Properties

Label 471.2.e.b.301.8
Level $471$
Weight $2$
Character 471.301
Analytic conductor $3.761$
Analytic rank $0$
Dimension $22$
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] = [471,2,Mod(169,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.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: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 301.8
Character \(\chi\) \(=\) 471.301
Dual form 471.2.e.b.169.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.32447 q^{2} +(0.500000 - 0.866025i) q^{3} -0.245772 q^{4} +(-2.05322 + 3.55628i) q^{5} +(0.662236 - 1.14703i) q^{6} -3.69381 q^{7} -2.97446 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+1.32447 q^{2} +(0.500000 - 0.866025i) q^{3} -0.245772 q^{4} +(-2.05322 + 3.55628i) q^{5} +(0.662236 - 1.14703i) q^{6} -3.69381 q^{7} -2.97446 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.71944 + 4.71020i) q^{10} +(0.214620 - 0.371733i) q^{11} +(-0.122886 + 0.212845i) q^{12} +(1.17636 + 2.03752i) q^{13} -4.89235 q^{14} +(2.05322 + 3.55628i) q^{15} -3.44805 q^{16} +(0.765484 - 1.32586i) q^{17} +(-0.662236 - 1.14703i) q^{18} +(-3.35849 + 5.81708i) q^{19} +(0.504625 - 0.874035i) q^{20} +(-1.84690 + 3.19893i) q^{21} +(0.284259 - 0.492351i) q^{22} +1.95301 q^{23} +(-1.48723 + 2.57596i) q^{24} +(-5.93144 - 10.2735i) q^{25} +(1.55806 + 2.69864i) q^{26} -1.00000 q^{27} +0.907835 q^{28} +6.08537 q^{29} +(2.71944 + 4.71020i) q^{30} +(-2.68966 - 4.65864i) q^{31} +1.38208 q^{32} +(-0.214620 - 0.371733i) q^{33} +(1.01386 - 1.75606i) q^{34} +(7.58420 - 13.1362i) q^{35} +(0.122886 + 0.212845i) q^{36} +(4.23513 + 7.33547i) q^{37} +(-4.44823 + 7.70457i) q^{38} +2.35273 q^{39} +(6.10723 - 10.5780i) q^{40} -9.93710 q^{41} +(-2.44617 + 4.23690i) q^{42} +(4.73108 + 8.19447i) q^{43} +(-0.0527477 + 0.0913617i) q^{44} +4.10644 q^{45} +2.58671 q^{46} +(-3.29832 - 5.71285i) q^{47} +(-1.72403 + 2.98610i) q^{48} +6.64421 q^{49} +(-7.85603 - 13.6070i) q^{50} +(-0.765484 - 1.32586i) q^{51} +(-0.289118 - 0.500766i) q^{52} +(4.67219 + 8.09247i) q^{53} -1.32447 q^{54} +(0.881327 + 1.52650i) q^{55} +10.9871 q^{56} +(3.35849 + 5.81708i) q^{57} +8.05991 q^{58} -3.06926 q^{59} +(-0.504625 - 0.874035i) q^{60} +(-4.87315 + 8.44054i) q^{61} +(-3.56239 - 6.17024i) q^{62} +(1.84690 + 3.19893i) q^{63} +8.72663 q^{64} -9.66135 q^{65} +(-0.284259 - 0.492351i) q^{66} -13.8840 q^{67} +(-0.188135 + 0.325859i) q^{68} +(0.976504 - 1.69135i) q^{69} +(10.0451 - 17.3986i) q^{70} +(0.536628 + 0.929468i) q^{71} +(1.48723 + 2.57596i) q^{72} +(2.85438 - 4.94393i) q^{73} +(5.60932 + 9.71563i) q^{74} -11.8629 q^{75} +(0.825424 - 1.42968i) q^{76} +(-0.792767 + 1.37311i) q^{77} +3.11613 q^{78} +7.18928 q^{79} +(7.07961 - 12.2623i) q^{80} +(-0.500000 + 0.866025i) q^{81} -13.1614 q^{82} +(-5.58924 - 9.68086i) q^{83} +(0.453917 - 0.786208i) q^{84} +(3.14342 + 5.44456i) q^{85} +(6.26618 + 10.8533i) q^{86} +(3.04269 - 5.27009i) q^{87} +(-0.638381 + 1.10571i) q^{88} +(0.330579 - 0.572580i) q^{89} +5.43887 q^{90} +(-4.34526 - 7.52622i) q^{91} -0.479995 q^{92} -5.37933 q^{93} +(-4.36853 - 7.56652i) q^{94} +(-13.7915 - 23.8875i) q^{95} +(0.691038 - 1.19691i) q^{96} +(1.13737 + 1.96997i) q^{97} +8.80008 q^{98} -0.429241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32447 0.936544 0.468272 0.883584i \(-0.344877\pi\)
0.468272 + 0.883584i \(0.344877\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.245772 −0.122886
\(5\) −2.05322 + 3.55628i −0.918229 + 1.59042i −0.116124 + 0.993235i \(0.537047\pi\)
−0.802104 + 0.597184i \(0.796286\pi\)
\(6\) 0.662236 1.14703i 0.270357 0.468272i
\(7\) −3.69381 −1.39613 −0.698064 0.716035i \(-0.745955\pi\)
−0.698064 + 0.716035i \(0.745955\pi\)
\(8\) −2.97446 −1.05163
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −2.71944 + 4.71020i −0.859961 + 1.48950i
\(11\) 0.214620 0.371733i 0.0647105 0.112082i −0.831855 0.554993i \(-0.812721\pi\)
0.896566 + 0.442911i \(0.146054\pi\)
\(12\) −0.122886 + 0.212845i −0.0354741 + 0.0614430i
\(13\) 1.17636 + 2.03752i 0.326265 + 0.565107i 0.981768 0.190086i \(-0.0608765\pi\)
−0.655503 + 0.755193i \(0.727543\pi\)
\(14\) −4.89235 −1.30753
\(15\) 2.05322 + 3.55628i 0.530139 + 0.918229i
\(16\) −3.44805 −0.862013
\(17\) 0.765484 1.32586i 0.185657 0.321568i −0.758141 0.652091i \(-0.773892\pi\)
0.943798 + 0.330523i \(0.107225\pi\)
\(18\) −0.662236 1.14703i −0.156091 0.270357i
\(19\) −3.35849 + 5.81708i −0.770492 + 1.33453i 0.166802 + 0.985990i \(0.446656\pi\)
−0.937294 + 0.348540i \(0.886677\pi\)
\(20\) 0.504625 0.874035i 0.112837 0.195440i
\(21\) −1.84690 + 3.19893i −0.403027 + 0.698064i
\(22\) 0.284259 0.492351i 0.0606042 0.104970i
\(23\) 1.95301 0.407230 0.203615 0.979051i \(-0.434731\pi\)
0.203615 + 0.979051i \(0.434731\pi\)
\(24\) −1.48723 + 2.57596i −0.303580 + 0.525816i
\(25\) −5.93144 10.2735i −1.18629 2.05471i
\(26\) 1.55806 + 2.69864i 0.305561 + 0.529248i
\(27\) −1.00000 −0.192450
\(28\) 0.907835 0.171565
\(29\) 6.08537 1.13003 0.565013 0.825082i \(-0.308871\pi\)
0.565013 + 0.825082i \(0.308871\pi\)
\(30\) 2.71944 + 4.71020i 0.496499 + 0.859961i
\(31\) −2.68966 4.65864i −0.483078 0.836716i 0.516733 0.856147i \(-0.327148\pi\)
−0.999811 + 0.0194308i \(0.993815\pi\)
\(32\) 1.38208 0.244319
\(33\) −0.214620 0.371733i −0.0373606 0.0647105i
\(34\) 1.01386 1.75606i 0.173876 0.301162i
\(35\) 7.58420 13.1362i 1.28196 2.22043i
\(36\) 0.122886 + 0.212845i 0.0204810 + 0.0354741i
\(37\) 4.23513 + 7.33547i 0.696252 + 1.20594i 0.969757 + 0.244073i \(0.0784837\pi\)
−0.273505 + 0.961871i \(0.588183\pi\)
\(38\) −4.44823 + 7.70457i −0.721599 + 1.24985i
\(39\) 2.35273 0.376738
\(40\) 6.10723 10.5780i 0.965638 1.67253i
\(41\) −9.93710 −1.55191 −0.775957 0.630785i \(-0.782733\pi\)
−0.775957 + 0.630785i \(0.782733\pi\)
\(42\) −2.44617 + 4.23690i −0.377453 + 0.653767i
\(43\) 4.73108 + 8.19447i 0.721483 + 1.24964i 0.960405 + 0.278606i \(0.0898724\pi\)
−0.238923 + 0.971039i \(0.576794\pi\)
\(44\) −0.0527477 + 0.0913617i −0.00795202 + 0.0137733i
\(45\) 4.10644 0.612152
\(46\) 2.58671 0.381389
\(47\) −3.29832 5.71285i −0.481109 0.833305i 0.518656 0.854983i \(-0.326433\pi\)
−0.999765 + 0.0216776i \(0.993099\pi\)
\(48\) −1.72403 + 2.98610i −0.248842 + 0.431006i
\(49\) 6.64421 0.949173
\(50\) −7.85603 13.6070i −1.11101 1.92433i
\(51\) −0.765484 1.32586i −0.107189 0.185657i
\(52\) −0.289118 0.500766i −0.0400934 0.0694438i
\(53\) 4.67219 + 8.09247i 0.641774 + 1.11159i 0.985036 + 0.172346i \(0.0551348\pi\)
−0.343262 + 0.939240i \(0.611532\pi\)
\(54\) −1.32447 −0.180238
\(55\) 0.881327 + 1.52650i 0.118838 + 0.205834i
\(56\) 10.9871 1.46821
\(57\) 3.35849 + 5.81708i 0.444844 + 0.770492i
\(58\) 8.05991 1.05832
\(59\) −3.06926 −0.399584 −0.199792 0.979838i \(-0.564027\pi\)
−0.199792 + 0.979838i \(0.564027\pi\)
\(60\) −0.504625 0.874035i −0.0651467 0.112837i
\(61\) −4.87315 + 8.44054i −0.623943 + 1.08070i 0.364801 + 0.931085i \(0.381137\pi\)
−0.988744 + 0.149616i \(0.952196\pi\)
\(62\) −3.56239 6.17024i −0.452424 0.783621i
\(63\) 1.84690 + 3.19893i 0.232688 + 0.403027i
\(64\) 8.72663 1.09083
\(65\) −9.66135 −1.19834
