Properties

Label 1183.2.e.g.170.6
Level $1183$
Weight $2$
Character 1183.170
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
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] = [1183,2,Mod(170,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.170");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), 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: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 170.6
Root \(0.217953 + 0.377506i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.g.508.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.929081 - 1.60921i) q^{2} +(-1.14703 - 1.98672i) q^{3} +(-0.726381 - 1.25813i) q^{4} +(-0.0986811 + 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 - 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +O(q^{10})\) \(q+(0.929081 - 1.60921i) q^{2} +(-1.14703 - 1.98672i) q^{3} +(-0.726381 - 1.25813i) q^{4} +(-0.0986811 + 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 - 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(0.183365 + 0.317598i) q^{10} +(-2.09137 - 3.62236i) q^{11} +(-1.66637 + 2.88623i) q^{12} +(1.92926 - 4.52187i) q^{14} +0.452762 q^{15} +(2.39750 - 4.15260i) q^{16} +(-0.420653 - 0.728592i) q^{17} +(2.10227 + 3.64125i) q^{18} +(0.675876 - 1.17065i) q^{19} +0.286720 q^{20} +(-3.64380 - 4.85406i) q^{21} -7.77220 q^{22} +(2.05760 - 3.56386i) q^{23} +(-1.16637 - 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} -1.69131 q^{27} +(-2.30751 - 3.07393i) q^{28} -8.23861 q^{29} +(0.420653 - 0.728592i) q^{30} +(-0.640350 - 1.10912i) q^{31} +(-3.43809 - 5.95495i) q^{32} +(-4.79774 + 8.30993i) q^{33} -1.56328 q^{34} +(-0.204914 + 0.480285i) q^{35} +3.28723 q^{36} +(1.52242 - 2.63692i) q^{37} +(-1.25589 - 2.17526i) q^{38} +(-0.100344 + 0.173802i) q^{40} -5.39696 q^{41} +(-11.1966 + 1.35384i) q^{42} +5.32778 q^{43} +(-3.03826 + 5.26242i) q^{44} +(-0.223290 - 0.386750i) q^{45} +(-3.82334 - 6.62223i) q^{46} +(-5.83204 + 10.1014i) q^{47} -11.0001 q^{48} +(6.79826 - 1.66842i) q^{49} +9.21843 q^{50} +(-0.965006 + 1.67144i) q^{51} +(-2.32398 - 4.02525i) q^{53} +(-1.57136 + 2.72168i) q^{54} +0.825514 q^{55} +(2.67089 - 0.322952i) q^{56} -3.10101 q^{57} +(-7.65434 + 13.2577i) q^{58} +(3.02905 + 5.24648i) q^{59} +(-0.328878 - 0.569634i) q^{60} +(5.68285 - 9.84298i) q^{61} -2.37975 q^{62} +(-2.34932 + 5.50644i) q^{63} -3.18704 q^{64} +(8.91498 + 15.4412i) q^{66} +(6.69851 + 11.6022i) q^{67} +(-0.611109 + 1.05847i) q^{68} -9.44053 q^{69} +(0.582500 + 0.775973i) q^{70} +5.97040 q^{71} +(-1.15044 + 1.99263i) q^{72} +(1.94273 + 3.36491i) q^{73} +(-2.82891 - 4.89982i) q^{74} +(5.69049 - 9.85622i) q^{75} -1.96377 q^{76} +(-6.64368 - 8.85034i) q^{77} +(5.36669 - 9.29537i) q^{79} +(0.473177 + 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(-5.01421 + 8.68486i) q^{82} -3.07390 q^{83} +(-3.46025 + 8.11027i) q^{84} +0.166042 q^{85} +(4.94994 - 8.57354i) q^{86} +(9.44997 + 16.3678i) q^{87} +(-2.12662 - 3.68341i) q^{88} +(-5.99207 + 10.3786i) q^{89} -0.829819 q^{90} -5.97840 q^{92} +(-1.46901 + 2.54439i) q^{93} +(10.8369 + 18.7700i) q^{94} +(0.133392 + 0.231042i) q^{95} +(-7.88721 + 13.6611i) q^{96} -19.4727 q^{97} +(3.63129 - 12.4900i) q^{98} +9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21} + 10 q^{22} - q^{23} + 11 q^{24} + 7 q^{25} - 8 q^{27} - 8 q^{28} - 6 q^{29} - 5 q^{30} - 16 q^{31} - 8 q^{32} - 16 q^{33} - 32 q^{34} - 28 q^{35} + 42 q^{36} + 13 q^{37} - 17 q^{38} - 5 q^{40} - 16 q^{41} - 52 q^{42} + 22 q^{43} - 21 q^{44} + 7 q^{45} - 16 q^{46} + q^{47} - 42 q^{48} + 6 q^{49} + 12 q^{50} - 20 q^{51} - 2 q^{53} + 18 q^{54} - 18 q^{55} + 9 q^{56} - 42 q^{57} + 8 q^{58} - 13 q^{59} - 20 q^{60} - 5 q^{61} - 10 q^{62} - 8 q^{63} - 30 q^{64} + 18 q^{66} + 11 q^{67} + 29 q^{68} - 46 q^{69} + 39 q^{70} + 12 q^{71} - 25 q^{72} + 30 q^{73} - 3 q^{74} - 3 q^{75} - 18 q^{76} + 11 q^{77} + 7 q^{79} + 7 q^{80} - 6 q^{81} + q^{82} + 54 q^{83} - 41 q^{84} - 2 q^{85} + 7 q^{86} + 16 q^{87} - 4 q^{89} - 16 q^{90} + 54 q^{92} + 7 q^{93} + 45 q^{94} - 6 q^{95} - 19 q^{96} - 70 q^{97} + 82 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.929081 1.60921i 0.656959 1.13789i −0.324440 0.945906i \(-0.605176\pi\)
0.981399 0.191980i \(-0.0614909\pi\)
\(3\) −1.14703 1.98672i −0.662240 1.14703i −0.980026 0.198871i \(-0.936272\pi\)
0.317785 0.948163i \(-0.397061\pi\)
\(4\) −0.726381 1.25813i −0.363191 0.629065i
\(5\) −0.0986811 + 0.170921i −0.0441315 + 0.0764381i −0.887247 0.461294i \(-0.847385\pi\)
0.843116 + 0.537732i \(0.180719\pi\)
\(6\) −4.26275 −1.74026
\(7\) 2.62662 0.317598i 0.992769 0.120041i
\(8\) 1.01686 0.359513
\(9\) −1.13137 + 1.95960i −0.377125 + 0.653199i
\(10\) 0.183365 + 0.317598i 0.0579852 + 0.100433i
\(11\) −2.09137 3.62236i −0.630571 1.09218i −0.987435 0.158025i \(-0.949487\pi\)
0.356864 0.934156i \(-0.383846\pi\)
\(12\) −1.66637 + 2.88623i −0.481039 + 0.833184i
\(13\) 0 0
\(14\) 1.92926 4.52187i 0.515616 1.20852i
\(15\) 0.452762 0.116903
\(16\) 2.39750 4.15260i 0.599376 1.03815i
\(17\) −0.420653 0.728592i −0.102023 0.176709i 0.810495 0.585746i \(-0.199198\pi\)
−0.912518 + 0.409036i \(0.865865\pi\)
\(18\) 2.10227 + 3.64125i 0.495511 + 0.858250i
\(19\) 0.675876 1.17065i 0.155057 0.268566i −0.778023 0.628236i \(-0.783777\pi\)
0.933080 + 0.359670i \(0.117111\pi\)
\(20\) 0.286720 0.0641126
\(21\) −3.64380 4.85406i −0.795143 1.05924i
\(22\) −7.77220 −1.65704
\(23\) 2.05760 3.56386i 0.429038 0.743116i −0.567750 0.823201i \(-0.692186\pi\)
0.996788 + 0.0800850i \(0.0255192\pi\)
\(24\) −1.16637 2.02021i −0.238084 0.412373i
\(25\) 2.48052 + 4.29639i 0.496105 + 0.859279i
\(26\) 0 0
\(27\) −1.69131 −0.325492
\(28\) −2.30751 3.07393i −0.436078 0.580918i
\(29\) −8.23861 −1.52987 −0.764936 0.644106i \(-0.777230\pi\)
−0.764936 + 0.644106i \(0.777230\pi\)
\(30\) 0.420653 0.728592i 0.0768003 0.133022i
\(31\) −0.640350 1.10912i −0.115010 0.199203i 0.802774 0.596284i \(-0.203357\pi\)
−0.917784 + 0.397080i \(0.870023\pi\)
\(32\) −3.43809 5.95495i −0.607774 1.05270i
\(33\) −4.79774 + 8.30993i −0.835180 + 1.44657i
\(34\) −1.56328 −0.268100
\(35\) −0.204914 + 0.480285i −0.0346367 + 0.0811829i
\(36\) 3.28723 0.547872
\(37\) 1.52242 2.63692i 0.250285 0.433506i −0.713319 0.700839i \(-0.752809\pi\)
0.963604 + 0.267333i \(0.0861423\pi\)
\(38\) −1.25589 2.17526i −0.203732 0.352874i
\(39\) 0 0
\(40\) −0.100344 + 0.173802i −0.0158659 + 0.0274805i
\(41\) −5.39696 −0.842863 −0.421431 0.906860i \(-0.638472\pi\)
−0.421431 + 0.906860i \(0.638472\pi\)
\(42\) −11.1966 + 1.35384i −1.72768 + 0.208902i
\(43\) 5.32778 0.812479 0.406239 0.913767i \(-0.366840\pi\)
0.406239 + 0.913767i \(0.366840\pi\)
\(44\) −3.03826 + 5.26242i −0.458035 + 0.793340i
\(45\) −0.223290 0.386750i −0.0332862 0.0576534i
\(46\) −3.82334 6.62223i −0.563721 0.976394i
\(47\) −5.83204 + 10.1014i −0.850690 + 1.47344i 0.0298969 + 0.999553i \(0.490482\pi\)
−0.880587 + 0.473885i \(0.842851\pi\)
\(48\) −11.0001 −1.58772
\(49\) 6.79826 1.66842i 0.971180 0.238346i
\(50\) 9.21843 1.30368
\(51\) −0.965006 + 1.67144i −0.135128 + 0.234048i
\(52\) 0 0
\(53\) −2.32398 4.02525i −0.319223 0.552911i 0.661103 0.750295i \(-0.270089\pi\)
−0.980326 + 0.197384i \(0.936755\pi\)
\(54\) −1.57136 + 2.72168i −0.213835 + 0.370373i
