Properties

Label 572.2.e.b.131.11
Level $572$
Weight $2$
Character 572.131
Analytic conductor $4.567$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(131,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.e (of order \(2\), degree \(1\), 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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 131.11
Character \(\chi\) \(=\) 572.131
Dual form 572.2.e.b.131.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25608 - 0.649821i) q^{2} -1.96816i q^{3} +(1.15547 + 1.63245i) q^{4} -3.24710 q^{5} +(-1.27895 + 2.47217i) q^{6} +4.43351 q^{7} +(-0.390556 - 2.80133i) q^{8} -0.873660 q^{9} +O(q^{10})\) \(q+(-1.25608 - 0.649821i) q^{2} -1.96816i q^{3} +(1.15547 + 1.63245i) q^{4} -3.24710 q^{5} +(-1.27895 + 2.47217i) q^{6} +4.43351 q^{7} +(-0.390556 - 2.80133i) q^{8} -0.873660 q^{9} +(4.07861 + 2.11003i) q^{10} +(2.97258 - 1.47098i) q^{11} +(3.21293 - 2.27414i) q^{12} -1.00000i q^{13} +(-5.56884 - 2.88099i) q^{14} +6.39082i q^{15} +(-1.32979 + 3.77249i) q^{16} +2.63117i q^{17} +(1.09739 + 0.567722i) q^{18} +4.71143 q^{19} +(-3.75191 - 5.30073i) q^{20} -8.72587i q^{21} +(-4.68966 - 0.0839736i) q^{22} +0.0430153i q^{23} +(-5.51348 + 0.768678i) q^{24} +5.54365 q^{25} +(-0.649821 + 1.25608i) q^{26} -4.18498i q^{27} +(5.12277 + 7.23749i) q^{28} -4.26688i q^{29} +(4.15288 - 8.02737i) q^{30} -6.80753i q^{31} +(4.12176 - 3.87441i) q^{32} +(-2.89513 - 5.85051i) q^{33} +(1.70979 - 3.30496i) q^{34} -14.3961 q^{35} +(-1.00948 - 1.42621i) q^{36} -1.79924 q^{37} +(-5.91793 - 3.06159i) q^{38} -1.96816 q^{39} +(1.26818 + 9.09621i) q^{40} -1.50014i q^{41} +(-5.67025 + 10.9604i) q^{42} -7.61693 q^{43} +(5.83602 + 3.15292i) q^{44} +2.83686 q^{45} +(0.0279522 - 0.0540306i) q^{46} +11.8706i q^{47} +(7.42486 + 2.61725i) q^{48} +12.6560 q^{49} +(-6.96326 - 3.60238i) q^{50} +5.17857 q^{51} +(1.63245 - 1.15547i) q^{52} -10.4429 q^{53} +(-2.71949 + 5.25667i) q^{54} +(-9.65225 + 4.77642i) q^{55} +(-1.73154 - 12.4197i) q^{56} -9.27286i q^{57} +(-2.77270 + 5.35953i) q^{58} -9.82553i q^{59} +(-10.4327 + 7.38437i) q^{60} -2.20258i q^{61} +(-4.42368 + 8.55080i) q^{62} -3.87338 q^{63} +(-7.69493 + 2.18816i) q^{64} +3.24710i q^{65} +(-0.165274 + 9.23002i) q^{66} +3.35101i q^{67} +(-4.29526 + 3.04023i) q^{68} +0.0846611 q^{69} +(18.0826 + 9.35485i) q^{70} -14.6471i q^{71} +(0.341213 + 2.44741i) q^{72} +7.04910i q^{73} +(2.25999 + 1.16918i) q^{74} -10.9108i q^{75} +(5.44390 + 7.69119i) q^{76} +(13.1790 - 6.52161i) q^{77} +(2.47217 + 1.27895i) q^{78} -1.99652 q^{79} +(4.31797 - 12.2496i) q^{80} -10.8577 q^{81} +(-0.974824 + 1.88430i) q^{82} +12.3355 q^{83} +(14.2446 - 10.0824i) q^{84} -8.54368i q^{85} +(9.56747 + 4.94964i) q^{86} -8.39790 q^{87} +(-5.28167 - 7.75268i) q^{88} +9.79840 q^{89} +(-3.56332 - 1.84345i) q^{90} -4.43351i q^{91} +(-0.0702204 + 0.0497028i) q^{92} -13.3983 q^{93} +(7.71374 - 14.9104i) q^{94} -15.2985 q^{95} +(-7.62547 - 8.11230i) q^{96} +10.6850 q^{97} +(-15.8970 - 8.22415i) q^{98} +(-2.59702 + 1.28514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25608 0.649821i −0.888182 0.459493i