\(66\) −0.284259 0.492351i −0.0349899 0.0606042i
\(67\) −13.8840 −1.69621 −0.848103 0.529832i \(-0.822255\pi\)
−0.848103 + 0.529832i \(0.822255\pi\)
\(68\) −0.188135 + 0.325859i −0.0228147 + 0.0395162i
\(69\) 0.976504 1.69135i 0.117557 0.203615i
\(70\) 10.0451 17.3986i 1.20062 2.07953i
\(71\) 0.536628 + 0.929468i 0.0636861 + 0.110308i 0.896110 0.443831i \(-0.146381\pi\)
−0.832424 + 0.554139i \(0.813048\pi\)
\(72\) 1.48723 + 2.57596i 0.175272 + 0.303580i
\(73\) 2.85438 4.94393i 0.334080 0.578643i −0.649228 0.760594i \(-0.724908\pi\)
0.983308 + 0.181951i \(0.0582412\pi\)
\(74\) 5.60932 + 9.71563i 0.652070 + 1.12942i
\(75\) −11.8629 −1.36981
\(76\) 0.825424 1.42968i 0.0946827 0.163995i
\(77\) −0.792767 + 1.37311i −0.0903441 + 0.156481i
\(78\) 3.11613 0.352832
\(79\) 7.18928 0.808858 0.404429 0.914569i \(-0.367470\pi\)
0.404429 + 0.914569i \(0.367470\pi\)
\(80\) 7.07961 12.2623i 0.791525 1.37096i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −13.1614 −1.45344
\(83\) −5.58924 9.68086i −0.613499 1.06261i −0.990646 0.136458i \(-0.956428\pi\)
0.377147 0.926154i \(-0.376905\pi\)
\(84\) 0.453917 0.786208i 0.0495264 0.0857823i
\(85\) 3.14342 + 5.44456i 0.340951 + 0.590545i
\(86\) 6.26618 + 10.8533i 0.675700 + 1.17035i
\(87\) 3.04269 5.27009i 0.326210 0.565013i
\(88\) −0.638381 + 1.10571i −0.0680516 + 0.117869i
\(89\) 0.330579 0.572580i 0.0350413 0.0606934i −0.847973 0.530040i \(-0.822177\pi\)
0.883014 + 0.469346i \(0.155510\pi\)
\(90\) 5.43887 0.573307
\(91\) −4.34526 7.52622i −0.455507 0.788962i
\(92\) −0.479995 −0.0500429
\(93\) −5.37933 −0.557810
\(94\) −4.36853 7.56652i −0.450580 0.780427i
\(95\) −13.7915 23.8875i −1.41497 2.45081i
\(96\) 0.691038 1.19691i 0.0705288 0.122160i
\(97\) 1.13737 + 1.96997i 0.115482 + 0.200021i 0.917972 0.396645i \(-0.129825\pi\)
−0.802490 + 0.596665i \(0.796492\pi\)
\(98\) 8.80008 0.888942
\(99\) −0.429241 −0.0431403
\(100\) 1.45778 + 2.52495i 0.145778 + 0.252495i
\(101\) 1.31245 0.130593 0.0652966 0.997866i \(-0.479201\pi\)
0.0652966 + 0.997866i \(0.479201\pi\)
\(102\) −1.01386 1.75606i −0.100387 0.173876i
\(103\) −5.53994 −0.545866 −0.272933 0.962033i \(-0.587994\pi\)
−0.272933 + 0.962033i \(0.587994\pi\)
\(104\) −3.49905 6.06054i −0.343110 0.594285i
\(105\) −7.58420 13.1362i −0.740143 1.28196i
\(106\) 6.18819 + 10.7183i 0.601050 + 1.04105i
\(107\) −1.28393 2.22382i −0.124122 0.214985i 0.797268 0.603626i \(-0.206278\pi\)
−0.921389 + 0.388641i \(0.872945\pi\)
\(108\) 0.245772 0.0236494
\(109\) −5.71543 + 9.89942i −0.547439 + 0.948192i 0.451010 + 0.892519i \(0.351064\pi\)
−0.998449 + 0.0556732i \(0.982270\pi\)
\(110\) 1.16729 + 2.02181i 0.111297 + 0.192772i
\(111\) 8.47027 0.803962
\(112\) 12.7364 1.20348
\(113\) −5.37142 + 9.30356i −0.505300 + 0.875206i 0.494681 + 0.869075i \(0.335285\pi\)
−0.999981 + 0.00613105i \(0.998048\pi\)
\(114\) 4.44823 + 7.70457i 0.416615 + 0.721599i
\(115\) −4.00996 + 6.94545i −0.373931 + 0.647667i
\(116\) −1.49561 −0.138864
\(117\) 1.17636 2.03752i 0.108755 0.188369i
\(118\) −4.06515 −0.374228
\(119\) −2.82755 + 4.89746i −0.259201 + 0.448950i
\(120\) −6.10723 10.5780i −0.557512 0.965638i
\(121\) 5.40788 + 9.36672i 0.491625 + 0.851520i
\(122\) −6.45436 + 11.1793i −0.584350 + 1.01212i
\(123\) −4.96855 + 8.60578i −0.447999 + 0.775957i
\(124\) 0.661045 + 1.14496i 0.0593635 + 0.102821i
\(125\) 28.1820 2.52067
\(126\) 2.44617 + 4.23690i 0.217922 + 0.377453i
\(127\) −4.21390 7.29869i −0.373923 0.647654i 0.616242 0.787557i \(-0.288654\pi\)
−0.990165 + 0.139903i \(0.955321\pi\)
\(128\) 8.79403 0.777289
\(129\) 9.46216 0.833096
\(130\) −12.7962 −1.12230
\(131\) −3.40489 5.89744i −0.297487 0.515262i 0.678074 0.734994i \(-0.262815\pi\)
−0.975560 + 0.219732i \(0.929482\pi\)
\(132\) 0.0527477 + 0.0913617i 0.00459110 + 0.00795202i
\(133\) 12.4056 21.4872i 1.07570 1.86318i
\(134\) −18.3890 −1.58857
\(135\) 2.05322 3.55628i 0.176713 0.306076i
\(136\) −2.27690 + 3.94371i −0.195243 + 0.338171i
\(137\) 0.794852 1.37672i 0.0679088 0.117621i −0.830072 0.557656i \(-0.811701\pi\)
0.897981 + 0.440035i \(0.145034\pi\)
\(138\) 1.29335 2.24015i 0.110098 0.190695i
\(139\) 11.4414 + 19.8170i 0.970443 + 1.68086i 0.694219 + 0.719764i \(0.255750\pi\)
0.276224 + 0.961093i \(0.410917\pi\)
\(140\) −1.86399 + 3.22852i −0.157536 + 0.272860i
\(141\) −6.59664 −0.555537
\(142\) 0.710750 + 1.23105i 0.0596448 + 0.103308i
\(143\) 1.00989 0.0844510
\(144\) 1.72403 + 2.98610i 0.143669 + 0.248842i
\(145\) −12.4946 + 21.6413i −1.03762 + 1.79721i
\(146\) 3.78055 6.54810i 0.312880 0.541924i
\(147\) 3.32211 5.75406i 0.274003 0.474587i
\(148\) −1.04088 1.80285i −0.0855596 0.148194i
\(149\) 18.7365 1.53496 0.767478 0.641075i \(-0.221511\pi\)
0.767478 + 0.641075i \(0.221511\pi\)
\(150\) −15.7121 −1.28288
\(151\) −6.10258 + 10.5700i −0.496621 + 0.860173i −0.999992 0.00389698i \(-0.998760\pi\)
0.503371 + 0.864070i \(0.332093\pi\)
\(152\) 9.98972 17.3027i 0.810273 1.40343i
\(153\) −1.53097 −0.123771
\(154\) −1.05000 + 1.81865i −0.0846112 + 0.146551i
\(155\) 22.0899 1.77430
\(156\) −0.578235 −0.0462959
\(157\) 1.42338 + 12.4489i 0.113598 + 0.993527i
\(158\) 9.52201 0.757531
\(159\) 9.34438 0.741057
\(160\) −2.83771 + 4.91506i −0.224341 + 0.388569i
\(161\) −7.21404 −0.568546
\(162\) −0.662236 + 1.14703i −0.0520302 + 0.0901190i
\(163\) 1.53395 2.65688i 0.120148 0.208103i −0.799678 0.600429i \(-0.794996\pi\)
0.919826 + 0.392327i \(0.128330\pi\)
\(164\) 2.44226 0.190709
\(165\) 1.76265 0.137222
\(166\) −7.40280 12.8220i −0.574569 0.995182i
\(167\) −0.0125513 + 0.0217395i −0.000971250 + 0.00168225i −0.866511 0.499159i \(-0.833642\pi\)
0.865539 + 0.500841i \(0.166976\pi\)
\(168\) 5.49355 9.51510i 0.423836 0.734106i
\(169\) 3.73233 6.46459i 0.287102 0.497276i
\(170\) 4.16337 + 7.21117i 0.319316 + 0.553071i
\(171\) 6.71699 0.513661
\(172\) −1.16277 2.01397i −0.0886602 0.153564i
\(173\) −19.3577 −1.47174 −0.735868 0.677125i \(-0.763225\pi\)
−0.735868 + 0.677125i \(0.763225\pi\)
\(174\) 4.02995 6.98009i 0.305510 0.529159i
\(175\) 21.9096 + 37.9485i 1.65621 + 2.86864i
\(176\) −0.740022 + 1.28176i −0.0557813 + 0.0966160i
\(177\) −1.53463 + 2.65806i −0.115350 + 0.199792i
\(178\) 0.437843 0.758367i 0.0328177 0.0568420i
\(179\) 6.55306 11.3502i 0.489799 0.848357i −0.510132 0.860096i \(-0.670404\pi\)
0.999931 + 0.0117394i \(0.00373686\pi\)
\(180\) −1.00925 −0.0752250
\(181\) −6.86093 + 11.8835i −0.509969 + 0.883292i 0.489964 + 0.871743i \(0.337010\pi\)
−0.999933 + 0.0115498i \(0.996324\pi\)
\(182\) −5.75518 9.96827i −0.426603 0.738897i
\(183\) 4.87315 + 8.44054i 0.360234 + 0.623943i
\(184\) −5.80915 −0.428256
\(185\) −34.7827 −2.55727
\(186\) −7.12478 −0.522414
\(187\) −0.328577 0.569112i −0.0240279 0.0416176i
\(188\) 0.810635 + 1.40406i 0.0591216 + 0.102402i
\(189\) 3.69381 0.268685
\(190\) −18.2664 31.6384i −1.32519 2.29529i
\(191\) 11.4553 19.8411i 0.828874 1.43565i −0.0700488 0.997544i \(-0.522315\pi\)
0.898922 0.438108i \(-0.144351\pi\)
\(192\) 4.36331 7.55748i 0.314895 0.545414i
\(193\) −9.78696 16.9515i −0.704481 1.22020i −0.966879 0.255237i \(-0.917847\pi\)
0.262398 0.964960i \(-0.415487\pi\)