\(55\) 0.825514 0.111312
\(56\) 2.67089 0.322952i 0.356913 0.0431562i
\(57\) −3.10101 −0.410739
\(58\) −7.65434 + 13.2577i −1.00506 + 1.74082i
\(59\) 3.02905 + 5.24648i 0.394349 + 0.683033i 0.993018 0.117964i \(-0.0376367\pi\)
−0.598669 + 0.800997i \(0.704303\pi\)
\(60\) −0.328878 0.569634i −0.0424580 0.0735394i
\(61\) 5.68285 9.84298i 0.727614 1.26026i −0.230275 0.973126i \(-0.573962\pi\)
0.957889 0.287139i \(-0.0927042\pi\)
\(62\) −2.37975 −0.302228
\(63\) −2.34932 + 5.50644i −0.295987 + 0.693746i
\(64\) −3.18704 −0.398380
\(65\) 0 0
\(66\) 8.91498 + 15.4412i 1.09736 + 1.90068i
\(67\) 6.69851 + 11.6022i 0.818354 + 1.41743i 0.906895 + 0.421357i \(0.138446\pi\)
−0.0885411 + 0.996073i \(0.528220\pi\)
\(68\) −0.611109 + 1.05847i −0.0741078 + 0.128358i
\(69\) −9.44053 −1.13651
\(70\) 0.582500 + 0.775973i 0.0696221 + 0.0927465i
\(71\) 5.97040 0.708556 0.354278 0.935140i \(-0.384727\pi\)
0.354278 + 0.935140i \(0.384727\pi\)
\(72\) −1.15044 + 1.99263i −0.135581 + 0.234833i
\(73\) 1.94273 + 3.36491i 0.227380 + 0.393833i 0.957031 0.289986i \(-0.0936508\pi\)
−0.729651 + 0.683820i \(0.760317\pi\)
\(74\) −2.82891 4.89982i −0.328854 0.569592i
\(75\) 5.69049 9.85622i 0.657081 1.13810i
\(76\) −1.96377 −0.225260
\(77\) −6.64368 8.85034i −0.757118 1.00859i
\(78\) 0 0
\(79\) 5.36669 9.29537i 0.603799 1.04581i −0.388441 0.921474i \(-0.626986\pi\)
0.992240 0.124337i \(-0.0396805\pi\)
\(80\) 0.473177 + 0.819566i 0.0529028 + 0.0916303i
\(81\) 5.33411 + 9.23895i 0.592679 + 1.02655i
\(82\) −5.01421 + 8.68486i −0.553726 + 0.959082i
\(83\) −3.07390 −0.337404 −0.168702 0.985667i \(-0.553958\pi\)
−0.168702 + 0.985667i \(0.553958\pi\)
\(84\) −3.46025 + 8.11027i −0.377544 + 0.884903i
\(85\) 0.166042 0.0180098
\(86\) 4.94994 8.57354i 0.533765 0.924509i
\(87\) 9.44997 + 16.3678i 1.01314 + 1.75482i
\(88\) −2.12662 3.68341i −0.226698 0.392653i
\(89\) −5.99207 + 10.3786i −0.635159 + 1.10013i 0.351323 + 0.936254i \(0.385732\pi\)
−0.986482 + 0.163873i \(0.947601\pi\)
\(90\) −0.829819 −0.0874706
\(91\) 0 0
\(92\) −5.97840 −0.623291
\(93\) −1.46901 + 2.54439i −0.152329 + 0.263841i
\(94\) 10.8369 + 18.7700i 1.11774 + 1.93598i
\(95\) 0.133392 + 0.231042i 0.0136858 + 0.0237045i
\(96\) −7.88721 + 13.6611i −0.804986 + 1.39428i
\(97\) −19.4727 −1.97716 −0.988578 0.150709i \(-0.951844\pi\)
−0.988578 + 0.150709i \(0.951844\pi\)
\(98\) 3.63129 12.4900i 0.366815 1.26168i
\(99\) 9.46448 0.951216
\(100\) 3.60361 6.24164i 0.360361 0.624164i
\(101\) 8.46697 + 14.6652i 0.842495 + 1.45924i 0.887779 + 0.460270i \(0.152247\pi\)
−0.0452843 + 0.998974i \(0.514419\pi\)
\(102\) 1.79314 + 3.10580i 0.177547 + 0.307520i
\(103\) 3.61712 6.26504i 0.356406 0.617313i −0.630952 0.775822i \(-0.717335\pi\)
0.987357 + 0.158509i \(0.0506688\pi\)
\(104\) 0 0
\(105\) 1.18923 0.143797i 0.116057 0.0140331i
\(106\) −8.63667 −0.838867
\(107\) 4.92625 8.53251i 0.476238 0.824869i −0.523391 0.852093i \(-0.675333\pi\)
0.999629 + 0.0272237i \(0.00866664\pi\)
\(108\) 1.22853 + 2.12788i 0.118216 + 0.204756i
\(109\) −6.90796 11.9649i −0.661662 1.14603i −0.980179 0.198115i \(-0.936518\pi\)
0.318516 0.947917i \(-0.396815\pi\)
\(110\) 0.766969 1.32843i 0.0731277 0.126661i
\(111\) −6.98509 −0.662995
\(112\) 4.97847 11.6687i 0.470421 1.10259i
\(113\) −4.26864 −0.401560 −0.200780 0.979636i \(-0.564348\pi\)
−0.200780 + 0.979636i \(0.564348\pi\)
\(114\) −2.88109 + 4.99019i −0.269839 + 0.467374i
\(115\) 0.406092 + 0.703371i 0.0378682 + 0.0655897i
\(116\) 5.98437 + 10.3652i 0.555635 + 0.962388i
\(117\) 0 0
\(118\) 11.2569 1.03629
\(119\) −1.33629 1.78014i −0.122498 0.163185i
\(120\) 0.460394 0.0420280
\(121\) −3.24765 + 5.62509i −0.295240 + 0.511372i
\(122\) −10.5596 18.2898i −0.956026 1.65589i
\(123\) 6.19049 + 10.7222i 0.558178 + 0.966792i
\(124\) −0.930276 + 1.61129i −0.0835412 + 0.144698i
\(125\) −1.96593 −0.175839
\(126\) 6.67833 + 8.89649i 0.594953 + 0.792562i
\(127\) −2.19024 −0.194352 −0.0971761 0.995267i \(-0.530981\pi\)
−0.0971761 + 0.995267i \(0.530981\pi\)
\(128\) 3.91516 6.78126i 0.346055 0.599385i
\(129\) −6.11114 10.5848i −0.538056 0.931941i
\(130\) 0 0
\(131\) −1.13806 + 1.97117i −0.0994326 + 0.172222i −0.911450 0.411411i \(-0.865036\pi\)
0.812017 + 0.583633i \(0.198369\pi\)
\(132\) 13.9400 1.21332
\(133\) 1.40347 3.28951i 0.121696 0.285237i
\(134\) 24.8938 2.15050
\(135\) 0.166900 0.289079i 0.0143645 0.0248800i
\(136\) −0.427743 0.740873i −0.0366787 0.0635293i
\(137\) 6.72399 + 11.6463i 0.574469 + 0.995010i 0.996099 + 0.0882417i \(0.0281248\pi\)
−0.421630 + 0.906768i \(0.638542\pi\)
\(138\) −8.77101 + 15.1918i −0.746638 + 1.29321i
\(139\) 4.04540 0.343126 0.171563 0.985173i \(-0.445118\pi\)
0.171563 + 0.985173i \(0.445118\pi\)
\(140\) 0.753106 0.0910619i 0.0636490 0.00769614i
\(141\) 26.7582 2.25344
\(142\) 5.54698 9.60765i 0.465492 0.806256i
\(143\) 0 0
\(144\) 5.42494 + 9.39628i 0.452079 + 0.783023i
\(145\) 0.812996 1.40815i 0.0675156 0.116940i
\(146\) 7.21982 0.597517
\(147\) −11.1125 11.5925i −0.916545 0.956135i
\(148\) −4.42344 −0.363605
\(149\) 7.67596 13.2952i 0.628840 1.08918i −0.358945 0.933359i \(-0.616864\pi\)
0.987785 0.155823i \(-0.0498031\pi\)
\(150\) −10.5738 18.3144i −0.863351 1.49537i
\(151\) 3.06054 + 5.30101i 0.249063 + 0.431390i 0.963266 0.268548i \(-0.0865439\pi\)
−0.714203 + 0.699939i \(0.753211\pi\)
\(152\) 0.687268 1.19038i 0.0557448 0.0965528i
\(153\) 1.90366 0.153902
\(154\) −20.4146 + 2.46844i −1.64506 + 0.198912i
\(155\) 0.252762 0.0203023
\(156\) 0 0
\(157\) −2.26834 3.92888i −0.181033 0.313559i 0.761199 0.648518i \(-0.224611\pi\)
−0.942233 + 0.334959i \(0.891278\pi\)
\(158\) −9.97217 17.2723i −0.793343 1.37411i
\(159\) −5.33137 + 9.23421i −0.422805 + 0.732320i
\(160\) 1.35710 0.107288
\(161\) 4.27265 10.0144i 0.336732 0.789245i
\(162\) 19.8233 1.55746
\(163\) 0.911271 1.57837i 0.0713762 0.123627i −0.828128 0.560538i \(-0.810594\pi\)
0.899505 + 0.436911i \(0.143928\pi\)
\(164\) 3.92025 + 6.79007i 0.306120 + 0.530215i
\(165\) −0.946893 1.64007i −0.0737155 0.127679i
\(166\) −2.85590 + 4.94656i −0.221661 + 0.383928i
\(167\) 10.7079 0.828606 0.414303 0.910139i \(-0.364025\pi\)
0.414303 + 0.910139i \(0.364025\pi\)
\(168\) −3.70522 4.93588i −0.285864 0.380812i
\(169\) 0 0
\(170\) 0.154266 0.267197i 0.0118317 0.0204931i
\(171\) 1.52934 + 2.64889i 0.116951 + 0.202566i
\(172\) −3.87000 6.70303i −0.295085 0.511102i
\(173\) 6.74634 11.6850i 0.512915 0.888395i −0.486973 0.873417i \(-0.661899\pi\)
0.999888 0.0149778i \(-0.00476775\pi\)
\(174\) 35.1191 2.66237
\(175\) 7.87992 + 10.4972i 0.595666 + 0.793512i
\(176\) −20.0563 −1.51180
\(177\) 6.94886 12.0358i 0.522308 0.904664i
\(178\) 11.1342 + 19.2851i 0.834547 + 1.44548i
\(179\) −5.23458 9.06657i −0.391251 0.677667i 0.601364 0.798975i \(-0.294624\pi\)
−0.992615 + 0.121309i \(0.961291\pi\)
\(180\) −0.324388 + 0.561857i −0.0241785 + 0.0418783i
\(181\) 12.5209 0.930674 0.465337 0.885133i \(-0.345933\pi\)
0.465337 + 0.885133i \(0.345933\pi\)
\(182\) 0 0
\(183\) −26.0737 −1.92742
\(184\) 2.09228 3.62393i 0.154245 0.267160i
\(185\) 0.300469 + 0.520428i 0.0220909 + 0.0382626i
\(186\) 2.72965 + 4.72789i 0.200148 + 0.346666i
\(187\) −1.75948 + 3.04751i −0.128666 + 0.222856i
\(188\) 16.9451 1.23585
