 0.262747i −0.931851 0.362840i \(-0.881807\pi\)
0.780154 + 0.625587i \(0.215140\pi\)
\(998\) 42.2348 73.1529i 1.33692 2.31561i
\(999\) −7.55148 32.7202i −0.238918 1.03522i
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 819.2.ew.a.176.14 336
9.2 odd 6 819.2.fy.a.722.14 yes 336
13.2 odd 12 819.2.fy.a.743.14 yes 336
117.2 even 12 inner 819.2.ew.a.470.14 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
819.2.ew.a.176.14 336 1.1 even 1 trivial
819.2.ew.a.470.14 yes 336 117.2 even 12 inner
819.2.fy.a.722.14 yes 336 9.2 odd 6
819.2.fy.a.743.14 yes 336 13.2 odd 12