\(194\) 1.50641 + 2.60918i 0.108154 + 0.187328i
\(195\) −4.83067 + 8.36697i −0.345932 + 0.599171i
\(196\) −1.63296 −0.116640
\(197\) 3.49793 6.05859i 0.249217 0.431657i −0.714092 0.700052i \(-0.753160\pi\)
0.963309 + 0.268395i \(0.0864934\pi\)
\(198\) −0.568518 −0.0404028
\(199\) 3.22382 5.58381i 0.228530 0.395826i −0.728842 0.684681i \(-0.759941\pi\)
0.957373 + 0.288855i \(0.0932747\pi\)
\(200\) 17.6428 + 30.5583i 1.24754 + 2.16080i
\(201\) −6.94202 + 12.0239i −0.489652 + 0.848103i
\(202\) 1.73830 0.122306
\(203\) −22.4782 −1.57766
\(204\) 0.188135 + 0.325859i 0.0131721 + 0.0228147i
\(205\) 20.4031 35.3392i 1.42501 2.46819i
\(206\) −7.33750 −0.511228
\(207\) −0.976504 1.69135i −0.0678717 0.117557i
\(208\) −4.05617 7.02549i −0.281245 0.487130i
\(209\) 1.44160 + 2.49693i 0.0997178 + 0.172716i
\(210\) −10.0451 17.3986i −0.693176 1.20062i
\(211\) 1.17153 0.0806518 0.0403259 0.999187i \(-0.487160\pi\)
0.0403259 + 0.999187i \(0.487160\pi\)
\(212\) −1.14829 1.98890i −0.0788651 0.136598i
\(213\) 1.07326 0.0735383
\(214\) −1.70052 2.94539i −0.116245 0.201343i
\(215\) −38.8558 −2.64994
\(216\) 2.97446 0.202387
\(217\) 9.93510 + 17.2081i 0.674439 + 1.16816i
\(218\) −7.56993 + 13.1115i −0.512700 + 0.888023i
\(219\) −2.85438 4.94393i −0.192881 0.334080i
\(220\) −0.216605 0.375172i −0.0146035 0.0252941i
\(221\) 3.60195 0.242294
\(222\) 11.2186 0.752946
\(223\) 12.0052 + 20.7935i 0.803925 + 1.39244i 0.917014 + 0.398854i \(0.130592\pi\)
−0.113089 + 0.993585i \(0.536075\pi\)
\(224\) −5.10513 −0.341101
\(225\) −5.93144 + 10.2735i −0.395429 + 0.684903i
\(226\) −7.11429 + 12.3223i −0.473236 + 0.819668i
\(227\) −7.40268 + 12.8218i −0.491333 + 0.851014i −0.999950 0.00997867i \(-0.996824\pi\)
0.508617 + 0.860993i \(0.330157\pi\)
\(228\) −0.825424 1.42968i −0.0546651 0.0946827i
\(229\) −8.46544 14.6626i −0.559412 0.968930i −0.997546 0.0700202i \(-0.977694\pi\)
0.438134 0.898910i \(-0.355640\pi\)
\(230\) −5.31108 + 9.19906i −0.350202 + 0.606568i
\(231\) 0.792767 + 1.37311i 0.0521602 + 0.0903441i
\(232\) −18.1007 −1.18837
\(233\) −8.30278 + 14.3808i −0.543933 + 0.942120i 0.454740 + 0.890624i \(0.349732\pi\)
−0.998673 + 0.0514960i \(0.983601\pi\)
\(234\) 1.55806 2.69864i 0.101854 0.176416i
\(235\) 27.0887 1.76707
\(236\) 0.754338 0.0491033
\(237\) 3.59464 6.22610i 0.233497 0.404429i
\(238\) −3.74501 + 6.48655i −0.242753 + 0.420461i
\(239\) 19.4025 1.25504 0.627522 0.778599i \(-0.284069\pi\)
0.627522 + 0.778599i \(0.284069\pi\)
\(240\) −7.07961 12.2623i −0.456987 0.791525i
\(241\) 8.95415 15.5090i 0.576787 0.999025i −0.419058 0.907960i \(-0.637639\pi\)
0.995845 0.0910652i \(-0.0290272\pi\)
\(242\) 7.16258 + 12.4060i 0.460428 + 0.797485i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 1.19768 2.07445i 0.0766739 0.132803i
\(245\) −13.6420 + 23.6287i −0.871558 + 1.50958i
\(246\) −6.58071 + 11.3981i −0.419571 + 0.726718i
\(247\) −15.8033 −1.00554
\(248\) 8.00031 + 13.8569i 0.508020 + 0.879917i
\(249\) −11.1785 −0.708408
\(250\) 37.3263 2.36072
\(251\) 0.0947791 + 0.164162i 0.00598240 + 0.0103618i 0.869001 0.494810i \(-0.164762\pi\)
−0.863019 + 0.505172i \(0.831429\pi\)
\(252\) −0.453917 0.786208i −0.0285941 0.0495264i
\(253\) 0.419156 0.725999i 0.0263521 0.0456431i
\(254\) −5.58119 9.66691i −0.350195 0.606556i
\(255\) 6.28683 0.393697
\(256\) −5.80581 −0.362863
\(257\) −4.07555 7.05906i −0.254226 0.440332i 0.710459 0.703739i \(-0.248487\pi\)
−0.964685 + 0.263406i \(0.915154\pi\)
\(258\) 12.5324 0.780231
\(259\) −15.6438 27.0958i −0.972057 1.68365i
\(260\) 2.37449 0.147260
\(261\) −3.04269 5.27009i −0.188338 0.326210i
\(262\) −4.50969 7.81100i −0.278609 0.482565i
\(263\) 0.830323 + 1.43816i 0.0511999 + 0.0886808i 0.890489 0.455004i \(-0.150362\pi\)
−0.839290 + 0.543685i \(0.817029\pi\)
\(264\) 0.638381 + 1.10571i 0.0392896 + 0.0680516i
\(265\) −38.3721 −2.35718
\(266\) 16.4309 28.4592i 1.00744 1.74494i
\(267\) −0.330579 0.572580i −0.0202311 0.0350413i
\(268\) 3.41231 0.208440
\(269\) 26.1622 1.59514 0.797569 0.603228i \(-0.206119\pi\)
0.797569 + 0.603228i \(0.206119\pi\)
\(270\) 2.71944 4.71020i 0.165500 0.286654i
\(271\) −2.77646 4.80898i −0.168658 0.292125i 0.769290 0.638900i \(-0.220610\pi\)
−0.937948 + 0.346775i \(0.887277\pi\)
\(272\) −2.63943 + 4.57163i −0.160039 + 0.277195i
\(273\) −8.69053 −0.525975
\(274\) 1.05276 1.82343i 0.0635995 0.110158i
\(275\) −5.09203 −0.307061
\(276\) −0.239997 + 0.415688i −0.0144462 + 0.0250215i
\(277\) 11.8128 + 20.4604i 0.709765 + 1.22935i 0.964944 + 0.262455i \(0.0845321\pi\)
−0.255179 + 0.966894i \(0.582135\pi\)
\(278\) 15.1538 + 26.2471i 0.908862 + 1.57420i
\(279\) −2.68966 + 4.65864i −0.161026 + 0.278905i
\(280\) −22.5589 + 39.0732i −1.34815 + 2.33507i
\(281\) 9.96368 + 17.2576i 0.594383 + 1.02950i 0.993634 + 0.112660i \(0.0359371\pi\)
−0.399250 + 0.916842i \(0.630730\pi\)
\(282\) −8.73706 −0.520285
\(283\) −0.645127 1.11739i −0.0383488 0.0664221i 0.846214 0.532843i \(-0.178876\pi\)
−0.884563 + 0.466421i \(0.845543\pi\)
\(284\) −0.131888 0.228437i −0.00782613 0.0135553i
\(285\) −27.5829 −1.63387
\(286\) 1.33757 0.0790921
\(287\) 36.7057 2.16667
\(288\) −0.691038 1.19691i −0.0407198 0.0705288i
\(289\) 7.32807 + 12.6926i 0.431063 + 0.746623i
\(290\) −16.5488 + 28.6633i −0.971778 + 1.68317i
\(291\) 2.27473 0.133347
\(292\) −0.701526 + 1.21508i −0.0410537 + 0.0711071i
\(293\) −9.31375 + 16.1319i −0.544115 + 0.942435i 0.454547 + 0.890723i \(0.349801\pi\)
−0.998662 + 0.0517122i \(0.983532\pi\)
\(294\) 4.40004 7.62109i 0.256615 0.444471i
\(295\) 6.30187 10.9152i 0.366909 0.635505i
\(296\) −12.5973 21.8191i −0.732201 1.26821i
\(297\) −0.214620 + 0.371733i −0.0124535 + 0.0215702i
\(298\) 24.8160 1.43755
\(299\) 2.29745 + 3.97930i 0.132865 + 0.230129i
\(300\) 2.91556 0.168330
\(301\) −17.4757 30.2688i −1.00728 1.74466i
\(302\) −8.08271 + 13.9997i −0.465108 + 0.805590i
\(303\) 0.656223 1.13661i 0.0376990 0.0652966i
\(304\) 11.5803 20.0576i 0.664174 1.15038i
\(305\) −20.0113 34.6606i −1.14584 1.98466i
\(306\) −2.02773 −0.115917
\(307\) −23.1941 −1.32376 −0.661879 0.749611i \(-0.730241\pi\)
−0.661879 + 0.749611i \(0.730241\pi\)
\(308\) 0.194840 0.337473i 0.0111020 0.0192293i
\(309\) −2.76997 + 4.79773i −0.157578 + 0.272933i
\(310\) 29.2575 1.66171
\(311\) −2.05469 + 3.55882i −0.116511 + 0.201802i −0.918383 0.395694i \(-0.870504\pi\)
0.801872 + 0.597496i \(0.203838\pi\)
\(312\) −6.99811 −0.396190
\(313\) 23.1132 1.30644 0.653218 0.757170i \(-0.273418\pi\)
0.653218 + 0.757170i \(0.273418\pi\)
\(314\) 1.88523 + 16.4882i 0.106390 + 0.930481i
\(315\) −15.1684 −0.854643
\(316\) −1.76693 −0.0993973
\(317\) 6.55839 11.3595i 0.368356 0.638012i −0.620953 0.783848i \(-0.713254\pi\)
0.989309 + 0.145837i \(0.0465874\pi\)
\(318\) 12.3764 0.694032
\(319\) 1.30605 2.26214i 0.0731245 0.126655i
\(320\) −17.9177 + 31.0344i −1.00163 + 1.73487i
\(321\) −2.56785 −0.143323
\(322\) −9.55479 −0.532468
\(323\) 5.14175 + 8.90577i 0.286095 + 0.495530i
\(324\) 0.122886 0.212845i 0.00682700 0.0118247i
\(325\) 13.9551 24.1709i 0.774088 1.34076i
\(326\) 2.03167 3.51896i 0.112524 0.194897i