\(189\) −4.44242 + 0.537156i −0.323139 + 0.0390724i
\(190\) 0.495729 0.0359640
\(191\) −6.55685 + 11.3568i −0.474437 + 0.821749i −0.999572 0.0292704i \(-0.990682\pi\)
0.525135 + 0.851019i \(0.324015\pi\)
\(192\) 3.65565 + 6.33176i 0.263823 + 0.456956i
\(193\) 0.520786 + 0.902028i 0.0374870 + 0.0649294i 0.884160 0.467184i \(-0.154731\pi\)
−0.846673 + 0.532113i \(0.821398\pi\)
\(194\) −18.0917 + 31.3358i −1.29891 + 2.24978i
\(195\) 0 0
\(196\) −7.03722 7.34118i −0.502658 0.524370i
\(197\) −1.47833 −0.105327 −0.0526635 0.998612i \(-0.516771\pi\)
−0.0526635 + 0.998612i \(0.516771\pi\)
\(198\) 8.79326 15.2304i 0.624910 1.08238i
\(199\) −7.04993 12.2108i −0.499756 0.865603i 0.500244 0.865885i \(-0.333244\pi\)
−1.00000 0.000281618i \(0.999910\pi\)
\(200\) 2.52233 + 4.36881i 0.178356 + 0.308922i
\(201\) 15.3668 26.6162i 1.08389 1.87736i
\(202\) 31.4660 2.21394
\(203\) −21.6397 + 2.61657i −1.51881 + 0.183647i
\(204\) 2.80385 0.196309
\(205\) 0.532578 0.922451i 0.0371968 0.0644268i
\(206\) −6.72120 11.6415i −0.468288 0.811099i
\(207\) 4.65582 + 8.06412i 0.323602 + 0.560495i
\(208\) 0 0
\(209\) −5.65402 −0.391097
\(210\) 0.873495 2.04733i 0.0602769 0.141279i
\(211\) 26.4692 1.82222 0.911108 0.412167i \(-0.135228\pi\)
0.911108 + 0.412167i \(0.135228\pi\)
\(212\) −3.37619 + 5.84774i −0.231878 + 0.401624i
\(213\) −6.84825 11.8615i −0.469234 0.812737i
\(214\) −9.15376 15.8548i −0.625738 1.08381i
\(215\) −0.525751 + 0.910628i −0.0358559 + 0.0621043i
\(216\) −1.71981 −0.117019
\(217\) −2.03421 2.70986i −0.138091 0.183957i
\(218\) −25.6722 −1.73874
\(219\) 4.45676 7.71934i 0.301160 0.521625i
\(220\) −0.599638 1.03860i −0.0404276 0.0700227i
\(221\) 0 0
\(222\) −6.48971 + 11.2405i −0.435561 + 0.754414i
\(223\) 0.728048 0.0487537 0.0243769 0.999703i \(-0.492240\pi\)
0.0243769 + 0.999703i \(0.492240\pi\)
\(224\) −10.9218 14.5495i −0.729746 0.972126i
\(225\) −11.2256 −0.748373
\(226\) −3.96591 + 6.86916i −0.263808 + 0.456929i
\(227\) −1.42598 2.46986i −0.0946454 0.163931i 0.814815 0.579721i \(-0.196838\pi\)
−0.909461 + 0.415790i \(0.863505\pi\)
\(228\) 2.25252 + 3.90147i 0.149177 + 0.258381i
\(229\) 1.58676 2.74835i 0.104856 0.181616i −0.808823 0.588052i \(-0.799895\pi\)
0.913679 + 0.406436i \(0.133228\pi\)
\(230\) 1.50917 0.0995116
\(231\) −9.96262 + 23.3508i −0.655492 + 1.53637i
\(232\) −8.37748 −0.550009
\(233\) −6.70354 + 11.6109i −0.439163 + 0.760653i −0.997625 0.0688769i \(-0.978058\pi\)
0.558462 + 0.829530i \(0.311392\pi\)
\(234\) 0 0
\(235\) −1.15102 1.99363i −0.0750845 0.130050i
\(236\) 4.40050 7.62188i 0.286448 0.496142i
\(237\) −24.6231 −1.59944
\(238\) −4.10614 + 0.496495i −0.266162 + 0.0321830i
\(239\) 15.5538 1.00609 0.503046 0.864259i \(-0.332212\pi\)
0.503046 + 0.864259i \(0.332212\pi\)
\(240\) 1.08550 1.88014i 0.0700687 0.121363i
\(241\) −3.78787 6.56078i −0.243998 0.422617i 0.717851 0.696196i \(-0.245126\pi\)
−0.961849 + 0.273579i \(0.911792\pi\)
\(242\) 6.03465 + 10.4523i 0.387922 + 0.671900i
\(243\) 9.69985 16.8006i 0.622245 1.07776i
\(244\) −16.5117 −1.05705
\(245\) −0.385693 + 1.32661i −0.0246410 + 0.0847537i
\(246\) 23.0059 1.46680
\(247\) 0 0
\(248\) −0.651143 1.12781i −0.0413476 0.0716162i
\(249\) 3.52587 + 6.10698i 0.223443 + 0.387014i
\(250\) −1.82651 + 3.16361i −0.115519 + 0.200084i
\(251\) 1.27476 0.0804624 0.0402312 0.999190i \(-0.487191\pi\)
0.0402312 + 0.999190i \(0.487191\pi\)
\(252\) 8.63432 1.04402i 0.543911 0.0657671i
\(253\) −17.2128 −1.08216
\(254\) −2.03491 + 3.52456i −0.127682 + 0.221151i
\(255\) −0.190456 0.329879i −0.0119268 0.0206578i
\(256\) −10.4620 18.1208i −0.653878 1.13255i
\(257\) 4.24010 7.34406i 0.264490 0.458110i −0.702940 0.711249i \(-0.748130\pi\)
0.967430 + 0.253139i \(0.0814631\pi\)
\(258\) −22.7110 −1.41392
\(259\) 3.16135 7.40970i 0.196437 0.460416i
\(260\) 0 0
\(261\) 9.32095 16.1444i 0.576952 0.999311i
\(262\) 2.11470 + 3.66276i 0.130646 + 0.226286i
\(263\) −6.39415 11.0750i −0.394280 0.682913i 0.598729 0.800952i \(-0.295673\pi\)
−0.993009 + 0.118038i \(0.962339\pi\)
\(264\) −4.87861 + 8.45000i −0.300258 + 0.520062i
\(265\) 0.917333 0.0563513
\(266\) −3.98959 5.31471i −0.244618 0.325866i
\(267\) 27.4925 1.68251
\(268\) 9.73135 16.8552i 0.594437 1.02959i
\(269\) 2.35586 + 4.08047i 0.143639 + 0.248790i 0.928864 0.370420i \(-0.120786\pi\)
−0.785225 + 0.619210i \(0.787453\pi\)
\(270\) −0.310127 0.537156i −0.0188737 0.0326903i
\(271\) −9.00562 + 15.5982i −0.547052 + 0.947522i 0.451422 + 0.892310i \(0.350917\pi\)
−0.998475 + 0.0552119i \(0.982417\pi\)
\(272\) −4.03407 −0.244601
\(273\) 0 0
\(274\) 24.9885 1.50961
\(275\) 10.3754 17.9707i 0.625659 1.08367i
\(276\) 6.85742 + 11.8774i 0.412768 + 0.714936i
\(277\) 13.0604 + 22.6213i 0.784725 + 1.35918i 0.929163 + 0.369670i \(0.120529\pi\)
−0.144438 + 0.989514i \(0.546137\pi\)
\(278\) 3.75850 6.50991i 0.225420 0.390439i
\(279\) 2.89790 0.173493
\(280\) −0.208368 + 0.488380i −0.0124523 + 0.0291863i
\(281\) 3.66197 0.218455 0.109227 0.994017i \(-0.465162\pi\)
0.109227 + 0.994017i \(0.465162\pi\)
\(282\) 24.8605 43.0596i 1.48042 2.56416i
\(283\) −3.82263 6.62099i −0.227232 0.393577i 0.729755 0.683709i \(-0.239634\pi\)
−0.956987 + 0.290132i \(0.906301\pi\)
\(284\) −4.33678 7.51153i −0.257341 0.445727i
\(285\) 0.306011 0.530027i 0.0181265 0.0313961i
\(286\) 0 0
\(287\) −14.1757 + 1.71406i −0.836768 + 0.101178i
\(288\) 15.5591 0.916827
\(289\) 8.14610 14.1095i 0.479183 0.829968i
\(290\) −1.51068 2.61657i −0.0887100 0.153650i
\(291\) 22.3359 + 38.6869i 1.30935 + 2.26787i
\(292\) 2.82233 4.88842i 0.165164 0.286073i
\(293\) 17.1534 1.00211 0.501056 0.865415i \(-0.332945\pi\)
0.501056 + 0.865415i \(0.332945\pi\)
\(294\) −28.9793 + 7.11205i −1.69011 + 0.414783i
\(295\) −1.19564 −0.0696130
\(296\) 1.54809 2.68136i 0.0899807 0.155851i
\(297\) 3.53715 + 6.12652i 0.205246 + 0.355497i
\(298\) −14.2632 24.7045i −0.826244 1.43110i
\(299\) 0 0
\(300\) −16.5339 −0.954583
\(301\) 13.9940 1.69209i 0.806604 0.0975306i
\(302\) 11.3740 0.654498
\(303\) 19.4238 33.6430i 1.11587 1.93274i
\(304\) −3.24083 5.61328i −0.185874 0.321944i
\(305\) 1.12158 + 1.94263i 0.0642215 + 0.111235i
\(306\) 1.76866 3.06340i 0.101107 0.175123i
\(307\) 28.0696 1.60201 0.801007 0.598655i \(-0.204298\pi\)
0.801007 + 0.598655i \(0.204298\pi\)
\(308\) −6.30902 + 14.7873i −0.359490 + 0.842586i
\(309\) −16.5959 −0.944105
\(310\) 0.234836 0.406748i 0.0133378 0.0231017i
\(311\) 11.7670 + 20.3811i 0.667248 + 1.15571i 0.978671 + 0.205436i \(0.0658611\pi\)
−0.311423 + 0.950271i \(0.600806\pi\)
\(312\) 0 0
\(313\) 1.67430 2.89997i 0.0946370 0.163916i −0.814820 0.579714i \(-0.803164\pi\)
0.909457 + 0.415798i \(0.136498\pi\)
\(314\) −8.42989 −0.475726
\(315\) −0.709330 0.944930i −0.0399662 0.0532408i
\(316\) −15.5930 −0.877177
\(317\) −3.63917 + 6.30323i −0.204396 + 0.354025i −0.949940 0.312432i \(-0.898856\pi\)
0.745544 + 0.666456i \(0.232190\pi\)
\(318\) 9.90655 + 17.1586i 0.555532 + 0.962209i
\(319\) 17.2300 + 29.8432i 0.964694 + 1.67090i
\(320\) 0.314501 0.544732i 0.0175811 0.0304514i
\(321\) −22.6023 −1.26154
\(322\) −12.1457 16.1798i −0.676852 0.901664i
\(323\) −1.13724 −0.0632775
\(324\) 7.74919 13.4220i 0.430511 0.745666i
\(325\) 0 0
\(326\) −1.69329 2.93286i −0.0937826 0.162436i