\(3\) 1.96816i 1.13632i −0.822919 0.568159i \(-0.807656\pi\)
0.822919 0.568159i \(-0.192344\pi\)
\(4\) 1.15547 + 1.63245i 0.577733 + 0.816226i
\(5\) −3.24710 −1.45215 −0.726073 0.687617i \(-0.758657\pi\)
−0.726073 + 0.687617i \(0.758657\pi\)
\(6\) −1.27895 + 2.47217i −0.522130 + 1.00926i
\(7\) 4.43351 1.67571 0.837855 0.545893i \(-0.183809\pi\)
0.837855 + 0.545893i \(0.183809\pi\)
\(8\) −0.390556 2.80133i −0.138083 0.990421i
\(9\) −0.873660 −0.291220
\(10\) 4.07861 + 2.11003i 1.28977 + 0.667251i
\(11\) 2.97258 1.47098i 0.896266 0.443518i
\(12\) 3.21293 2.27414i 0.927492 0.656489i
\(13\) 1.00000i 0.277350i
\(14\) −5.56884 2.88099i −1.48833 0.769976i
\(15\) 6.39082i 1.65010i
\(16\) −1.32979 + 3.77249i −0.332449 + 0.943121i
\(17\) 2.63117i 0.638153i 0.947729 + 0.319076i \(0.103373\pi\)
−0.947729 + 0.319076i \(0.896627\pi\)
\(18\) 1.09739 + 0.567722i 0.258656 + 0.133813i
\(19\) 4.71143 1.08088 0.540439 0.841383i \(-0.318258\pi\)
0.540439 + 0.841383i \(0.318258\pi\)
\(20\) −3.75191 5.30073i −0.838954 1.18528i
\(21\) 8.72587i 1.90414i
\(22\) −4.68966 0.0839736i −0.999840 0.0179032i
\(23\) 0.0430153i 0.00896931i 0.999990 + 0.00448466i \(0.00142752\pi\)
−0.999990 + 0.00448466i \(0.998572\pi\)
\(24\) −5.51348 + 0.768678i −1.12543 + 0.156906i
\(25\) 5.54365 1.10873
\(26\) −0.649821 + 1.25608i −0.127440 + 0.246337i
\(27\) 4.18498i 0.805400i
\(28\) 5.12277 + 7.23749i 0.968113 + 1.36776i
\(29\) 4.26688i 0.792339i −0.918177 0.396169i \(-0.870339\pi\)
0.918177 0.396169i \(-0.129661\pi\)
\(30\) 4.15288 8.02737i 0.758209 1.46559i
\(31\) 6.80753i 1.22267i −0.791372 0.611335i \(-0.790633\pi\)
0.791372 0.611335i \(-0.209367\pi\)
\(32\) 4.12176 3.87441i 0.728632 0.684905i
\(33\) −2.89513 5.85051i −0.503977 1.01844i
\(34\) 1.70979 3.30496i 0.293226 0.566796i
\(35\) −14.3961 −2.43338
\(36\) −1.00948 1.42621i −0.168247 0.237701i
\(37\) −1.79924 −0.295793 −0.147897 0.989003i \(-0.547250\pi\)
−0.147897 + 0.989003i \(0.547250\pi\)
\(38\) −5.91793 3.06159i −0.960015 0.496655i
\(39\) −1.96816 −0.315158
\(40\) 1.26818 + 9.09621i 0.200516 + 1.43824i
\(41\) 1.50014i 0.234283i −0.993115 0.117142i \(-0.962627\pi\)
0.993115 0.117142i \(-0.0373731\pi\)
\(42\) −5.67025 + 10.9604i −0.874938 + 1.69122i
\(43\) −7.61693 −1.16157 −0.580786 0.814057i \(-0.697255\pi\)
−0.580786 + 0.814057i \(0.697255\pi\)
\(44\) 5.83602 + 3.15292i 0.879813 + 0.475320i
\(45\) 2.83686 0.422894
\(46\) 0.0279522 0.0540306i 0.00412133 0.00796638i
\(47\) 11.8706i 1.73150i 0.500477 + 0.865750i \(0.333158\pi\)
−0.500477 + 0.865750i \(0.666842\pi\)
\(48\) 7.42486 + 2.61725i 1.07169 + 0.377767i
\(49\) 12.6560 1.80800
\(50\) −6.96326 3.60238i −0.984754 0.509453i
\(51\) 5.17857 0.725145
\(52\) 1.63245 1.15547i 0.226380 0.160234i
\(53\) −10.4429 −1.43444 −0.717220 0.696846i \(-0.754586\pi\)
−0.717220 + 0.696846i \(0.754586\pi\)