\(327\) 5.71543 + 9.89942i 0.316064 + 0.547439i
\(328\) 29.5576 1.63204
\(329\) 12.1834 + 21.1022i 0.671690 + 1.16340i
\(330\) 2.33459 0.128515
\(331\) −11.5903 + 20.0749i −0.637058 + 1.10342i 0.349017 + 0.937116i \(0.386515\pi\)
−0.986075 + 0.166300i \(0.946818\pi\)
\(332\) 1.37368 + 2.37928i 0.0753905 + 0.130580i
\(333\) 4.23513 7.33547i 0.232084 0.401981i
\(334\) −0.0166239 + 0.0287934i −0.000909618 + 0.00157550i
\(335\) 28.5070 49.3756i 1.55750 2.69768i
\(336\) 6.36822 11.0301i 0.347415 0.601740i
\(337\) −10.0712 −0.548615 −0.274307 0.961642i \(-0.588449\pi\)
−0.274307 + 0.961642i \(0.588449\pi\)
\(338\) 4.94337 8.56217i 0.268884 0.465721i
\(339\) 5.37142 + 9.30356i 0.291735 + 0.505300i
\(340\) −0.772564 1.33812i −0.0418982 0.0725698i
\(341\) −2.30903 −0.125041
\(342\) 8.89647 0.481066
\(343\) 1.31421 0.0709607
\(344\) −14.0724 24.3741i −0.758734 1.31417i
\(345\) 4.00996 + 6.94545i 0.215889 + 0.373931i
\(346\) −25.6387 −1.37834
\(347\) 6.63666 + 11.4950i 0.356275 + 0.617086i 0.987335 0.158648i \(-0.0507134\pi\)
−0.631060 + 0.775734i \(0.717380\pi\)
\(348\) −0.747807 + 1.29524i −0.0400867 + 0.0694322i
\(349\) −8.13102 + 14.0833i −0.435244 + 0.753864i −0.997315 0.0732244i \(-0.976671\pi\)
0.562072 + 0.827088i \(0.310004\pi\)
\(350\) 29.0186 + 50.2618i 1.55111 + 2.68660i
\(351\) −1.17636 2.03752i −0.0627897 0.108755i
\(352\) 0.296622 0.513764i 0.0158100 0.0273837i
\(353\) −18.3823 −0.978390 −0.489195 0.872174i \(-0.662709\pi\)
−0.489195 + 0.872174i \(0.662709\pi\)
\(354\) −2.03258 + 3.52052i −0.108030 + 0.187114i
\(355\) −4.40727 −0.233913
\(356\) −0.0812471 + 0.140724i −0.00430609 + 0.00745837i
\(357\) 2.82755 + 4.89746i 0.149650 + 0.259201i
\(358\) 8.67935 15.0331i 0.458718 0.794523i
\(359\) −0.310445 −0.0163847 −0.00819234 0.999966i \(-0.502608\pi\)
−0.00819234 + 0.999966i \(0.502608\pi\)
\(360\) −12.2145 −0.643759
\(361\) −13.0590 22.6188i −0.687314 1.19046i
\(362\) −9.08712 + 15.7393i −0.477608 + 0.827242i
\(363\) 10.8158 0.567680
\(364\) 1.06794 + 1.84973i 0.0559755 + 0.0969524i
\(365\) 11.7213 + 20.3020i 0.613523 + 1.06265i
\(366\) 6.45436 + 11.1793i 0.337375 + 0.584350i
\(367\) −11.9759 20.7429i −0.625137 1.08277i −0.988514 0.151127i \(-0.951710\pi\)
0.363378 0.931642i \(-0.381623\pi\)
\(368\) −6.73407 −0.351038
\(369\) 4.96855 + 8.60578i 0.258652 + 0.447999i
\(370\) −46.0687 −2.39500
\(371\) −17.2582 29.8920i −0.895999 1.55192i
\(372\) 1.32209 0.0685471
\(373\) −16.6412 −0.861651 −0.430826 0.902435i \(-0.641778\pi\)
−0.430826 + 0.902435i \(0.641778\pi\)
\(374\) −0.435191 0.753774i −0.0225032 0.0389767i
\(375\) 14.0910 24.4063i 0.727656 1.26034i
\(376\) 9.81073 + 16.9927i 0.505950 + 0.876331i
\(377\) 7.15862 + 12.3991i 0.368687 + 0.638585i
\(378\) 4.89235 0.251635
\(379\) −19.0309 −0.977553 −0.488777 0.872409i \(-0.662557\pi\)
−0.488777 + 0.872409i \(0.662557\pi\)
\(380\) 3.38956 + 5.87089i 0.173881 + 0.301170i
\(381\) −8.42780 −0.431769
\(382\) 15.1722 26.2790i 0.776276 1.34455i
\(383\) −1.75435 + 3.03863i −0.0896432 + 0.155267i −0.907360 0.420354i \(-0.861906\pi\)
0.817717 + 0.575620i \(0.195239\pi\)
\(384\) 4.39701 7.61585i 0.224384 0.388645i
\(385\) −3.25545 5.63861i −0.165913 0.287370i
\(386\) −12.9626 22.4518i −0.659777 1.14277i
\(387\) 4.73108 8.19447i 0.240494 0.416548i
\(388\) −0.279533 0.484165i −0.0141911 0.0245797i
\(389\) −25.1623 −1.27578 −0.637888 0.770129i \(-0.720192\pi\)
−0.637888 + 0.770129i \(0.720192\pi\)
\(390\) −6.39810 + 11.0818i −0.323980 + 0.561150i
\(391\) 1.49500 2.58941i 0.0756052 0.130952i
\(392\) −19.7630 −0.998181
\(393\) −6.80978 −0.343508
\(394\) 4.63291 8.02444i 0.233403 0.404265i
\(395\) −14.7612 + 25.5671i −0.742716 + 1.28642i
\(396\) 0.105495 0.00530134
\(397\) −2.29616 3.97706i −0.115241 0.199603i 0.802635 0.596470i \(-0.203431\pi\)
−0.917876 + 0.396867i \(0.870097\pi\)
\(398\) 4.26986 7.39561i 0.214029 0.370708i
\(399\) −12.4056 21.4872i −0.621058 1.07570i
\(400\) 20.4519 + 35.4237i 1.02260 + 1.77119i
\(401\) −12.5987 + 21.8216i −0.629150 + 1.08972i 0.358573 + 0.933502i \(0.383264\pi\)
−0.987723 + 0.156218i \(0.950070\pi\)
\(402\) −9.19451 + 15.9254i −0.458581 + 0.794285i
\(403\) 6.32805 10.9605i 0.315223 0.545982i
\(404\) −0.322562 −0.0160481
\(405\) −2.05322 3.55628i −0.102025 0.176713i
\(406\) −29.7717 −1.47755
\(407\) 3.63579 0.180219
\(408\) 2.27690 + 3.94371i 0.112724 + 0.195243i
\(409\) 4.52293 + 7.83395i 0.223645 + 0.387364i 0.955912 0.293653i \(-0.0948711\pi\)
−0.732267 + 0.681017i \(0.761538\pi\)
\(410\) 27.0233 46.8058i 1.33459 2.31157i
\(411\) −0.794852 1.37672i −0.0392071 0.0679088i
\(412\) 1.36156 0.0670793
\(413\) 11.3373 0.557870
\(414\) −1.29335 2.24015i −0.0635648 0.110098i
\(415\) 45.9038 2.25333
\(416\) 1.62583 + 2.81601i 0.0797127 + 0.138066i
\(417\) 22.8827 1.12057
\(418\) 1.90936 + 3.30712i 0.0933901 + 0.161756i
\(419\) 11.5864 + 20.0683i 0.566035 + 0.980401i 0.996953 + 0.0780099i \(0.0248566\pi\)
−0.430918 + 0.902391i \(0.641810\pi\)
\(420\) 1.86399 + 3.22852i 0.0909532 + 0.157536i
\(421\) −7.27810 12.6060i −0.354713 0.614381i 0.632356 0.774678i \(-0.282088\pi\)
−0.987069 + 0.160297i \(0.948755\pi\)
\(422\) 1.55167 0.0755339
\(423\) −3.29832 + 5.71285i −0.160370 + 0.277768i
\(424\) −13.8973 24.0708i −0.674910 1.16898i
\(425\) −18.1617 −0.880971
\(426\) 1.42150 0.0688719
\(427\) 18.0005 31.1777i 0.871104 1.50880i
\(428\) 0.315553 + 0.546554i 0.0152528 + 0.0264187i
\(429\) 0.504944 0.874588i 0.0243789 0.0422255i
\(430\) −51.4635 −2.48179
\(431\) 14.4568 25.0400i 0.696362 1.20613i −0.273358 0.961912i \(-0.588134\pi\)
0.969719 0.244221i \(-0.0785324\pi\)
\(432\) 3.44805 0.165894
\(433\) 4.24578 7.35390i 0.204039 0.353406i −0.745787 0.666184i \(-0.767926\pi\)
0.949826 + 0.312778i \(0.101260\pi\)
\(434\) 13.1588 + 22.7917i 0.631641 + 1.09403i
\(435\) 12.4946 + 21.6413i 0.599071 + 1.03762i
\(436\) 1.40469 2.43300i 0.0672726 0.116520i
\(437\) −6.55917 + 11.3608i −0.313768 + 0.543461i
\(438\) −3.78055 6.54810i −0.180641 0.312880i
\(439\) 28.3381 1.35251 0.676253 0.736670i \(-0.263603\pi\)
0.676253 + 0.736670i \(0.263603\pi\)
\(440\) −2.62147 4.54053i −0.124974 0.216461i
\(441\) −3.32211 5.75406i −0.158196 0.274003i
\(442\) 4.77069 0.226919
\(443\) 16.0616 0.763110 0.381555 0.924346i \(-0.375389\pi\)
0.381555 + 0.924346i \(0.375389\pi\)
\(444\) −2.08176 −0.0987958
\(445\) 1.35750 + 2.35127i 0.0643519 + 0.111461i
\(446\) 15.9005 + 27.5405i 0.752911 + 1.30408i
\(447\) 9.36827 16.2263i 0.443104 0.767478i
\(448\) −32.2345 −1.52294
\(449\) 14.6417 25.3602i 0.690986 1.19682i −0.280529 0.959845i \(-0.590510\pi\)
0.971515 0.236977i \(-0.0761566\pi\)
\(450\) −7.85603 + 13.6070i −0.370337 + 0.641442i
\(451\) −2.13271 + 3.69395i −0.100425 + 0.173941i
\(452\) 1.32014 2.28656i 0.0620943 0.107551i
\(453\) 6.10258 + 10.5700i 0.286724 + 0.496621i
\(454\) −9.80465 + 16.9822i −0.460155 + 0.797012i
\(455\) 35.6872 1.67304
\(456\) −9.98972 17.3027i −0.467812 0.810273i
\(457\) −10.0387 −0.469593 −0.234796 0.972045i \(-0.575442\pi\)
−0.234796 + 0.972045i \(0.575442\pi\)
\(458\) −11.2122 19.4202i −0.523914 0.907445i