\(327\) −15.8473 + 27.4484i −0.876359 + 1.51790i
\(328\) −5.48792 −0.303020
\(329\) −12.1104 + 28.3847i −0.667666 + 1.56490i
\(330\) −3.51896 −0.193712
\(331\) −7.16168 + 12.4044i −0.393642 + 0.681807i −0.992927 0.118728i \(-0.962118\pi\)
0.599285 + 0.800536i \(0.295452\pi\)
\(332\) 2.23282 + 3.86736i 0.122542 + 0.212249i
\(333\) 3.44486 + 5.96668i 0.188777 + 0.326972i
\(334\) 9.94855 17.2314i 0.544360 0.942860i
\(335\) −2.64407 −0.144461
\(336\) −28.8930 + 3.49360i −1.57624 + 0.190592i
\(337\) 17.1802 0.935868 0.467934 0.883764i \(-0.344999\pi\)
0.467934 + 0.883764i \(0.344999\pi\)
\(338\) 0 0
\(339\) 4.89627 + 8.48060i 0.265929 + 0.460603i
\(340\) −0.120610 0.208902i −0.00654098 0.0113293i
\(341\) −2.67841 + 4.63915i −0.145044 + 0.251224i
\(342\) 5.68351 0.307329
\(343\) 17.3266 6.54142i 0.935547 0.353203i
\(344\) 5.41758 0.292096
\(345\) 0.931602 1.61358i 0.0501558 0.0868723i
\(346\) −12.5358 21.7126i −0.673928 1.16728i
\(347\) 3.85139 + 6.67080i 0.206753 + 0.358107i 0.950690 0.310143i \(-0.100377\pi\)
−0.743937 + 0.668250i \(0.767044\pi\)
\(348\) 13.7286 23.7786i 0.735928 1.27466i
\(349\) −22.3701 −1.19744 −0.598721 0.800958i \(-0.704324\pi\)
−0.598721 + 0.800958i \(0.704324\pi\)
\(350\) 24.2133 2.92776i 1.29426 0.156495i
\(351\) 0 0
\(352\) −14.3806 + 24.9080i −0.766490 + 1.32760i
\(353\) −11.1311 19.2797i −0.592451 1.02616i −0.993901 0.110275i \(-0.964827\pi\)
0.401450 0.915881i \(-0.368506\pi\)
\(354\) −12.9121 22.3644i −0.686270 1.18865i
\(355\) −0.589165 + 1.02046i −0.0312697 + 0.0541606i
\(356\) 17.4101 0.922735
\(357\) −2.00386 + 4.69672i −0.106055 + 0.248577i
\(358\) −19.4534 −1.02814
\(359\) −1.37921 + 2.38887i −0.0727920 + 0.126079i −0.900124 0.435634i \(-0.856524\pi\)
0.827332 + 0.561713i \(0.189858\pi\)
\(360\) −0.227054 0.393269i −0.0119668 0.0207271i
\(361\) 8.58638 + 14.8721i 0.451915 + 0.782740i
\(362\) 11.6330 20.1489i 0.611415 1.05900i
\(363\) 14.9006 0.782081
\(364\) 0 0
\(365\) −0.766844 −0.0401385
\(366\) −24.2246 + 41.9582i −1.26624 + 2.19319i
\(367\) 7.07485 + 12.2540i 0.369304 + 0.639654i 0.989457 0.144827i \(-0.0462626\pi\)
−0.620153 + 0.784481i \(0.712929\pi\)
\(368\) −9.86618 17.0887i −0.514310 0.890812i
\(369\) 6.10597 10.5759i 0.317864 0.550557i
\(370\) 1.11664 0.0580514
\(371\) −7.38263 9.83472i −0.383287 0.510593i
\(372\) 4.26823 0.221298
\(373\) 2.52142 4.36723i 0.130554 0.226127i −0.793336 0.608784i \(-0.791658\pi\)
0.923890 + 0.382657i \(0.124991\pi\)
\(374\) 3.26940 + 5.66276i 0.169056 + 0.292814i
\(375\) 2.25499 + 3.90576i 0.116447 + 0.201693i
\(376\) −5.93034 + 10.2716i −0.305834 + 0.529720i
\(377\) 0 0
\(378\) −3.26297 + 7.64787i −0.167829 + 0.393364i
\(379\) 6.05964 0.311263 0.155631 0.987815i \(-0.450259\pi\)
0.155631 + 0.987815i \(0.450259\pi\)
\(380\) 0.193787 0.335650i 0.00994109 0.0172185i
\(381\) 2.51228 + 4.35139i 0.128708 + 0.222929i
\(382\) 12.1837 + 21.1028i 0.623371 + 1.07971i
\(383\) −2.27052 + 3.93266i −0.116018 + 0.200950i −0.918186 0.396149i \(-0.870346\pi\)
0.802168 + 0.597098i \(0.203680\pi\)
\(384\) −17.9633 −0.916686
\(385\) 2.16831 0.262182i 0.110507 0.0133620i
\(386\) 1.93541 0.0985098
\(387\) −6.02771 + 10.4403i −0.306406 + 0.530710i
\(388\) 14.1446 + 24.4992i 0.718085 + 1.24376i
\(389\) −2.25383 3.90374i −0.114273 0.197927i 0.803216 0.595688i \(-0.203121\pi\)
−0.917489 + 0.397761i \(0.869787\pi\)
\(390\) 0 0
\(391\) −3.46213 −0.175088
\(392\) 6.91285 1.69654i 0.349152 0.0856883i
\(393\) 5.22157 0.263393
\(394\) −1.37349 + 2.37896i −0.0691955 + 0.119850i
\(395\) 1.05918 + 1.83456i 0.0532932 + 0.0923065i
\(396\) −6.87482 11.9075i −0.345473 0.598376i
\(397\) 2.00174 3.46712i 0.100465 0.174010i −0.811412 0.584475i \(-0.801300\pi\)
0.911876 + 0.410465i \(0.134634\pi\)
\(398\) −26.1998 −1.31328
\(399\) −8.14518 + 0.984875i −0.407769 + 0.0493054i
\(400\) 23.7883 1.18941
\(401\) 6.30674 10.9236i 0.314944 0.545498i −0.664482 0.747304i \(-0.731348\pi\)
0.979426 + 0.201806i \(0.0646810\pi\)
\(402\) −28.5541 49.4571i −1.42415 2.46670i
\(403\) 0 0
\(404\) 12.3005 21.3051i 0.611972 1.05997i
\(405\) −2.10550 −0.104623
\(406\) −15.8944 + 37.2539i −0.788826 + 1.84888i
\(407\) −12.7358 −0.631290
\(408\) −0.981272 + 1.69961i −0.0485802 + 0.0841434i
\(409\) 10.3476 + 17.9226i 0.511657 + 0.886216i 0.999909 + 0.0135128i \(0.00430140\pi\)
−0.488252 + 0.872703i \(0.662365\pi\)
\(410\) −0.989615 1.71406i −0.0488736 0.0846516i
\(411\) 15.4253 26.7174i 0.760873 1.31787i
\(412\) −10.5096 −0.517773
\(413\) 9.62244 + 12.8185i 0.473490 + 0.630756i
\(414\) 17.3025 0.850373
\(415\) 0.303336 0.525393i 0.0148902 0.0257905i
\(416\) 0 0
\(417\) −4.64021 8.03708i −0.227232 0.393577i
\(418\) −5.25304 + 9.09854i −0.256935 + 0.445024i
\(419\) −21.8175 −1.06586 −0.532928 0.846161i \(-0.678908\pi\)
−0.532928 + 0.846161i \(0.678908\pi\)
\(420\) −1.04475 1.39176i −0.0509787 0.0679109i
\(421\) −9.42727 −0.459457 −0.229728 0.973255i \(-0.573784\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(422\) 24.5920 42.5947i 1.19712 2.07348i
\(423\) −13.1964 22.8569i −0.641632 1.11134i
\(424\) −2.36315 4.09310i −0.114765 0.198779i
\(425\) 2.08688 3.61458i 0.101228 0.175333i
\(426\) −25.4503 −1.23307
\(427\) 11.8006 27.6586i 0.571070 1.33850i
\(428\) −14.3133 −0.691861
\(429\) 0 0
\(430\) 0.976930 + 1.69209i 0.0471118 + 0.0816000i
\(431\) 10.2138 + 17.6908i 0.491980 + 0.852134i 0.999957 0.00923613i \(-0.00293999\pi\)
−0.507977 + 0.861370i \(0.669607\pi\)
\(432\) −4.05491 + 7.02332i −0.195092 + 0.337909i
\(433\) 26.3486 1.26623 0.633117 0.774056i \(-0.281775\pi\)
0.633117 + 0.774056i \(0.281775\pi\)
\(434\) −6.25069 + 0.755803i −0.300043 + 0.0362797i
\(435\) −3.73014 −0.178846
\(436\) −10.0356 + 17.3822i −0.480619 + 0.832457i
\(437\) −2.78136 4.81745i −0.133050 0.230450i
\(438\) −8.28138 14.3438i −0.395700 0.685372i
\(439\) −12.5655 + 21.7641i −0.599720 + 1.03875i 0.393142 + 0.919478i \(0.371388\pi\)
−0.992862 + 0.119267i \(0.961945\pi\)
\(440\) 0.839429 0.0400182
\(441\) −4.42195 + 15.2095i −0.210569 + 0.724260i
\(442\) 0 0
\(443\) −9.25995 + 16.0387i −0.439953 + 0.762022i −0.997685 0.0679994i \(-0.978338\pi\)
0.557732 + 0.830021i \(0.311672\pi\)
\(444\) 5.07384 + 8.78815i 0.240794 + 0.417067i
\(445\) −1.18261 2.04834i −0.0560611 0.0971006i
\(446\) 0.676415 1.17159i 0.0320292 0.0554762i
\(447\) −35.2184 −1.66577
\(448\) −8.37115 + 1.01220i −0.395500 + 0.0478219i
\(449\) −11.6431 −0.549471 −0.274736 0.961520i \(-0.588590\pi\)
−0.274736 + 0.961520i \(0.588590\pi\)
\(450\) −10.4295 + 18.0644i −0.491651 + 0.851564i
\(451\) 11.2870 + 19.5497i 0.531485 + 0.920559i
\(452\) 3.10066 + 5.37050i 0.145843 + 0.252607i
\(453\) 7.02109 12.1609i 0.329880 0.571368i
\(454\) −5.29939 −0.248713
\(455\) 0 0
\(456\) −3.15328 −0.147666
\(457\) 10.2592 17.7695i 0.479906 0.831222i −0.519828 0.854271i \(-0.674004\pi\)
0.999734 + 0.0230490i \(0.00733739\pi\)
\(458\) −2.94845 5.10687i −0.137772 0.238629i
\(459\) 0.711453 + 1.23227i 0.0332078 + 0.0575176i
\(460\) 0.589955 1.02183i 0.0275068 0.0476431i
\(461\) −2.04075 −0.0950473 −0.0475236 0.998870i \(-0.515133\pi\)
−0.0475236 + 0.998870i \(0.515133\pi\)
\(462\) 28.3203 + 37.7268i 1.31758 + 1.75521i
\(463\) −3.03155 −0.140888 −0.0704441 0.997516i \(-0.522442\pi\)