\(54\) −2.71949 + 5.25667i −0.370075 + 0.715342i
\(55\) −9.65225 + 4.77642i −1.30151 + 0.644053i
\(56\) −1.73154 12.4197i −0.231386 1.65966i
\(57\) 9.27286i 1.22822i
\(58\) −2.77270 + 5.35953i −0.364074 + 0.703741i
\(59\) 9.82553i 1.27918i −0.768718 0.639588i \(-0.779105\pi\)
0.768718 0.639588i \(-0.220895\pi\)
\(60\) −10.4327 + 7.38437i −1.34686 + 0.953318i
\(61\) 2.20258i 0.282012i −0.990009 0.141006i \(-0.954966\pi\)
0.990009 0.141006i \(-0.0450337\pi\)
\(62\) −4.42368 + 8.55080i −0.561807 + 1.08595i
\(63\) −3.87338 −0.488000
\(64\) −7.69493 + 2.18816i −0.961866 + 0.273520i
\(65\) 3.24710i 0.402753i
\(66\) −0.165274 + 9.23002i −0.0203438 + 1.13614i
\(67\) 3.35101i 0.409391i 0.978826 + 0.204695i \(0.0656203\pi\)
−0.978826 + 0.204695i \(0.934380\pi\)
\(68\) −4.29526 + 3.04023i −0.520877 + 0.368682i
\(69\) 0.0846611 0.0101920
\(70\) 18.0826 + 9.35485i 2.16128 + 1.11812i
\(71\) 14.6471i 1.73829i −0.494561 0.869143i \(-0.664671\pi\)
0.494561 0.869143i \(-0.335329\pi\)
\(72\) 0.341213 + 2.44741i 0.0402124 + 0.288430i
\(73\) 7.04910i 0.825035i 0.910950 + 0.412517i \(0.135350\pi\)
−0.910950 + 0.412517i \(0.864650\pi\)
\(74\) 2.25999 + 1.16918i 0.262718 + 0.135915i
\(75\) 10.9108i 1.25987i
\(76\) 5.44390 + 7.69119i 0.624459 + 0.882240i
\(77\) 13.1790 6.52161i 1.50188 0.743207i
\(78\) 2.47217 + 1.27895i 0.279918 + 0.144813i
\(79\) −1.99652 −0.224626 −0.112313 0.993673i \(-0.535826\pi\)
−0.112313 + 0.993673i \(0.535826\pi\)
\(80\) 4.31797 12.2496i 0.482764 1.36955i
\(81\) −10.8577 −1.20641
\(82\) −0.974824 + 1.88430i −0.107651 + 0.208086i
\(83\) 12.3355 1.35400 0.677000 0.735983i \(-0.263280\pi\)
0.677000 + 0.735983i \(0.263280\pi\)
\(84\) 14.2446 10.0824i 1.55421 1.10009i
\(85\) 8.54368i 0.926692i
\(86\) 9.56747 + 4.94964i 1.03169 + 0.533733i
\(87\) −8.39790 −0.900349
\(88\) −5.28167 7.75268i −0.563028 0.826438i
\(89\) 9.79840 1.03863 0.519314 0.854584i \(-0.326188\pi\)
0.519314 + 0.854584i \(0.326188\pi\)
\(90\) −3.56332 1.84345i −0.375607 0.194317i
\(91\) 4.43351i 0.464758i
\(92\) −0.0702204 + 0.0497028i −0.00732098 + 0.00518187i
\(93\) −13.3983 −1.38934
\(94\) 7.71374 14.9104i 0.795611 1.53789i
\(95\) −15.2985 −1.56959
\(96\) −7.62547 8.11230i −0.778271 0.827958i
\(97\) 10.6850 1.08490 0.542448 0.840089i \(-0.317497\pi\)
0.542448 + 0.840089i \(0.317497\pi\)
\(98\) −15.8970 8.22415i −1.60584 0.830764i
\(99\) −2.59702 + 1.28514i −0.261010 + 0.129161i
\(100\) 6.40551 + 9.04974i 0.640551 + 0.904974i
\(101\) 14.1836i 1.41132i 0.708549 + 0.705661i \(0.249350\pi\)
−0.708549 + 0.705661i \(0.750650\pi\)
\(102\) −6.50469 3.36514i −0.644060 0.333199i
\(103\) 2.61974i 0.258131i 0.991636 + 0.129066i \(0.0411978\pi\)
−0.991636 + 0.129066i \(0.958802\pi\)
\(104\) −2.80133 + 0.390556i −0.274693 + 0.0382972i
\(105\) 28.3338i 2.76509i
\(106\) 13.1171 + 6.78600i 1.27404 + 0.659115i
\(107\) 12.0361 1.16358 0.581788 0.813340i \(-0.302353\pi\)
0.581788 + 0.813340i \(0.302353\pi\)
\(108\) 6.83178 4.83561i 0.657388 0.465306i