\(459\) −0.765484 + 1.32586i −0.0357297 + 0.0618857i
\(460\) 0.985536 1.70700i 0.0459508 0.0795892i
\(461\) 14.7359 25.5233i 0.686319 1.18874i −0.286702 0.958020i \(-0.592559\pi\)
0.973020 0.230719i \(-0.0741077\pi\)
\(462\) 1.05000 + 1.81865i 0.0488503 + 0.0846112i
\(463\) −24.6185 −1.14412 −0.572059 0.820213i \(-0.693855\pi\)
−0.572059 + 0.820213i \(0.693855\pi\)
\(464\) −20.9827 −0.974096
\(465\) 11.0450 19.1304i 0.512198 0.887152i
\(466\) −10.9968 + 19.0470i −0.509417 + 0.882337i
\(467\) −7.63755 −0.353424 −0.176712 0.984263i \(-0.556546\pi\)
−0.176712 + 0.984263i \(0.556546\pi\)
\(468\) −0.289118 + 0.500766i −0.0133645 + 0.0231479i
\(469\) 51.2850 2.36812
\(470\) 35.8783 1.65494
\(471\) 11.4927 + 4.99174i 0.529556 + 0.230007i
\(472\) 9.12940 0.420215
\(473\) 4.06154 0.186750
\(474\) 4.76101 8.24630i 0.218680 0.378765i
\(475\) 79.6828 3.65610
\(476\) 0.694933 1.20366i 0.0318522 0.0551696i
\(477\) 4.67219 8.09247i 0.213925 0.370529i
\(478\) 25.6981 1.17540
\(479\) 26.9637 1.23200 0.616001 0.787745i \(-0.288752\pi\)
0.616001 + 0.787745i \(0.288752\pi\)
\(480\) 2.83771 + 4.91506i 0.129523 + 0.224341i
\(481\) −9.96413 + 17.2584i −0.454325 + 0.786914i
\(482\) 11.8595 20.5413i 0.540186 0.935630i
\(483\) −3.60702 + 6.24754i −0.164125 + 0.284273i
\(484\) −1.32910 2.30208i −0.0604139 0.104640i
\(485\) −9.34105 −0.424155
\(486\) 0.662236 + 1.14703i 0.0300397 + 0.0520302i
\(487\) −2.26360 −0.102574 −0.0512868 0.998684i \(-0.516332\pi\)
−0.0512868 + 0.998684i \(0.516332\pi\)
\(488\) 14.4950 25.1061i 0.656158 1.13650i
\(489\) −1.53395 2.65688i −0.0693675 0.120148i
\(490\) −18.0685 + 31.2956i −0.816252 + 1.41379i
\(491\) 10.4739 18.1413i 0.472680 0.818706i −0.526831 0.849970i \(-0.676620\pi\)
0.999511 + 0.0312643i \(0.00995335\pi\)
\(492\) 1.22113 2.11506i 0.0550528 0.0953543i
\(493\) 4.65826 8.06833i 0.209797 0.363380i
\(494\) −20.9310 −0.941730
\(495\) 0.881327 1.52650i 0.0396127 0.0686112i
\(496\) 9.27410 + 16.0632i 0.416420 + 0.721260i
\(497\) −1.98220 3.43327i −0.0889139 0.154003i
\(498\) −14.8056 −0.663455
\(499\) 16.3218 0.730664 0.365332 0.930877i \(-0.380955\pi\)
0.365332 + 0.930877i \(0.380955\pi\)
\(500\) −6.92635 −0.309756
\(501\) 0.0125513 + 0.0217395i 0.000560751 + 0.000971250i
\(502\) 0.125532 + 0.217428i 0.00560278 + 0.00970430i
\(503\) 44.6201 1.98951 0.994756 0.102273i \(-0.0326116\pi\)
0.994756 + 0.102273i \(0.0326116\pi\)
\(504\) −5.49355 9.51510i −0.244702 0.423836i
\(505\) −2.69474 + 4.66743i −0.119914 + 0.207698i
\(506\) 0.555160 0.961565i 0.0246799 0.0427468i
\(507\) −3.73233 6.46459i −0.165759 0.287102i
\(508\) 1.03566 + 1.79381i 0.0459499 + 0.0795876i
\(509\) −8.28770 + 14.3547i −0.367346 + 0.636262i −0.989150 0.146911i \(-0.953067\pi\)
0.621804 + 0.783173i \(0.286400\pi\)
\(510\) 8.32674 0.368714
\(511\) −10.5435 + 18.2619i −0.466418 + 0.807860i
\(512\) −25.2777 −1.11713
\(513\) 3.35849 5.81708i 0.148281 0.256831i
\(514\) −5.39796 9.34954i −0.238094 0.412390i
\(515\) 11.3747 19.7016i 0.501230 0.868156i
\(516\) −2.32553 −0.102376
\(517\) −2.83155 −0.124531
\(518\) −20.7197 35.8877i −0.910373 1.57681i
\(519\) −9.67883 + 16.7642i −0.424853 + 0.735868i
\(520\) 28.7373 1.26022
\(521\) −14.2912 24.7531i −0.626110 1.08445i −0.988325 0.152360i \(-0.951313\pi\)
0.362215 0.932095i \(-0.382021\pi\)
\(522\) −4.02995 6.98009i −0.176386 0.305510i
\(523\) −7.63600 13.2259i −0.333899 0.578330i 0.649374 0.760469i \(-0.275031\pi\)
−0.983273 + 0.182140i \(0.941698\pi\)
\(524\) 0.836827 + 1.44943i 0.0365570 + 0.0633185i
\(525\) 43.8192 1.91243
\(526\) 1.09974 + 1.90480i 0.0479509 + 0.0830534i
\(527\) −8.23558 −0.358748
\(528\) 0.740022 + 1.28176i 0.0322053 + 0.0557813i
\(529\) −19.1858 −0.834163
\(530\) −50.8229 −2.20760
\(531\) 1.53463 + 2.65806i 0.0665973 + 0.115350i
\(532\) −3.04896 + 5.28095i −0.132189 + 0.228958i
\(533\) −11.6897 20.2471i −0.506335 0.876998i
\(534\) −0.437843 0.758367i −0.0189473 0.0328177i
\(535\) 10.5447 0.455889
\(536\) 41.2976 1.78378
\(537\) −6.55306 11.3502i −0.282786 0.489799i
\(538\) 34.6511 1.49392
\(539\) 1.42598 2.46988i 0.0614215 0.106385i
\(540\) −0.504625 + 0.874035i −0.0217156 + 0.0376125i
\(541\) −7.19393 + 12.4602i −0.309291 + 0.535708i −0.978207 0.207630i \(-0.933425\pi\)
0.668916 + 0.743338i \(0.266758\pi\)
\(542\) −3.67735 6.36936i −0.157956 0.273587i
\(543\) 6.86093 + 11.8835i 0.294431 + 0.509969i
\(544\) 1.05796 1.83244i 0.0453596 0.0785651i
\(545\) −23.4701 40.6514i −1.00535 1.74131i
\(546\) −11.5104 −0.492598
\(547\) 6.98784 12.1033i 0.298778 0.517499i −0.677078 0.735911i \(-0.736754\pi\)
0.975857 + 0.218412i \(0.0700875\pi\)
\(548\) −0.195352 + 0.338360i −0.00834504 + 0.0144540i
\(549\) 9.74630 0.415962
\(550\) −6.74425 −0.287576
\(551\) −20.4377 + 35.3991i −0.870675 + 1.50805i
\(552\) −2.90458 + 5.03087i −0.123627 + 0.214128i
\(553\) −26.5558 −1.12927
\(554\) 15.6458 + 27.0993i 0.664726 + 1.15134i
\(555\) −17.3913 + 30.1227i −0.738221 + 1.27864i
\(556\) −2.81197 4.87047i −0.119254 0.206554i
\(557\) 9.34061 + 16.1784i 0.395774 + 0.685501i 0.993200 0.116423i \(-0.0371429\pi\)
−0.597425 + 0.801924i \(0.703810\pi\)
\(558\) −3.56239 + 6.17024i −0.150808 + 0.261207i
\(559\) −11.1309 + 19.2794i −0.470789 + 0.815430i
\(560\) −26.1507 + 45.2944i −1.10507 + 1.91404i
\(561\) −0.657154 −0.0277451
\(562\) 13.1966 + 22.8572i 0.556666 + 0.964174i
\(563\) −29.5188 −1.24407 −0.622034 0.782990i \(-0.713693\pi\)
−0.622034 + 0.782990i \(0.713693\pi\)
\(564\) 1.62127 0.0682677
\(565\) −22.0574 38.2046i −0.927962 1.60728i
\(566\) −0.854453 1.47996i −0.0359154 0.0622072i
\(567\) 1.84690 3.19893i 0.0775627 0.134342i
\(568\) −1.59618 2.76467i −0.0669743 0.116003i
\(569\) 29.3278 1.22948 0.614742 0.788728i \(-0.289260\pi\)
0.614742 + 0.788728i \(0.289260\pi\)
\(570\) −36.5328 −1.53019
\(571\) −20.6703 35.8021i −0.865026 1.49827i −0.867021 0.498272i \(-0.833968\pi\)
0.00199457 0.999998i \(-0.499365\pi\)
\(572\) −0.248202 −0.0103779
\(573\) −11.4553 19.8411i −0.478550 0.828874i
\(574\) 48.6158 2.02918
\(575\) −11.5841 20.0643i −0.483092 0.836740i
\(576\) −4.36331 7.55748i −0.181805 0.314895i
\(577\) 6.00504 + 10.4010i 0.249993 + 0.433001i 0.963524 0.267623i \(-0.0862383\pi\)
−0.713530 + 0.700624i \(0.752905\pi\)
\(578\) 9.70583 + 16.8110i 0.403709 + 0.699245i
\(579\) −19.5739 −0.813464
\(580\) 3.07083 5.31883i 0.127509 0.220852i
\(581\) 20.6456 + 35.7592i 0.856523 + 1.48354i
\(582\) 3.01282 0.124885
\(583\) 4.01099 0.166118
\(584\) −8.49024 + 14.7055i −0.351329 + 0.608519i
\(585\) 4.83067 + 8.36697i 0.199724 + 0.345932i
\(586\) −12.3358 + 21.3662i −0.509587 + 0.882631i
\(587\) −8.96665 −0.370093 −0.185047 0.982730i \(-0.559244\pi\)
−0.185047 + 0.982730i \(0.559244\pi\)
\(588\) −0.816481 + 1.41419i −0.0336711 + 0.0583201i
\(589\) 36.1329 1.48883
\(590\) 8.34666 14.4568i 0.343626 0.595178i
\(591\) −3.49793 6.05859i −0.143886 0.249217i
\(592\) −14.6030 25.2931i −0.600178 1.03954i
\(593\) 17.6972 30.6525i 0.726738 1.25875i −0.231517 0.972831i \(-0.574369\pi\)
0.958255 0.285916i \(-0.0922978\pi\)
\(594\) −0.284259 + 0.492351i −0.0116633 + 0.0202014i
\(595\) −11.6112 20.1111i −0.476012 0.824477i