−0.0704441 + 0.997516i \(0.522442\pi\)
\(464\) −19.7521 + 34.2116i −0.916968 + 1.58824i
\(465\) −0.289926 0.502167i −0.0134450 0.0232874i
\(466\) 12.4563 + 21.5749i 0.577025 + 0.999436i
\(467\) 6.46371 11.1955i 0.299105 0.518065i −0.676827 0.736142i \(-0.736645\pi\)
0.975931 + 0.218078i \(0.0699787\pi\)
\(468\) 0 0
\(469\) 21.2793 + 28.3470i 0.982585 + 1.30894i
\(470\) −4.27757 −0.197310
\(471\) −5.20373 + 9.01312i −0.239775 + 0.415303i
\(472\) 3.08011 + 5.33491i 0.141774 + 0.245559i
\(473\) −11.1423 19.2991i −0.512326 0.887374i
\(474\) −22.8768 + 39.6238i −1.05077 + 1.81998i
\(475\) 6.70611 0.307697
\(476\) −1.26898 + 2.97429i −0.0581637 + 0.136326i
\(477\) 10.5172 0.481548
\(478\) 14.4507 25.0294i 0.660962 1.14482i
\(479\) 18.2911 + 31.6810i 0.835740 + 1.44754i 0.893427 + 0.449209i \(0.148294\pi\)
−0.0576873 + 0.998335i \(0.518373\pi\)
\(480\) −1.55664 2.69618i −0.0710505 0.123063i
\(481\) 0 0
\(482\) −14.0769 −0.641187
\(483\) −24.7967 + 2.99830i −1.12829 + 0.136427i
\(484\) 9.43611 0.428914
\(485\) 1.92159 3.32829i 0.0872550 0.151130i
\(486\) −18.0239 31.2183i −0.817580 1.41609i
\(487\) 18.3748 + 31.8261i 0.832642 + 1.44218i 0.895936 + 0.444183i \(0.146506\pi\)
−0.0632939 + 0.997995i \(0.520161\pi\)
\(488\) 5.77864 10.0089i 0.261587 0.453081i
\(489\) −4.18103 −0.189073
\(490\) 1.77645 + 1.85319i 0.0802520 + 0.0837184i
\(491\) −8.19797 −0.369969 −0.184985 0.982741i \(-0.559224\pi\)
−0.184985 + 0.982741i \(0.559224\pi\)
\(492\) 8.99331 15.5769i 0.405450 0.702260i
\(493\) 3.46560 + 6.00259i 0.156083 + 0.270343i
\(494\) 0 0
\(495\) −0.933965 + 1.61768i −0.0419786 + 0.0727091i
\(496\) −6.14096 −0.275737
\(497\) 15.6820 1.89619i 0.703432 0.0850556i
\(498\) 13.1033 0.587171
\(499\) −21.6266 + 37.4584i −0.968141 + 1.67687i −0.267211 + 0.963638i \(0.586102\pi\)
−0.700929 + 0.713231i \(0.747231\pi\)
\(500\) 1.42802 + 2.47340i 0.0638629 + 0.110614i
\(501\) −12.2824 21.2737i −0.548736 0.950439i
\(502\) 1.18436 2.05137i 0.0528605 0.0915571i
\(503\) 0.0181922 0.000811149 0.000405575 1.00000i \(-0.499871\pi\)
0.000405575 1.00000i \(0.499871\pi\)
\(504\) −2.38892 + 5.59925i −0.106411 + 0.249411i
\(505\) −3.34212 −0.148722
\(506\) −15.9920 + 27.6990i −0.710933 + 1.23137i
\(507\) 0 0
\(508\) 1.59095 + 2.75560i 0.0705869 + 0.122260i
\(509\) 21.5503 37.3262i 0.955200 1.65446i 0.221292 0.975208i \(-0.428973\pi\)
0.733909 0.679248i \(-0.237694\pi\)
\(510\) −0.707795 −0.0313417
\(511\) 6.17151 + 8.22134i 0.273012 + 0.363691i
\(512\) −23.2197 −1.02617
\(513\) −1.14311 + 1.97993i −0.0504697 + 0.0874161i
\(514\) −7.87878 13.6464i −0.347518 0.601919i
\(515\) 0.713884 + 1.23648i 0.0314575 + 0.0544859i
\(516\) −8.87804 + 15.3772i −0.390834 + 0.676944i
\(517\) 48.7877 2.14568
\(518\) −8.98664 11.9715i −0.394850 0.525997i
\(519\) −30.9531 −1.35869
\(520\) 0 0
\(521\) −10.4770 18.1467i −0.459006 0.795022i 0.539903 0.841727i \(-0.318461\pi\)
−0.998909 + 0.0467056i \(0.985128\pi\)
\(522\) −17.3198 29.9988i −0.758068 1.31301i
\(523\) 17.3701 30.0860i 0.759543 1.31557i −0.183541 0.983012i \(-0.558756\pi\)
0.943084 0.332555i \(-0.107911\pi\)
\(524\) 3.30666 0.144452
\(525\) 11.8164 27.6958i 0.515712 1.20875i
\(526\) −23.7627 −1.03610
\(527\) −0.538730 + 0.933107i −0.0234674 + 0.0406468i
\(528\) 23.0052 + 39.8462i 1.00117 + 1.73408i
\(529\) 3.03260 + 5.25262i 0.131852 + 0.228375i
\(530\) 0.852276 1.47619i 0.0370205 0.0641214i
\(531\) −13.7080 −0.594875
\(532\) −5.15809 + 0.623691i −0.223631 + 0.0270404i
\(533\) 0 0
\(534\) 25.5427 44.2413i 1.10534 1.91451i
\(535\) 0.972255 + 1.68400i 0.0420343 + 0.0728055i
\(536\) 6.81142 + 11.7977i 0.294209 + 0.509584i
\(537\) −12.0085 + 20.7993i −0.518205 + 0.897557i
\(538\) 8.75513 0.377460
\(539\) −20.2613 21.1365i −0.872715 0.910411i
\(540\) −0.484932 −0.0208682
\(541\) −1.64923 + 2.85655i −0.0709059 + 0.122813i −0.899299 0.437335i \(-0.855922\pi\)
0.828393 + 0.560148i \(0.189256\pi\)
\(542\) 16.7339 + 28.9839i 0.718782 + 1.24497i
\(543\) −14.3619 24.8756i −0.616330 1.06752i
\(544\) −2.89249 + 5.00993i −0.124014 + 0.214799i
\(545\) 2.72674 0.116801
\(546\) 0 0
\(547\) 21.9417 0.938161 0.469080 0.883155i \(-0.344585\pi\)
0.469080 + 0.883155i \(0.344585\pi\)
\(548\) 9.76836 16.9193i 0.417284 0.722756i
\(549\) 12.8589 + 22.2722i 0.548803 + 0.950554i
\(550\) −19.2791 33.3924i −0.822065 1.42386i
\(551\) −5.56828 + 9.64455i −0.237217 + 0.410871i
\(552\) −9.59965 −0.408588
\(553\) 11.1440 26.1199i 0.473893 1.11073i
\(554\) 48.5368 2.06213
\(555\) 0.689297 1.19390i 0.0292590 0.0506781i
\(556\) −2.93850 5.08963i −0.124620 0.215848i
\(557\) −7.14329 12.3725i −0.302671 0.524241i 0.674069 0.738668i \(-0.264545\pi\)
−0.976740 + 0.214427i \(0.931212\pi\)
\(558\) 2.69238 4.66334i 0.113978 0.197415i
\(559\) 0 0
\(560\) 1.50315 + 2.00241i 0.0635196 + 0.0846172i
\(561\) 8.07273 0.340831
\(562\) 3.40226 5.89289i 0.143516 0.248577i
\(563\) −3.39392 5.87844i −0.143037 0.247747i 0.785602 0.618732i \(-0.212353\pi\)
−0.928639 + 0.370985i \(0.879020\pi\)
\(564\) −19.4366 33.6652i −0.818430 1.41756i
\(565\) 0.421234 0.729599i 0.0177215 0.0306945i
\(566\) −14.2061 −0.597128
\(567\) 16.9449 + 22.5731i 0.711621 + 0.947981i
\(568\) 6.07103 0.254735
\(569\) 8.66061 15.0006i 0.363072 0.628859i −0.625393 0.780310i \(-0.715061\pi\)
0.988465 + 0.151451i \(0.0483947\pi\)
\(570\) −0.568618 0.984875i −0.0238168 0.0412519i
\(571\) 6.50581 + 11.2684i 0.272260 + 0.471568i 0.969440 0.245328i \(-0.0788957\pi\)
−0.697180 + 0.716896i \(0.745562\pi\)
\(572\) 0 0
\(573\) 30.0837 1.25676
\(574\) −10.4121 + 24.4043i −0.434593 + 1.01862i
\(575\) 20.4157 0.851392
\(576\) 3.60574 6.24532i 0.150239 0.260222i
\(577\) −0.365767 0.633528i −0.0152271 0.0263741i 0.858311 0.513129i \(-0.171514\pi\)
−0.873539 + 0.486755i \(0.838180\pi\)
\(578\) −15.1368 26.2177i −0.629607 1.09051i
\(579\) 1.19472 2.06931i 0.0496508 0.0859978i
\(580\) −2.36218 −0.0980842
\(581\) −8.07396 + 0.976265i −0.334964 + 0.0405023i
\(582\) 83.0073 3.44076
\(583\) −9.72061 + 16.8366i −0.402586 + 0.697300i
\(584\) 1.97548 + 3.42163i 0.0817459 + 0.141588i
\(585\) 0 0
\(586\) 15.9369 27.6035i 0.658347 1.14029i
\(587\) 8.52284 0.351775 0.175888 0.984410i \(-0.443720\pi\)
0.175888 + 0.984410i \(0.443720\pi\)
\(588\) −6.51296 + 22.4016i −0.268590 + 0.923825i
\(589\) −1.73119 −0.0713323
\(590\) −1.11085 + 1.92404i −0.0457329 + 0.0792117i
\(591\) 1.69570 + 2.93704i 0.0697517 + 0.120814i
\(592\) −7.30004 12.6440i −0.300030 0.519667i
\(593\) −15.6547 + 27.1147i −0.642860 + 1.11347i 0.341932 + 0.939725i \(0.388919\pi\)
−0.984791 + 0.173741i \(0.944415\pi\)
\(594\) 13.1452 0.539353
\(595\) 0.436129 0.0527346i 0.0178795 0.00216191i
\(596\) −22.3027 −0.913554
\(597\) −16.1730 + 28.0125i −0.661917 + 1.14647i
\(598\) 0 0
\(599\) 0.375116 + 0.649720i 0.0153268 + 0.0265468i 0.873587 0.486668i \(-0.161788\pi\)
−0.858260 + 0.513215i \(0.828454\pi\)
\(600\) 5.78641 10.0224i 0.236229 0.409161i
\(601\) −9.55305 −0.389677 −0.194838 0.980835i \(-0.562418\pi\)
−0.194838 + 0.980835i \(0.562418\pi\)
\(602\) 10.2787 24.0915i 0.418927 0.981897i
\(603\) −30.3141 −1.23449
\(604\) 4.44624 7.70111i 0.180915 0.313354i
\(605\) −0.640963 1.11018i −0.0260588 0.0451352i