\(596\) −4.60492 −0.188625
\(597\) −3.22382 5.58381i −0.131942 0.228530i
\(598\) 3.04291 + 5.27047i 0.124434 + 0.215526i
\(599\) 17.3550 0.709106 0.354553 0.935036i \(-0.384633\pi\)
0.354553 + 0.935036i \(0.384633\pi\)
\(600\) 35.2857 1.44053
\(601\) −19.8373 −0.809179 −0.404590 0.914498i \(-0.632586\pi\)
−0.404590 + 0.914498i \(0.632586\pi\)
\(602\) −23.1461 40.0902i −0.943364 1.63395i
\(603\) 6.94202 + 12.0239i 0.282701 + 0.489652i
\(604\) 1.49984 2.59781i 0.0610278 0.105703i
\(605\) −44.4143 −1.80570
\(606\) 0.869149 1.50541i 0.0353068 0.0611531i
\(607\) −15.9725 + 27.6652i −0.648303 + 1.12289i 0.335225 + 0.942138i \(0.391188\pi\)
−0.983528 + 0.180756i \(0.942146\pi\)
\(608\) −4.64170 + 8.03966i −0.188246 + 0.326051i
\(609\) −11.2391 + 19.4667i −0.455431 + 0.788830i
\(610\) −26.5044 45.9070i −1.07313 1.85872i
\(611\) 7.76005 13.4408i 0.313938 0.543757i
\(612\) 0.376269 0.0152098
\(613\) 7.95929 + 13.7859i 0.321473 + 0.556807i 0.980792 0.195056i \(-0.0624888\pi\)
−0.659319 + 0.751863i \(0.729155\pi\)
\(614\) −30.7200 −1.23976
\(615\) −20.4031 35.3392i −0.822731 1.42501i
\(616\) 2.35806 4.08427i 0.0950088 0.164560i
\(617\) −14.4686 + 25.0603i −0.582484 + 1.00889i 0.412700 + 0.910867i \(0.364586\pi\)
−0.995184 + 0.0980244i \(0.968748\pi\)
\(618\) −3.66875 + 6.35446i −0.147579 + 0.255614i
\(619\) −8.27505 14.3328i −0.332602 0.576084i 0.650419 0.759576i \(-0.274593\pi\)
−0.983021 + 0.183492i \(0.941260\pi\)
\(620\) −5.42908 −0.218037
\(621\) −1.95301 −0.0783715
\(622\) −2.72138 + 4.71356i −0.109117 + 0.188997i
\(623\) −1.22110 + 2.11500i −0.0489222 + 0.0847357i
\(624\) −8.11233 −0.324753
\(625\) −28.2067 + 48.8554i −1.12827 + 1.95422i
\(626\) 30.6128 1.22353
\(627\) 2.88321 0.115144
\(628\) −0.349828 3.05958i −0.0139596 0.122091i
\(629\) 12.9677 0.517057
\(630\) −20.0901 −0.800410
\(631\) 1.10751 1.91827i 0.0440894 0.0763650i −0.843139 0.537696i \(-0.819295\pi\)
0.887228 + 0.461331i \(0.152628\pi\)
\(632\) −21.3843 −0.850620
\(633\) 0.585767 1.01458i 0.0232822 0.0403259i
\(634\) 8.68641 15.0453i 0.344982 0.597526i
\(635\) 34.6083 1.37339
\(636\) −2.29659 −0.0910656
\(637\) 7.81602 + 13.5377i 0.309682 + 0.536385i
\(638\) 1.72982 2.99614i 0.0684843 0.118618i
\(639\) 0.536628 0.929468i 0.0212287 0.0367692i
\(640\) −18.0561 + 31.2741i −0.713729 + 1.23622i
\(641\) 8.58773 + 14.8744i 0.339195 + 0.587503i 0.984282 0.176607i \(-0.0565121\pi\)
−0.645087 + 0.764109i \(0.723179\pi\)
\(642\) −3.40105 −0.134229
\(643\) 5.76022 + 9.97699i 0.227161 + 0.393454i 0.956966 0.290202i \(-0.0937224\pi\)
−0.729805 + 0.683656i \(0.760389\pi\)
\(644\) 1.77301 0.0698663
\(645\) −19.4279 + 33.6501i −0.764973 + 1.32497i
\(646\) 6.81011 + 11.7954i 0.267940 + 0.464086i
\(647\) −0.476192 + 0.824788i −0.0187210 + 0.0324258i −0.875234 0.483699i \(-0.839293\pi\)
0.856513 + 0.516125i \(0.172626\pi\)
\(648\) 1.48723 2.57596i 0.0584240 0.101193i
\(649\) −0.658726 + 1.14095i −0.0258573 + 0.0447861i
\(650\) 18.4831 32.0137i 0.724967 1.25568i
\(651\) 19.8702 0.778775
\(652\) −0.377002 + 0.652986i −0.0147645 + 0.0255729i
\(653\) 7.59087 + 13.1478i 0.297054 + 0.514512i 0.975461 0.220174i \(-0.0706626\pi\)
−0.678407 + 0.734687i \(0.737329\pi\)
\(654\) 7.56993 + 13.1115i 0.296008 + 0.512700i
\(655\) 27.9640 1.09264
\(656\) 34.2636 1.33777
\(657\) −5.70876 −0.222720
\(658\) 16.1365 + 27.9493i 0.629067 + 1.08958i
\(659\) −6.33771 10.9772i −0.246882 0.427612i 0.715777 0.698329i \(-0.246073\pi\)
−0.962659 + 0.270717i \(0.912739\pi\)
\(660\) −0.433211 −0.0168627
\(661\) 11.8957 + 20.6040i 0.462689 + 0.801401i 0.999094 0.0425595i \(-0.0135512\pi\)
−0.536405 + 0.843961i \(0.680218\pi\)
\(662\) −15.3510 + 26.5887i −0.596632 + 1.03340i
\(663\) 1.80098 3.11938i 0.0699441 0.121147i
\(664\) 16.6250 + 28.7954i 0.645175 + 1.11748i
\(665\) 50.9430 + 88.2359i 1.97549 + 3.42164i
\(666\) 5.60932 9.71563i 0.217357 0.376473i
\(667\) 11.8848 0.460181
\(668\) 0.00308476 0.00534296i 0.000119353 0.000206725i
\(669\) 24.0103 0.928293
\(670\) 37.7567 65.3966i 1.45867 2.52649i
\(671\) 2.09176 + 3.62303i 0.0807513 + 0.139865i
\(672\) −2.55256 + 4.42117i −0.0984673 + 0.170550i
\(673\) 31.2291 1.20379 0.601897 0.798574i \(-0.294412\pi\)
0.601897 + 0.798574i \(0.294412\pi\)
\(674\) −13.3391 −0.513802
\(675\) 5.93144 + 10.2735i 0.228301 + 0.395429i
\(676\) −0.917303 + 1.58882i −0.0352809 + 0.0611083i
\(677\) −43.9667 −1.68978 −0.844889 0.534942i \(-0.820333\pi\)
−0.844889 + 0.534942i \(0.820333\pi\)
\(678\) 7.11429 + 12.3223i 0.273223 + 0.473236i
\(679\) −4.20121 7.27670i −0.161228 0.279254i
\(680\) −9.34998 16.1946i −0.358555 0.621036i
\(681\) 7.40268 + 12.8218i 0.283671 + 0.491333i
\(682\) −3.05824 −0.117106
\(683\) −13.6091 23.5716i −0.520737 0.901943i −0.999709 0.0241132i \(-0.992324\pi\)
0.478972 0.877830i \(-0.341010\pi\)
\(684\) −1.65085 −0.0631218
\(685\) 3.26401 + 5.65344i 0.124712 + 0.216007i
\(686\) 1.74064 0.0664578
\(687\) −16.9309 −0.645953
\(688\) −16.3130 28.2550i −0.621927 1.07721i
\(689\) −10.9924 + 19.0394i −0.418777 + 0.725343i
\(690\) 5.31108 + 9.19906i 0.202189 + 0.350202i
\(691\) 23.3655 + 40.4702i 0.888866 + 1.53956i 0.841218 + 0.540696i \(0.181839\pi\)
0.0476480 + 0.998864i \(0.484827\pi\)
\(692\) 4.75757 0.180856
\(693\) 1.58553 0.0602294
\(694\) 8.79008 + 15.2249i 0.333667 + 0.577928i
\(695\) −93.9666 −3.56435
\(696\) −9.05036 + 15.6757i −0.343053 + 0.594185i
\(697\) −7.60669 + 13.1752i −0.288124 + 0.499046i
\(698\) −10.7693 + 18.6530i −0.407625 + 0.706026i
\(699\) 8.30278 + 14.3808i 0.314040 + 0.543933i
\(700\) −5.38476 9.32668i −0.203525 0.352516i
\(701\) 9.20063 15.9360i 0.347503 0.601893i −0.638302 0.769786i \(-0.720363\pi\)
0.985805 + 0.167893i \(0.0536963\pi\)
\(702\) −1.55806 2.69864i −0.0588053 0.101854i
\(703\) −56.8947 −2.14582
\(704\) 1.87291 3.24398i 0.0705880 0.122262i
\(705\) 13.5444 23.4595i 0.510110 0.883536i
\(706\) −24.3468 −0.916305
\(707\) −4.84792 −0.182325
\(708\) 0.377169 0.653276i 0.0141749 0.0245516i
\(709\) −5.71706 + 9.90224i −0.214709 + 0.371887i −0.953182 0.302396i \(-0.902214\pi\)
0.738474 + 0.674282i \(0.235547\pi\)
\(710\) −5.83731 −0.219070
\(711\) −3.59464 6.22610i −0.134810 0.233497i
\(712\) −0.983296 + 1.70312i −0.0368506 + 0.0638271i
\(713\) −5.25294 9.09836i −0.196724 0.340736i
\(714\) 3.74501 + 6.48655i 0.140154 + 0.242753i
\(715\) −2.07352 + 3.59145i −0.0775454 + 0.134312i
\(716\) −1.61056 + 2.78957i −0.0601894 + 0.104251i
\(717\) 9.70125 16.8031i 0.362300 0.627522i
\(718\) −0.411176 −0.0153450
\(719\) 21.9655 + 38.0453i 0.819174 + 1.41885i 0.906291 + 0.422654i \(0.138901\pi\)
−0.0871169 + 0.996198i \(0.527765\pi\)
\(720\) −14.1592 −0.527683
\(721\) 20.4635 0.762099
\(722\) −17.2963 29.9580i −0.643700 1.11492i
\(723\) −8.95415 15.5090i −0.333008 0.576787i
\(724\) 1.68623 2.92063i 0.0626681 0.108544i
\(725\) −36.0950 62.5184i −1.34053 2.32187i
\(726\) 14.3252 0.531657
\(727\) −36.5297 −1.35481 −0.677405 0.735610i \(-0.736896\pi\)
−0.677405 + 0.735610i \(0.736896\pi\)
\(728\) 12.9248 + 22.3865i 0.479026 + 0.829698i
\(729\) 1.00000 0.0370370
\(730\) 15.5246 + 26.8894i 0.574591 + 0.995221i
\(731\) 14.4863 0.535794
\(732\) −1.19768 2.07445i −0.0442677 0.0766739i
\(733\) −2.94043 5.09298i −0.108607 0.188113i 0.806599 0.591099i \(-0.201306\pi\)
−0.915206 + 0.402986i \(0.867972\pi\)
\(734\) −15.8617 27.4734i −0.585468 1.01406i
\(735\) 13.6420 + 23.6287i 0.503194 + 0.871558i
\(736\) 2.69921 0.0994941
\(737\) −2.97980 + 5.16116i −0.109762 + 0.190114i
\(738\) 6.58071 + 11.3981i 0.242239 + 0.419571i
\(739\) 29.7338 1.09377 0.546887 0.837206i \(-0.315813\pi\)
0.546887 + 0.837206i \(0.315813\pi\)
\(740\) 8.54861 0.314253
\(741\) −7.90163 + 13.6860i −0.290274 + 0.502769i
\(742\) −22.8580 39.5912i −0.839142 1.45344i
\(743\) −8.50203 + 14.7260i −0.311909 + 0.540243i −0.978776 0.204935i \(-0.934302\pi\)
0.666866 + 0.745177i \(0.267635\pi\)
\(744\) 16.0006 0.586611
\(745\) −38.4703 + 66.6324i −1.40944 + 2.44122i
\(746\) −22.0409 −0.806974
\(747\) −5.58924 + 9.68086i −0.204500 + 0.354204i
\(748\) 0.0807551 + 0.139872i 0.00295270 + 0.00511422i
\(749\) 4.74257 + 8.21438i 0.173290 + 0.300147i
\(750\) 18.6631 32.3255i 0.681482 1.18036i
\(751\) 6.79611 11.7712i 0.247994 0.429537i −0.714975 0.699150i \(-0.753562\pi\)
0.962969 + 0.269612i \(0.0868955\pi\)
\(752\) 11.3728 + 19.6982i 0.414722 + 0.718320i
\(753\) 0.189558 0.00690788
\(754\) 9.48139 + 16.4223i 0.345292 + 0.598063i
\(755\) −25.0599 43.4050i −0.912024 1.57967i
\(756\) −0.907835 −0.0330176
\(757\) −1.51356 −0.0550112 −0.0275056 0.999622i \(-0.508756\pi\)
−0.0275056 + 0.999622i \(0.508756\pi\)
\(758\) −25.2060 −0.915521
\(759\) −0.419156 0.725999i −0.0152144 0.0263521i
\(760\) 41.0222 + 71.0526i 1.48803 + 2.57735i
\(761\) 15.8443 27.4432i 0.574356 0.994814i −0.421755 0.906710i \(-0.638586\pi\)
0.996111 0.0881043i \(-0.0280809\pi\)
\(762\) −11.1624 −0.404371
\(763\) 21.1117 36.5665i 0.764295 1.32380i
\(764\) −2.81538 + 4.87639i −0.101857 + 0.176422i
\(765\) 3.14342 5.44456i 0.113650 0.196848i
\(766\) −2.32359 + 4.02458i −0.0839548 + 0.145414i
\(767\) −3.61057 6.25369i −0.130370 0.225808i
\(768\) −2.90290 + 5.02798i −0.104750 + 0.181431i
\(769\) −33.1361 −1.19492 −0.597459 0.801900i \(-0.703823\pi\)
−0.597459 + 0.801900i \(0.703823\pi\)
\(770\) −4.31176 7.46818i −0.155385 0.269134i
\(771\) −8.15110 −0.293555
\(772\) 2.40536 + 4.16621i 0.0865708 + 0.149945i
\(773\) −4.62049 + 8.00292i −0.166187 + 0.287845i −0.937076 0.349125i \(-0.886479\pi\)
0.770889 + 0.636970i \(0.219812\pi\)
\(774\) 6.26618 10.8533i 0.225233 0.390116i
\(775\) −31.9072 + 55.2648i −1.14614 + 1.98517i
\(776\) −3.38305 5.85962i −0.121444 0.210348i
\(777\) −31.2875 −1.12243
\(778\) −33.3267 −1.19482
\(779\) 33.3737 57.8050i 1.19574 2.07108i
\(780\) 1.18724 2.05637i 0.0425102 0.0736298i
\(781\) 0.460686 0.0164846
\(782\) 1.98008 3.42960i 0.0708076 0.122642i
\(783\) −6.08537 −0.217473
\(784\) −22.9096 −0.818200
\(785\) −47.1942 20.4983i −1.68443 0.731616i
\(786\) −9.01937 −0.321710
\(787\) 37.1471 1.32415 0.662075 0.749438i \(-0.269676\pi\)
0.662075 + 0.749438i \(0.269676\pi\)
\(788\) −0.859693 + 1.48903i −0.0306253 + 0.0530446i
\(789\) 1.66065 0.0591205
\(790\) −19.5508 + 33.8630i −0.695586 + 1.20479i
\(791\) 19.8410 34.3656i 0.705464 1.22190i
\(792\) 1.27676 0.0453677
\(793\) −22.9304 −0.814283
\(794\) −3.04120 5.26751i −0.107928 0.186937i
\(795\) −19.1861 + 33.2313i −0.680460 + 1.17859i
\(796\) −0.792324 + 1.37235i −0.0280832 + 0.0486415i
\(797\) 15.8021 27.3701i 0.559739 0.969497i −0.437778 0.899083i \(-0.644235\pi\)
0.997518 0.0704143i \(-0.0224321\pi\)
\(798\) −16.4309 28.4592i −0.581648 1.00744i
\(799\) −10.0992 −0.357285
\(800\) −8.19770 14.1988i −0.289833 0.502005i
\(801\) −0.661158 −0.0233609
\(802\) −16.6867 + 28.9021i −0.589226 + 1.02057i
\(803\) −1.22522 2.12214i −0.0432369 0.0748885i
\(804\) 1.70615 2.95515i 0.0601714 0.104220i
\(805\) 14.8120 25.6552i 0.522055 0.904226i
\(806\) 8.38133 14.5169i 0.295220 0.511336i
\(807\) 13.0811 22.6571i 0.460477 0.797569i
\(808\) −3.90382 −0.137336
\(809\) −4.36683 + 7.56358i −0.153530 + 0.265921i −0.932523 0.361111i \(-0.882397\pi\)
0.778993 + 0.627033i \(0.215731\pi\)
\(810\) −2.71944 4.71020i −0.0955512 0.165500i
\(811\) 1.70727 + 2.95707i 0.0599502 + 0.103837i 0.894443 0.447182i \(-0.147572\pi\)
−0.834493 + 0.551019i \(0.814239\pi\)
\(812\) 5.52451 0.193872
\(813\) −5.55293 −0.194750
\(814\) 4.81550 0.168783
\(815\) 6.29907 + 10.9103i 0.220647 + 0.382172i
\(816\) 2.63943 + 4.57163i 0.0923985 + 0.160039i
\(817\) −63.5572 −2.22359
\(818\) 5.99050 + 10.3759i 0.209453 + 0.362783i
\(819\) −4.34526 + 7.52622i −0.151836 + 0.262987i
\(820\) −5.01451 + 8.68538i −0.175114 + 0.303307i
\(821\) −0.331118 0.573514i −0.0115561 0.0200158i 0.860190 0.509974i \(-0.170345\pi\)
−0.871746 + 0.489959i \(0.837012\pi\)
\(822\) −1.05276 1.82343i −0.0367192 0.0635995i
\(823\) −15.1637 + 26.2643i −0.528574 + 0.915516i 0.470871 + 0.882202i \(0.343940\pi\)
−0.999445 + 0.0333144i \(0.989394\pi\)
\(824\) 16.4783 0.574050
\(825\) −2.54601 + 4.40983i −0.0886409 + 0.153530i
\(826\) 15.0159 0.522469
\(827\) −17.5350 + 30.3714i −0.609750 + 1.05612i 0.381531 + 0.924356i \(0.375397\pi\)
−0.991281 + 0.131762i \(0.957936\pi\)
\(828\) 0.239997 + 0.415688i 0.00834049 + 0.0144462i
\(829\) −22.5841 + 39.1169i −0.784380 + 1.35859i 0.144989 + 0.989433i \(0.453685\pi\)
−0.929369 + 0.369152i \(0.879648\pi\)
\(830\) 60.7984 2.11034
\(831\) 23.6257 0.819566
\(832\) 10.2657 + 17.7807i 0.355899 + 0.616435i
\(833\) 5.08604 8.80928i 0.176221 0.305223i
\(834\) 30.3075 1.04946
\(835\) −0.0515412 0.0892721i −0.00178366 0.00308939i
\(836\) −0.354306 0.613676i −0.0122539 0.0212244i
\(837\) 2.68966 + 4.65864i 0.0929684 + 0.161026i
\(838\) 15.3459 + 26.5799i 0.530116 + 0.918188i
\(839\) −30.7730 −1.06240 −0.531201 0.847246i \(-0.678259\pi\)
−0.531201 + 0.847246i \(0.678259\pi\)
\(840\) 22.5589 + 39.0732i 0.778357 + 1.34815i
\(841\) 8.03175 0.276957
\(842\) −9.63965 16.6964i −0.332204 0.575394i
\(843\) 19.9274 0.686335
\(844\) −0.287931 −0.00991098
\(845\) 15.3266 + 26.5465i 0.527251 + 0.913226i
\(846\) −4.36853 + 7.56652i −0.150193 + 0.260142i
\(847\) −19.9757 34.5988i −0.686372 1.18883i
\(848\) −16.1099 27.9032i −0.553218 0.958201i
\(849\) −1.29025 −0.0442814
\(850\) −24.0547 −0.825068
\(851\) 8.27125 + 14.3262i 0.283535 + 0.491097i
\(852\) −0.263777 −0.00903684
\(853\) −0.742393 + 1.28586i −0.0254191 + 0.0440271i −0.878455 0.477825i \(-0.841425\pi\)
0.853036 + 0.521852i \(0.174759\pi\)
\(854\) 23.8411 41.2941i 0.815827 1.41305i
\(855\) −13.7915 + 23.8875i −0.471658 + 0.816936i
\(856\) 3.81899 + 6.61468i 0.130530 + 0.226085i
\(857\) 17.5817 + 30.4523i 0.600578 + 1.04023i 0.992734 + 0.120332i \(0.0383960\pi\)
−0.392156 + 0.919899i \(0.628271\pi\)
\(858\) 0.668784 1.15837i 0.0228319 0.0395460i
\(859\) −4.00596 6.93853i −0.136682 0.236740i 0.789557 0.613677i \(-0.210310\pi\)
−0.926239 + 0.376938i \(0.876977\pi\)
\(860\) 9.54967 0.325641
\(861\) 18.3529 31.7881i 0.625464 1.08334i
\(862\) 19.1477 33.1648i 0.652173 1.12960i
\(863\) −17.5909 −0.598801 −0.299401 0.954127i \(-0.596787\pi\)
−0.299401 + 0.954127i \(0.596787\pi\)
\(864\) −1.38208 −0.0470192