\(606\) −36.0925 62.5141i −1.46616 2.53946i
\(607\) −11.1197 + 19.2599i −0.451336 + 0.781737i −0.998469 0.0553087i \(-0.982386\pi\)
0.547133 + 0.837045i \(0.315719\pi\)
\(608\) −9.29489 −0.376958
\(609\) 30.0199 + 39.9908i 1.21647 + 1.62051i
\(610\) 4.16815 0.168764
\(611\) 0 0
\(612\) −1.38278 2.39505i −0.0558957 0.0968143i
\(613\) −4.13993 7.17057i −0.167210 0.289617i 0.770228 0.637769i \(-0.220143\pi\)
−0.937438 + 0.348152i \(0.886809\pi\)
\(614\) 26.0789 45.1699i 1.05246 1.82291i
\(615\) −2.44354 −0.0985330
\(616\) −6.75567 8.99952i −0.272194 0.362601i
\(617\) −20.3312 −0.818503 −0.409252 0.912422i \(-0.634210\pi\)
−0.409252 + 0.912422i \(0.634210\pi\)
\(618\) −15.4189 + 26.7063i −0.620238 + 1.07428i
\(619\) 2.67049 + 4.62542i 0.107336 + 0.185911i 0.914690 0.404156i \(-0.132435\pi\)
−0.807354 + 0.590067i \(0.799101\pi\)
\(620\) −0.183601 0.318007i −0.00737361 0.0127715i
\(621\) −3.48003 + 6.02758i −0.139649 + 0.241879i
\(622\) 43.7301 1.75342
\(623\) −12.4427 + 29.1636i −0.498506 + 1.16842i
\(624\) 0 0
\(625\) −12.2086 + 21.1459i −0.488345 + 0.845838i
\(626\) −3.11112 5.38862i −0.124345 0.215372i
\(627\) 6.48536 + 11.2330i 0.259000 + 0.448601i
\(628\) −3.29536 + 5.70773i −0.131499 + 0.227763i
\(629\) −2.56165 −0.102140
\(630\) −2.17962 + 0.263549i −0.0868381 + 0.0105001i
\(631\) −6.46662 −0.257432 −0.128716 0.991681i \(-0.541086\pi\)
−0.128716 + 0.991681i \(0.541086\pi\)
\(632\) 5.45714 9.45205i 0.217074 0.375982i
\(633\) −30.3611 52.5870i −1.20675 2.09014i
\(634\) 6.76217 + 11.7124i 0.268560 + 0.465160i
\(635\) 0.216135 0.374357i 0.00857707 0.0148559i
\(636\) 15.4904 0.614236
\(637\) 0 0
\(638\) 64.0322 2.53506
\(639\) −6.75475 + 11.6996i −0.267214 + 0.462828i
\(640\) 0.772706 + 1.33837i 0.0305439 + 0.0529035i
\(641\) −11.6644 20.2034i −0.460717 0.797985i 0.538280 0.842766i \(-0.319074\pi\)
−0.998997 + 0.0447808i \(0.985741\pi\)
\(642\) −20.9993 + 36.3719i −0.828778 + 1.43549i
\(643\) 3.58878 0.141527 0.0707637 0.997493i \(-0.477456\pi\)
0.0707637 + 0.997493i \(0.477456\pi\)
\(644\) −15.7030 + 1.89873i −0.618784 + 0.0748204i
\(645\) 2.41222 0.0949810
\(646\) −1.05658 + 1.83006i −0.0415707 + 0.0720026i
\(647\) 19.8262 + 34.3400i 0.779448 + 1.35004i 0.932260 + 0.361788i \(0.117834\pi\)
−0.152812 + 0.988255i \(0.548833\pi\)
\(648\) 5.42402 + 9.39467i 0.213076 + 0.369058i
\(649\) 12.6697 21.9446i 0.497331 0.861402i
\(650\) 0 0
\(651\) −3.05042 + 7.14970i −0.119556 + 0.280219i
\(652\) −2.64772 −0.103693
\(653\) −9.06777 + 15.7058i −0.354849 + 0.614617i −0.987092 0.160153i \(-0.948801\pi\)
0.632243 + 0.774770i \(0.282135\pi\)
\(654\) 29.4469 + 51.0035i 1.15146 + 1.99439i
\(655\) −0.224610 0.389035i −0.00877623 0.0152009i
\(656\) −12.9392 + 22.4114i −0.505192 + 0.875017i
\(657\) −8.79183 −0.343002
\(658\) 34.4256 + 45.8599i 1.34205 + 1.78780i
\(659\) 13.4810 0.525147 0.262573 0.964912i \(-0.415429\pi\)
0.262573 + 0.964912i \(0.415429\pi\)
\(660\) −1.37561 + 2.38263i −0.0535456 + 0.0927437i
\(661\) 5.15611 + 8.93064i 0.200549 + 0.347362i 0.948706 0.316161i \(-0.102394\pi\)
−0.748156 + 0.663523i \(0.769061\pi\)
\(662\) 13.3076 + 23.0494i 0.517213 + 0.895839i
\(663\) 0 0
\(664\) −3.12571 −0.121301
\(665\) 0.423750 + 0.564495i 0.0164323 + 0.0218902i
\(666\) 12.8022 0.496076
\(667\) −16.9517 + 29.3613i −0.656374 + 1.13687i
\(668\) −7.77805 13.4720i −0.300942 0.521247i
\(669\) −0.835096 1.44643i −0.0322867 0.0559222i
\(670\) −2.45655 + 4.25487i −0.0949049 + 0.164380i
\(671\) −47.5397 −1.83525
\(672\) −16.3780 + 38.3874i −0.631795 + 1.48082i
\(673\) −9.23056 −0.355812 −0.177906 0.984048i \(-0.556932\pi\)
−0.177906 + 0.984048i \(0.556932\pi\)
\(674\) 15.9618 27.6467i 0.614827 1.06491i
\(675\) −4.19533 7.26652i −0.161478 0.279689i
\(676\) 0 0
\(677\) 10.5467 18.2674i 0.405343 0.702075i −0.589018 0.808120i \(-0.700485\pi\)
0.994361 + 0.106045i \(0.0338187\pi\)
\(678\) 18.1961 0.698818
\(679\) −51.1475 + 6.18450i −1.96286 + 0.237340i
\(680\) 0.168841 0.00647474
\(681\) −3.27129 + 5.66604i −0.125356 + 0.217123i
\(682\) 4.97693 + 8.62029i 0.190576 + 0.330088i
\(683\) −19.1106 33.1005i −0.731246 1.26656i −0.956351 0.292221i \(-0.905606\pi\)
0.225104 0.974335i \(-0.427728\pi\)
\(684\) 2.22176 3.84821i 0.0849512 0.147140i
\(685\) −2.65412 −0.101409
\(686\) 5.57122 33.9597i 0.212710 1.29659i
\(687\) −7.28027 −0.277760
\(688\) 12.7734 22.1241i 0.486980 0.843474i
\(689\) 0 0
\(690\) −1.73107 2.99830i −0.0659006 0.114143i
\(691\) −13.1161 + 22.7178i −0.498960 + 0.864224i −0.999999 0.00120019i \(-0.999618\pi\)
0.501039 + 0.865425i \(0.332951\pi\)
\(692\) −19.6017 −0.745144
\(693\) 24.8596 3.00590i 0.944338 0.114185i
\(694\) 14.3130 0.543314
\(695\) −0.399204 + 0.691442i −0.0151427 + 0.0262279i
\(696\) 9.60925 + 16.6437i 0.364238 + 0.630878i
\(697\) 2.27024 + 3.93218i 0.0859916 + 0.148942i
\(698\) −20.7836 + 35.9982i −0.786670 + 1.36255i
\(699\) 30.7567 1.16333
\(700\) 7.48299 17.5389i 0.282830 0.662909i
\(701\) −46.7346 −1.76514 −0.882570 0.470180i \(-0.844189\pi\)
−0.882570 + 0.470180i \(0.844189\pi\)
\(702\) 0 0
\(703\) −2.05794 3.56446i −0.0776167 0.134436i
\(704\) 6.66528 + 11.5446i 0.251207 + 0.435104i
\(705\) −2.64053 + 4.57353i −0.0994480 + 0.172249i
\(706\) −41.3669 −1.55687
\(707\) 26.8972 + 35.8309i 1.01157 + 1.34756i
\(708\) −20.1901 −0.758789
\(709\) −23.7232 + 41.0898i −0.890944 + 1.54316i −0.0521988 + 0.998637i \(0.516623\pi\)
−0.838745 + 0.544524i \(0.816710\pi\)
\(710\) 1.09476 + 1.89619i 0.0410858 + 0.0711626i
\(711\) 12.1435 + 21.0331i 0.455415 + 0.788802i
\(712\) −6.09307 + 10.5535i −0.228348 + 0.395510i
\(713\) −5.27032 −0.197375
\(714\) 5.69629 + 7.58827i 0.213178 + 0.283984i
\(715\) 0 0
\(716\) −7.60461 + 13.1716i −0.284197 + 0.492244i
\(717\) −17.8408 30.9011i −0.666275 1.15402i
\(718\) 2.56280 + 4.43890i 0.0956428 + 0.165658i
\(719\) 24.6190 42.6413i 0.918133 1.59025i 0.115884 0.993263i \(-0.463030\pi\)
0.802249 0.596990i \(-0.203637\pi\)
\(720\) −2.14136 −0.0798037
\(721\) 7.51104 17.6047i 0.279726 0.655632i
\(722\) 31.9098 1.18756
\(723\) −8.68963 + 15.0509i −0.323171 + 0.559748i
\(724\) −9.09498 15.7530i −0.338012 0.585454i
\(725\) −20.4361 35.3963i −0.758977 1.31459i
\(726\) 13.8439 23.9783i 0.513795 0.889919i
\(727\) −32.0495 −1.18865 −0.594325 0.804225i \(-0.702581\pi\)
−0.594325 + 0.804225i \(0.702581\pi\)
\(728\) 0 0
\(729\) −12.4996 −0.462947
\(730\) −0.712460 + 1.23402i −0.0263693 + 0.0456730i
\(731\) −2.24114 3.88178i −0.0828917 0.143573i
\(732\) 18.9394 + 32.8041i 0.700022 + 1.21247i
\(733\) 14.1005 24.4228i 0.520813 0.902075i −0.478894 0.877873i \(-0.658962\pi\)
0.999707 0.0242025i \(-0.00770464\pi\)
\(734\) 26.2924 0.970472
\(735\) 3.07800 0.755398i 0.113534 0.0278633i
\(736\) −28.2968 −1.04303
\(737\) 28.0181 48.5288i 1.03206 1.78758i
\(738\) −11.3459 19.6516i −0.417648 0.723387i
\(739\) −21.2685 36.8381i −0.782375 1.35511i −0.930555 0.366153i \(-0.880675\pi\)
0.148180 0.988960i \(-0.452658\pi\)
\(740\) 0.436510 0.756058i 0.0160464 0.0277932i
\(741\) 0 0
\(742\) −22.6852 + 2.74299i −0.832801 + 0.100698i
\(743\) −15.9142 −0.583836 −0.291918 0.956443i \(-0.594294\pi\)
−0.291918 + 0.956443i \(0.594294\pi\)
\(744\) −1.49377 + 2.58728i −0.0547641 + 0.0948543i
\(745\) 1.51495 + 2.62396i 0.0555033 + 0.0961346i