\(865\) 39.7456 68.8413i 1.35139 2.34067i
\(866\) 5.62342 9.74004i 0.191091 0.330980i
\(867\) 14.6561 0.497748
\(868\) −2.44177 4.22927i −0.0828791 0.143551i
\(869\) 1.54297 2.67250i 0.0523416 0.0906583i
\(870\) 16.5488 + 28.6633i 0.561056 + 0.971778i
\(871\) −16.3327 28.2891i −0.553412 0.958538i
\(872\) 17.0003 29.4455i 0.575704 0.997149i
\(873\) 1.13737 1.96997i 0.0384940 0.0666735i
\(874\) −8.68744 + 15.0471i −0.293857 + 0.508975i
\(875\) −104.099 −3.51918
\(876\) 0.701526 + 1.21508i 0.0237024 + 0.0410537i
\(877\) −25.0843 −0.847035 −0.423518 0.905888i \(-0.639205\pi\)
−0.423518 + 0.905888i \(0.639205\pi\)
\(878\) 37.5331 1.26668
\(879\) 9.31375 + 16.1319i 0.314145 + 0.544115i
\(880\) −3.03886 5.26346i −0.102440 0.177431i
\(881\) 22.9002 39.6644i 0.771529 1.33633i −0.165196 0.986261i \(-0.552826\pi\)
0.936725 0.350067i \(-0.113841\pi\)
\(882\) −4.40004 7.62109i −0.148157 0.256615i
\(883\) −11.5593 −0.389001 −0.194501 0.980902i \(-0.562309\pi\)
−0.194501 + 0.980902i \(0.562309\pi\)
\(884\) −0.885260 −0.0297745
\(885\) −6.30187 10.9152i −0.211835 0.366909i
\(886\) 21.2732 0.714686
\(887\) −3.06528 5.30922i −0.102922 0.178266i 0.809965 0.586478i \(-0.199486\pi\)
−0.912887 + 0.408212i \(0.866153\pi\)
\(888\) −25.1945 −0.845472
\(889\) 15.5653 + 26.9599i 0.522044 + 0.904207i
\(890\) 1.79798 + 3.11419i 0.0602684 + 0.104388i
\(891\) 0.214620 + 0.371733i 0.00719005 + 0.0124535i
\(892\) −2.95053 5.11047i −0.0987912 0.171111i
\(893\) 44.3095 1.48276
\(894\) 12.4080 21.4913i 0.414986 0.718777i
\(895\) 26.9098 + 46.6091i 0.899495 + 1.55797i
\(896\) −32.4834 −1.08520
\(897\) 4.59490 0.153419
\(898\) 19.3926 33.5889i 0.647138 1.12088i
\(899\) −16.3676 28.3495i −0.545890 0.945510i
\(900\) 1.45778 2.52495i 0.0485927 0.0841651i
\(901\) 14.3059 0.476600
\(902\) −2.82471 + 4.89254i −0.0940526 + 0.162904i
\(903\) −34.9514 −1.16311
\(904\) 15.9771 27.6731i 0.531390 0.920394i
\(905\) −28.1740 48.7988i −0.936536 1.62213i
\(906\) 8.08271 + 13.9997i 0.268530 + 0.465108i
\(907\) 0.703869 1.21914i 0.0233716 0.0404808i −0.854103 0.520104i \(-0.825893\pi\)
0.877475 + 0.479623i \(0.159227\pi\)
\(908\) 1.81937 3.15125i 0.0603780 0.104578i
\(909\) −0.656223 1.13661i −0.0217655 0.0376990i
\(910\) 47.2667 1.56687
\(911\) 17.4290 + 30.1879i 0.577448 + 1.00017i 0.995771 + 0.0918711i \(0.0292848\pi\)
−0.418323 + 0.908298i \(0.637382\pi\)
\(912\) −11.5803 20.0576i −0.383461 0.664174i
\(913\) −4.79826 −0.158799
\(914\) −13.2960 −0.439794
\(915\) −40.0226 −1.32311
\(916\) 2.08057 + 3.60365i 0.0687439 + 0.119068i
\(917\) 12.5770 + 21.7840i 0.415330 + 0.719372i
\(918\) −1.01386 + 1.75606i −0.0334625 + 0.0579587i
\(919\) −45.7684 −1.50976 −0.754879 0.655864i \(-0.772305\pi\)
−0.754879 + 0.655864i \(0.772305\pi\)
\(920\) 11.9275 20.6590i 0.393237 0.681107i
\(921\) −11.5971 + 20.0867i −0.382136 + 0.661879i
\(922\) 19.5173 33.8049i 0.642767 1.11331i
\(923\) −1.26254 + 2.18679i −0.0415571 + 0.0719789i
\(924\) −0.194840 0.337473i −0.00640976 0.0111020i
\(925\) 50.2409 87.0197i 1.65191 2.86119i
\(926\) −32.6065 −1.07152
\(927\) 2.76997 + 4.79773i 0.0909777 + 0.157578i
\(928\) 8.41045 0.276087
\(929\) 17.8929 + 30.9914i 0.587047 + 1.01680i 0.994617 + 0.103622i \(0.0330432\pi\)
−0.407569 + 0.913174i \(0.633624\pi\)
\(930\) 14.6287 25.3377i 0.479695 0.830857i
\(931\) −22.3146 + 38.6499i −0.731330 + 1.26670i
\(932\) 2.04059 3.53441i 0.0668418 0.115773i
\(933\) 2.05469 + 3.55882i 0.0672674 + 0.116511i
\(934\) −10.1157 −0.330997
\(935\) 2.69857 0.0882525
\(936\) −3.49905 + 6.06054i −0.114370 + 0.198095i
\(937\) 6.44187 11.1576i 0.210447 0.364504i −0.741408 0.671055i \(-0.765842\pi\)
0.951854 + 0.306551i \(0.0991749\pi\)
\(938\) 67.9255 2.21785
\(939\) 11.5566 20.0166i 0.377136 0.653218i
\(940\) −6.65765 −0.217149
\(941\) 56.2699 1.83435 0.917174 0.398487i \(-0.130465\pi\)
0.917174 + 0.398487i \(0.130465\pi\)
\(942\) 15.2218 + 6.61143i 0.495953 + 0.215412i
\(943\) −19.4072 −0.631987
\(944\) 10.5830 0.344446
\(945\) −7.58420 + 13.1362i −0.246714 + 0.427322i
\(946\) 5.37940 0.174900
\(947\) −15.6433 + 27.0949i −0.508338 + 0.880467i 0.491615 + 0.870812i \(0.336407\pi\)
−0.999953 + 0.00965487i \(0.996927\pi\)
\(948\) −0.883463 + 1.53020i −0.0286935 + 0.0496987i
\(949\) 13.4312 0.435994
\(950\) 105.538 3.42409
\(951\) −6.55839 11.3595i −0.212671 0.368356i
\(952\) 8.41045 14.5673i 0.272584 0.472130i
\(953\) −2.55116 + 4.41874i −0.0826402 + 0.143137i −0.904383 0.426721i \(-0.859669\pi\)
0.821743 + 0.569858i \(0.193002\pi\)
\(954\) 6.18819 10.7183i 0.200350 0.347016i
\(955\) 47.0404 + 81.4763i 1.52219 + 2.63651i
\(956\) −4.76859 −0.154227
\(957\) −1.30605 2.26214i −0.0422184 0.0731245i
\(958\) 35.7127 1.15382
\(959\) −2.93603 + 5.08535i −0.0948093 + 0.164215i
\(960\) 17.9177 + 31.0344i 0.578291 + 1.00163i
\(961\) 1.03141 1.78645i 0.0332712 0.0576274i
\(962\) −13.1972 + 22.8582i −0.425495 + 0.736979i
\(963\) −1.28393 + 2.22382i −0.0413739 + 0.0716617i
\(964\) −2.20068 + 3.81169i −0.0708791 + 0.122766i
\(965\) 80.3792 2.58750
\(966\) −4.77740 + 8.27469i −0.153710 + 0.266234i
\(967\) −2.40548 4.16641i −0.0773549 0.133983i 0.824753 0.565493i \(-0.191314\pi\)
−0.902108 + 0.431510i \(0.857981\pi\)
\(968\) −16.0855 27.8610i −0.517009 0.895485i
\(969\) 10.2835 0.330354
\(970\) −12.3720 −0.397240
\(971\) −38.1458 −1.22416 −0.612079 0.790797i \(-0.709666\pi\)
−0.612079 + 0.790797i \(0.709666\pi\)
\(972\) −0.122886 0.212845i −0.00394157 0.00682700i
\(973\) −42.2622 73.2002i −1.35486 2.34669i
\(974\) −2.99808 −0.0960646
\(975\) −13.9551 24.1709i −0.446920 0.774088i
\(976\) 16.8029 29.1034i 0.537847 0.931578i
\(977\) 4.95186 8.57688i 0.158424 0.274399i −0.775876 0.630885i \(-0.782692\pi\)
0.934301 + 0.356486i \(0.116025\pi\)
\(978\) −2.03167 3.51896i −0.0649657 0.112524i
\(979\) −0.141898 0.245775i −0.00453508 0.00785500i
\(980\) 3.35283 5.80728i 0.107102 0.185507i
\(981\) 11.4309 0.364959
\(982\) 13.8724 24.0277i 0.442685 0.766754i
\(983\) 46.4859 1.48267 0.741335 0.671135i \(-0.234193\pi\)
0.741335 + 0.671135i \(0.234193\pi\)
\(984\) 14.7788 25.5976i 0.471130 0.816021i
\(985\) 14.3640 + 24.8793i 0.457677 + 0.792719i
\(986\) 6.16973 10.6863i 0.196484 0.340321i
\(987\) 24.3667 0.775601
\(988\) 3.88400 0.123566
\(989\) 9.23984 + 16.0039i 0.293810 + 0.508893i
\(990\) 1.16729 2.02181i 0.0370990 0.0642574i
\(991\) −13.7158 −0.435698 −0.217849 0.975982i \(-0.569904\pi\)
−0.217849 + 0.975982i \(0.569904\pi\)
\(992\) −3.71732 6.43859i −0.118025 0.204426i
\(993\) 11.5903 + 20.0749i 0.367805 + 0.637058i
\(994\) −2.62537 4.54728i −0.0832718 0.144231i
\(995\) 13.2384 + 22.9296i 0.419686 + 0.726918i
\(996\) 2.74736 0.0870534
\(997\) −19.0529 33.0006i −0.603412 1.04514i −0.992300 0.123855i \(-0.960474\pi\)
0.388888 0.921285i \(-0.372859\pi\)
\(998\) 21.6178 0.684299
\(999\) −4.23513 7.33547i −0.133994 0.232084i
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 471.2.e.b.301.8 yes 22
157.12 even 3 inner 471.2.e.b.169.8 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.e.b.169.8 22 157.12 even 3 inner
471.2.e.b.301.8 yes 22 1.1 even 1 trivial