\(746\) −4.68521 8.11502i −0.171538 0.297112i
\(747\) 3.47773 6.02360i 0.127243 0.220392i
\(748\) 5.11221 0.186921
\(749\) 10.2295 23.9762i 0.373777 0.876072i
\(750\) 8.38028 0.306005
\(751\) −9.09981 + 15.7613i −0.332057 + 0.575139i −0.982915 0.184060i \(-0.941076\pi\)
0.650858 + 0.759199i \(0.274409\pi\)
\(752\) 27.9646 + 48.4362i 1.01977 + 1.76629i
\(753\) −1.46220 2.53260i −0.0532855 0.0922931i
\(754\) 0 0
\(755\) −1.20807 −0.0439662
\(756\) 3.90270 + 5.19896i 0.141940 + 0.189084i
\(757\) −44.9004 −1.63193 −0.815967 0.578099i \(-0.803795\pi\)
−0.815967 + 0.578099i \(0.803795\pi\)
\(758\) 5.62989 9.75126i 0.204487 0.354182i
\(759\) 19.7436 + 34.1970i 0.716648 + 1.24127i
\(760\) 0.135641 + 0.234937i 0.00492021 + 0.00852205i
\(761\) −13.2444 + 22.9399i −0.480108 + 0.831572i −0.999740 0.0228184i \(-0.992736\pi\)
0.519631 + 0.854391i \(0.326069\pi\)
\(762\) 9.33644 0.338223
\(763\) −21.9446 29.2334i −0.794449 1.05832i
\(764\) 19.0511 0.689244
\(765\) −0.187856 + 0.325375i −0.00679193 + 0.0117640i
\(766\) 4.21900 + 7.30752i 0.152439 + 0.264031i
\(767\) 0 0
\(768\) −24.0006 + 41.5703i −0.866049 + 1.50004i
\(769\) −13.9625 −0.503502 −0.251751 0.967792i \(-0.581006\pi\)
−0.251751 + 0.967792i \(0.581006\pi\)
\(770\) 1.59263 3.73287i 0.0573944 0.134523i
\(771\) −19.4541 −0.700623
\(772\) 0.756579 1.31043i 0.0272299 0.0471635i
\(773\) 6.40564 + 11.0949i 0.230395 + 0.399056i 0.957924 0.287021i \(-0.0926648\pi\)
−0.727529 + 0.686077i \(0.759332\pi\)
\(774\) 11.2005 + 19.3998i 0.402592 + 0.697310i
\(775\) 3.17681 5.50239i 0.114114 0.197652i
\(776\) −19.8010 −0.710813
\(777\) −18.3472 + 2.21845i −0.658201 + 0.0795865i
\(778\) −8.37594 −0.300292
\(779\) −3.64767 + 6.31795i −0.130691 + 0.226364i
\(780\) 0 0
\(781\) −12.4863 21.6269i −0.446795 0.773871i
\(782\) −3.21660 + 5.57132i −0.115025 + 0.199230i
\(783\) 13.9340 0.497961
\(784\) 9.37058 32.2305i 0.334664 1.15109i
\(785\) 0.895370 0.0319571
\(786\) 4.85125 8.40262i 0.173039 0.299712i
\(787\) −13.6599 23.6597i −0.486924 0.843377i 0.512963 0.858411i \(-0.328548\pi\)
−0.999887 + 0.0150334i \(0.995215\pi\)
\(788\) 1.07383 + 1.85993i 0.0382537 + 0.0662574i
\(789\) −14.6686 + 25.4068i −0.522217 + 0.904506i
\(790\) 3.93626 0.140046
\(791\) −11.2121 + 1.35571i −0.398656 + 0.0482036i
\(792\) 9.62401 0.341974
\(793\) 0 0
\(794\) −3.71956 6.44247i −0.132002 0.228635i
\(795\) −1.05221 1.82248i −0.0373181 0.0646369i
\(796\) −10.2419 + 17.7394i −0.363013 + 0.628758i
\(797\) −29.4003 −1.04141 −0.520707 0.853736i \(-0.674332\pi\)
−0.520707 + 0.853736i \(0.674332\pi\)
\(798\) −5.98265 + 14.0224i −0.211783 + 0.496386i
\(799\) 9.81305 0.347161
\(800\) 17.0565 29.5428i 0.603040 1.04450i
\(801\) −13.5586 23.4841i −0.479068 0.829770i
\(802\) −11.7189 20.2978i −0.413810 0.716740i
\(803\) 8.12594 14.0745i 0.286758 0.496680i
\(804\) −44.6487 −1.57464
\(805\) 1.29004 + 1.71852i 0.0454679 + 0.0605697i
\(806\) 0 0
\(807\) 5.40450 9.36087i 0.190247 0.329518i
\(808\) 8.60968 + 14.9124i 0.302888 + 0.524617i
\(809\) 3.00617 + 5.20683i 0.105691 + 0.183063i 0.914020 0.405668i \(-0.132961\pi\)
−0.808329 + 0.588731i \(0.799628\pi\)
\(810\) −1.95618 + 3.38821i −0.0687332 + 0.119049i
\(811\) −8.44807 −0.296652 −0.148326 0.988939i \(-0.547388\pi\)
−0.148326 + 0.988939i \(0.547388\pi\)
\(812\) 19.0107 + 25.3249i 0.667143 + 0.888730i
\(813\) 41.3190 1.44912
\(814\) −11.8326 + 20.4946i −0.414732 + 0.718337i
\(815\) 0.179850 + 0.311510i 0.00629989 + 0.0109117i
\(816\) 4.62721 + 8.01456i 0.161985 + 0.280566i
\(817\) 3.60092 6.23697i 0.125980 0.218204i
\(818\) 38.4551 1.34455
\(819\) 0 0
\(820\) −1.54742 −0.0540382
\(821\) −17.1318 + 29.6731i −0.597903 + 1.03560i 0.395228 + 0.918583i \(0.370666\pi\)
−0.993130 + 0.117014i \(0.962668\pi\)
\(822\) −28.6627 49.6452i −0.999725 1.73157i
\(823\) 3.11866 + 5.40168i 0.108710 + 0.188291i 0.915248 0.402891i \(-0.131995\pi\)
−0.806538 + 0.591182i \(0.798661\pi\)
\(824\) 3.67809 6.37064i 0.128132 0.221932i
\(825\) −47.6037 −1.65735
\(826\) 29.5677 3.57518i 1.02879 0.124397i
\(827\) −19.5232 −0.678889 −0.339445 0.940626i \(-0.610239\pi\)
−0.339445 + 0.940626i \(0.610239\pi\)
\(828\) 6.76380 11.7152i 0.235058 0.407133i
\(829\) −16.3383 28.2988i −0.567453 0.982857i −0.996817 0.0797254i \(-0.974596\pi\)
0.429364 0.903131i \(-0.358738\pi\)
\(830\) −0.563647 0.976265i −0.0195645 0.0338866i
\(831\) 29.9615 51.8949i 1.03935 1.80021i
\(832\) 0 0
\(833\) −4.07530 4.25133i −0.141201 0.147300i
\(834\) −17.2445 −0.597128
\(835\) −1.05667 + 1.83021i −0.0365677 + 0.0633370i
\(836\) 4.10698 + 7.11349i 0.142043 + 0.246025i
\(837\) 1.08303 + 1.87586i 0.0374349 + 0.0648392i
\(838\) −20.2702 + 35.1091i −0.700223 + 1.21282i
\(839\) −24.7427 −0.854212 −0.427106 0.904202i \(-0.640467\pi\)
−0.427106 + 0.904202i \(0.640467\pi\)
\(840\) 1.20928 0.146220i 0.0417241 0.00504508i
\(841\) 38.8748 1.34051
\(842\) −8.75869 + 15.1705i −0.301844 + 0.522810i
\(843\) −4.20040 7.27531i −0.144669 0.250575i
\(844\) −19.2267 33.3017i −0.661812 1.14629i
\(845\) 0 0
\(846\) −49.0422 −1.68610
\(847\) −6.74381 + 15.8064i −0.231720 + 0.543115i
\(848\) −22.2870 −0.765339
\(849\) −8.76938 + 15.1890i −0.300964 + 0.521285i
\(850\) −3.87776 6.71647i −0.133006 0.230373i
\(851\) −6.26507 10.8514i −0.214764 0.371982i
\(852\) −9.94888 + 17.2320i −0.340843 + 0.590357i
\(853\) −18.2245 −0.623994 −0.311997 0.950083i \(-0.600998\pi\)
−0.311997 + 0.950083i \(0.600998\pi\)
\(854\) −33.5450 44.6868i −1.14789 1.52915i
\(855\) −0.603667 −0.0206450
\(856\) 5.00928 8.67633i 0.171214 0.296551i
\(857\) −1.27340 2.20559i −0.0434984 0.0753414i 0.843457 0.537197i \(-0.180517\pi\)
−0.886955 + 0.461856i \(0.847184\pi\)
\(858\) 0 0
\(859\) −27.0045 + 46.7732i −0.921382 + 1.59588i −0.124104 + 0.992269i \(0.539606\pi\)
−0.797278 + 0.603612i \(0.793728\pi\)
\(860\) 1.52758 0.0520902
\(861\) 19.6654 + 26.1972i 0.670196 + 0.892797i
\(862\) 37.9577 1.29284
\(863\) 0.621545 1.07655i 0.0211576 0.0366461i −0.855253 0.518211i \(-0.826598\pi\)
0.876410 + 0.481565i \(0.159931\pi\)
\(864\) 5.81487 + 10.0716i 0.197826 + 0.342644i
\(865\) 1.33147 + 2.30618i 0.0452715 + 0.0784125i
\(866\) 24.4800 42.4006i 0.831864 1.44083i
\(867\) −37.3754 −1.26934
\(868\) −1.93174 + 4.52769i −0.0655675 + 0.153680i
\(869\) −44.8949 −1.52295
\(870\) −3.46560 + 6.00259i −0.117495 + 0.203507i
\(871\) 0 0
\(872\) −7.02440 12.1666i −0.237876 0.412013i
\(873\) 22.0309 38.1587i 0.745634 1.29148i
\(874\) −10.3364 −0.349635
\(875\) −5.16376 + 0.624377i −0.174567 + 0.0211078i
\(876\) −12.9492 −0.437514
\(877\) 0.401330 0.695125i 0.0135520 0.0234727i −0.859170 0.511690i \(-0.829019\pi\)
0.872722 + 0.488218i \(0.162353\pi\)
\(878\) 23.3488 + 40.4412i 0.787983 + 1.36483i
\(879\) −19.6755 34.0790i −0.663639 1.14946i
\(880\) 1.97917 3.42803i 0.0667179 0.115559i
\(881\) −37.0636 −1.24870 −0.624352 0.781143i \(-0.714637\pi\)
−0.624352 + 0.781143i \(0.714637\pi\)
\(882\) 20.3669 + 21.2467i 0.685791 + 0.715413i
\(883\) −22.8671 −0.769539 −0.384770 0.923013i \(-0.625719\pi\)
−0.384770 + 0.923013i \(0.625719\pi\)
\(884\) 0 0
\(885\) 1.37144 + 2.37541i 0.0461005 + 0.0798484i
\(886\) 17.2065 + 29.8025i 0.578063 + 1.00123i
\(887\) 24.6287 42.6581i 0.826950 1.43232i −0.0734699 0.997297i \(-0.523407\pi\)
0.900420 0.435022i \(-0.143259\pi\)
\(888\) −7.10283 −0.238355
\(889\) −5.75292 + 0.695616i −0.192947 + 0.0233302i
\(890\) −4.39496 −0.147319
\(891\) 22.3112 38.6441i 0.747452 1.29463i
\(892\) −0.528840 0.915978i −0.0177069 0.0306692i
\(893\) 7.88347 + 13.6546i 0.263810 + 0.456932i
\(894\) −32.7207 + 56.6739i −1.09434 + 1.89546i
\(895\) 2.06622 0.0690661
\(896\) 8.12993 19.0552i 0.271602 0.636591i
\(897\) 0 0
\(898\) −10.8174 + 18.7362i −0.360980 + 0.625236i
\(899\) 5.27559 + 9.13760i 0.175951 + 0.304756i
\(900\) 8.15406 + 14.1233i 0.271802 + 0.470775i
\(901\) −1.95518 + 3.38647i −0.0651365 + 0.112820i
\(902\) 41.9462 1.39666
\(903\) −19.4134 25.8614i −0.646036 0.860613i
\(904\) −4.34059 −0.144366
\(905\) −1.23558 + 2.14009i −0.0410721 + 0.0711390i
\(906\) −13.0463 22.5969i −0.433435 0.750731i
\(907\) 2.50228 + 4.33407i 0.0830867 + 0.143910i 0.904574 0.426316i \(-0.140189\pi\)
−0.821488 + 0.570226i \(0.806855\pi\)
\(908\) −2.07161 + 3.58813i −0.0687487 + 0.119076i
\(909\) −38.3172 −1.27090
\(910\) 0 0
\(911\) 49.0582 1.62537 0.812685 0.582703i \(-0.198005\pi\)
0.812685 + 0.582703i \(0.198005\pi\)
\(912\) −7.43468 + 12.8772i −0.246187 + 0.426408i
\(913\) 6.42866 + 11.1348i 0.212757 + 0.368507i
\(914\) −19.0633 33.0186i −0.630557 1.09216i
\(915\) 2.57298 4.45653i 0.0850601 0.147328i
\(916\) −4.61037 −0.152331
\(917\) −2.36320 + 5.53897i −0.0780399 + 0.182913i
\(918\) 2.64399 0.0872646
\(919\) −14.8028 + 25.6392i −0.488299 + 0.845758i −0.999909 0.0134590i \(-0.995716\pi\)
0.511611 + 0.859217i \(0.329049\pi\)
\(920\) 0.412937 + 0.715227i 0.0136141 + 0.0235803i
\(921\) −32.1967 55.7664i −1.06092 1.83756i
\(922\) −1.89602 + 3.28401i −0.0624422 + 0.108153i
\(923\) 0 0
\(924\) 36.6150 4.42731i 1.20454 0.145648i
\(925\) 15.1056 0.496670
\(926\) −2.81656 + 4.87842i −0.0925578 + 0.160315i
\(927\) 8.18464 + 14.1762i 0.268819 + 0.465608i
\(928\) 28.3251 + 49.0605i 0.929817 + 1.61049i
\(929\) 8.41525 14.5756i 0.276095 0.478211i −0.694316 0.719671i \(-0.744293\pi\)
0.970411 + 0.241460i \(0.0776261\pi\)
\(930\) −1.07746 −0.0353313
\(931\) 2.64164 9.08604i 0.0865764 0.297783i
\(932\) 19.4773 0.638000
\(933\) 26.9944 46.7557i 0.883757 1.53071i
\(934\) −12.0106 20.8030i −0.392999 0.680695i
\(935\) −0.347255 0.601463i −0.0113565 0.0196699i
\(936\) 0 0
\(937\) 44.0131 1.43784 0.718922 0.695091i \(-0.244636\pi\)
0.718922 + 0.695091i \(0.244636\pi\)
\(938\) 65.3866 7.90624i 2.13495 0.258148i
\(939\) −7.68191 −0.250690
\(940\) −1.67216 + 2.89627i −0.0545400 + 0.0944660i
\(941\) 26.5338 + 45.9578i 0.864976 + 1.49818i 0.867071 + 0.498184i \(0.166000\pi\)
−0.00209573 + 0.999998i \(0.500667\pi\)
\(942\) 9.66937 + 16.7478i 0.315045 + 0.545674i
\(943\) −11.1048 + 19.2340i −0.361620 + 0.626345i
\(944\) 29.0487 0.945453
\(945\) 0.346572 0.812309i 0.0112740 0.0264244i
\(946\) −41.4086 −1.34631
\(947\) −13.9409 + 24.1463i −0.453017 + 0.784649i −0.998572 0.0534265i \(-0.982986\pi\)
0.545555 + 0.838075i \(0.316319\pi\)
\(948\) 17.8857 + 30.9790i 0.580902 + 1.00615i
\(949\) 0 0
\(950\) 6.23051 10.7916i 0.202145 0.350125i
\(951\) 16.6970 0.541438
\(952\) −1.35882 1.81014i −0.0440396 0.0586670i
\(953\) −36.3568 −1.17771 −0.588856 0.808238i \(-0.700421\pi\)
−0.588856 + 0.808238i \(0.700421\pi\)
\(954\) 9.77130 16.9244i 0.316357 0.547947i
\(955\) −1.29407 2.24140i −0.0418753 0.0725301i
\(956\) −11.2980 19.5687i −0.365403 0.632897i
\(957\) 39.5267 68.4623i 1.27772 2.21307i
\(958\) 67.9754 2.19619
\(959\) 21.3602 + 28.4548i 0.689757 + 0.918855i
\(960\) −1.44297 −0.0465718
\(961\) 14.6799 25.4263i 0.473545 0.820205i
\(962\) 0 0
\(963\) 11.1469 + 19.3069i 0.359202 + 0.622157i
\(964\) −5.50287 + 9.53126i −0.177236 + 0.306981i
\(965\) −0.205567 −0.00661744
\(966\) −18.2132 + 42.6888i −0.586000 + 1.37349i
\(967\) 15.2681 0.490988 0.245494 0.969398i \(-0.421050\pi\)
0.245494 + 0.969398i \(0.421050\pi\)
\(968\) −3.30239 + 5.71990i −0.106143 + 0.183845i
\(969\) 1.30445 + 2.25937i 0.0419049 + 0.0725815i
\(970\) −3.57063 6.18450i −0.114646 0.198572i
\(971\) 18.4460 31.9494i 0.591961 1.02531i −0.402008 0.915636i \(-0.631687\pi\)
0.993968 0.109669i \(-0.0349792\pi\)
\(972\) −28.1831 −0.903975
\(973\) 10.6257 1.28481i 0.340645 0.0411891i
\(974\) 68.2867 2.18805
\(975\) 0 0
\(976\) −27.2493 47.1972i −0.872229 1.51074i
\(977\) −0.221957 0.384441i −0.00710104 0.0122994i 0.862453 0.506137i \(-0.168927\pi\)
−0.869554 + 0.493838i \(0.835594\pi\)
\(978\) −3.88452 + 6.72818i −0.124213 + 0.215144i
\(979\) 50.1265 1.60205
\(980\) 1.94920 0.478370i 0.0622649 0.0152810i
\(981\) 31.2619 0.998117
\(982\) −7.61658 + 13.1923i −0.243055 + 0.420983i
\(983\) 22.7802 + 39.4564i 0.726575 + 1.25846i 0.958323 + 0.285688i \(0.0922222\pi\)
−0.231748 + 0.972776i \(0.574444\pi\)
\(984\) 6.29483 + 10.9030i 0.200672 + 0.347574i
\(985\) 0.145884 0.252678i 0.00464824 0.00805099i
\(986\) 12.8793 0.410160
\(987\) 70.2835 8.49835i 2.23715 0.270505i
\(988\) 0 0
\(989\) 10.9624 18.9875i 0.348585 0.603766i
\(990\) 1.73546 + 3.00590i 0.0551565 + 0.0955338i
\(991\) −26.8148 46.4445i −0.851799 1.47536i −0.879583 0.475745i \(-0.842178\pi\)
0.0277842 0.999614i \(-0.491155\pi\)
\(992\) −4.40316 + 7.62650i −0.139801 + 0.242142i
\(993\) 32.8588 1.04274
\(994\) 11.5184 26.9974i 0.365342 0.856304i
\(995\) 2.78278 0.0882200
\(996\) 5.12225 8.87199i 0.162305 0.281120i
\(997\) −14.5426 25.1886i −0.460569 0.797730i 0.538420 0.842677i \(-0.319021\pi\)
−0.998989 + 0.0449470i \(0.985688\pi\)
\(998\) 40.1857 + 69.6038i 1.27206 + 2.20327i
\(999\) −2.57489 + 4.45984i −0.0814658 + 0.141103i
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 1183.2.e.g.170.6 12
7.2 even 3 8281.2.a.ce.1.1 6
7.4 even 3 inner 1183.2.e.g.508.6 12
7.5 odd 6 8281.2.a.cf.1.1 6
13.4 even 6 91.2.h.b.16.6 yes 12
13.10 even 6 91.2.g.b.9.1 12
13.12 even 2 1183.2.e.h.170.1 12
39.17 odd 6 819.2.s.d.289.1 12
39.23 odd 6 819.2.n.d.100.6 12
91.4 even 6 91.2.g.b.81.1 yes 12
91.10 odd 6 637.2.h.l.165.6 12
91.12 odd 6 8281.2.a.ca.1.6 6
91.17 odd 6 637.2.g.l.263.1 12
91.23 even 6 637.2.f.k.295.1 12
91.25 even 6 1183.2.e.h.508.1 12
91.30 even 6 637.2.f.k.393.1 12
91.51 even 6 8281.2.a.bz.1.6 6
91.62 odd 6 637.2.g.l.373.1 12
91.69 odd 6 637.2.h.l.471.6 12
91.75 odd 6 637.2.f.j.295.1 12
91.82 odd 6 637.2.f.j.393.1 12
91.88 even 6 91.2.h.b.74.6 yes 12
273.95 odd 6 819.2.n.d.172.6 12
273.179 odd 6 819.2.s.d.802.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.1 12 13.10 even 6
91.2.g.b.81.1 yes 12 91.4 even 6
91.2.h.b.16.6 yes 12 13.4 even 6
91.2.h.b.74.6 yes 12 91.88 even 6
637.2.f.j.295.1 12 91.75 odd 6
637.2.f.j.393.1 12 91.82 odd 6
637.2.f.k.295.1 12 91.23 even 6
637.2.f.k.393.1 12 91.30 even 6
637.2.g.l.263.1 12 91.17 odd 6
637.2.g.l.373.1 12 91.62 odd 6
637.2.h.l.165.6 12 91.10 odd 6
637.2.h.l.471.6 12 91.69 odd 6
819.2.n.d.100.6 12 39.23 odd 6
819.2.n.d.172.6 12 273.95 odd 6
819.2.s.d.289.1 12 39.17 odd 6
819.2.s.d.802.1 12 273.179 odd 6
1183.2.e.g.170.6 12 1.1 even 1 trivial
1183.2.e.g.508.6 12 7.4 even 3 inner
1183.2.e.h.170.1 12 13.12 even 2
1183.2.e.h.508.1 12 91.25 even 6
8281.2.a.bz.1.6 6 91.51 even 6
8281.2.a.ca.1.6 6 91.12 odd 6
8281.2.a.ce.1.1 6 7.2 even 3
8281.2.a.cf.1.1 6 7.5 odd 6