\(109\) 16.6400i 1.59383i −0.604094 0.796913i \(-0.706465\pi\)
0.604094 0.796913i \(-0.293535\pi\)
\(110\) 15.2278 + 0.272670i 1.45191 + 0.0259981i
\(111\) 3.54120i 0.336116i
\(112\) −5.89566 + 16.7254i −0.557087 + 1.58040i
\(113\) −19.1558 −1.80203 −0.901015 0.433788i \(-0.857177\pi\)
−0.901015 + 0.433788i \(0.857177\pi\)
\(114\) −6.02570 + 11.6474i −0.564358 + 1.09088i
\(115\) 0.139675i 0.0130248i
\(116\) 6.96547 4.93023i 0.646727 0.457761i
\(117\) 0.873660i 0.0807699i
\(118\) −6.38483 + 12.3416i −0.587772 + 1.13614i
\(119\) 11.6653i 1.06936i
\(120\) 17.9028 2.49597i 1.63429 0.227850i
\(121\) 6.67243 8.74521i 0.606584 0.795019i
\(122\) −1.43128 + 2.76662i −0.129582 + 0.250478i
\(123\) −2.95253 −0.266220
\(124\) 11.1130 7.86588i 0.997974 0.706377i
\(125\) −1.76529 −0.157893
\(126\) 4.86527 + 2.51700i 0.433433 + 0.224232i
\(127\) 0.128545 0.0114065 0.00570327 0.999984i \(-0.498185\pi\)
0.00570327 + 0.999984i \(0.498185\pi\)
\(128\) 11.0873 + 2.25183i 0.979992 + 0.199035i
\(129\) 14.9914i 1.31992i
\(130\) 2.11003 4.07861i 0.185062 0.357718i
\(131\) 13.9983 1.22304 0.611520 0.791229i \(-0.290558\pi\)
0.611520 + 0.791229i \(0.290558\pi\)
\(132\) 6.20545 11.4862i 0.540115 0.999748i
\(133\) 20.8882 1.81124
\(134\) 2.17755 4.20913i 0.188112 0.363613i
\(135\) 13.5890i 1.16956i
\(136\) 7.37079 1.02762i 0.632040 0.0881178i
\(137\) 1.61613 0.138075 0.0690377 0.997614i \(-0.478007\pi\)
0.0690377 + 0.997614i \(0.478007\pi\)
\(138\) −0.106341 0.0550145i −0.00905235 0.00468315i
\(139\) 7.22209 0.612569 0.306285 0.951940i \(-0.400914\pi\)
0.306285 + 0.951940i \(0.400914\pi\)
\(140\) −16.6342 23.5009i −1.40584 1.98618i
\(141\) 23.3632 1.96754
\(142\) −9.51796 + 18.3979i −0.798729 + 1.54391i
\(143\) −1.47098 2.97258i −0.123010 0.248579i
\(144\) 1.16179 3.29587i 0.0968156 0.274656i
\(145\) 13.8550i 1.15059i
\(146\) 4.58065 8.85422i 0.379097 0.732781i
\(147\) 24.9091i 2.05447i
\(148\) −2.07896 2.93717i −0.170890 0.241434i
\(149\) 5.41263i 0.443420i 0.975113 + 0.221710i \(0.0711638\pi\)
−0.975113 + 0.221710i \(0.928836\pi\)
\(150\) −7.09006 + 13.7048i −0.578901 + 1.11899i
\(151\) −4.89798 −0.398592 −0.199296 0.979939i \(-0.563866\pi\)
−0.199296 + 0.979939i \(0.563866\pi\)
\(152\) −1.84008 13.1983i −0.149250 1.07052i
\(153\) 2.29875i 0.185843i
\(154\) −20.7917 0.372298i −1.67544 0.0300006i
\(155\) 22.1047i 1.77550i
\(156\) −2.27414 3.21293i −0.182077 0.257240i
\(157\) −19.0917 −1.52369 −0.761843 0.647761i \(-0.775705\pi\)
−0.761843 + 0.647761i \(0.775705\pi\)
\(158\) 2.50779 + 1.29738i 0.199509 + 0.103214i
\(159\) 20.5533i 1.62998i
\(160\) −13.3838 + 12.5806i −1.05808 + 0.994583i
\(161\) 0.190709i 0.0150300i
\(162\) 13.6381 + 7.05555i 1.07151 + 0.554337i
\(163\) 3.00305i 0.235217i 0.993060 + 0.117608i \(0.0375228\pi\)
−0.993060 + 0.117608i \(0.962477\pi\)
\(164\) 2.44891 1.73337i 0.191228 0.135353i
\(165\) 9.40077 + 18.9972i 0.731849 + 1.47893i
\(166\) −15.4944 8.01588i −1.20260 0.622153i
\(167\) 8.68938 0.672405 0.336202 0.941790i \(-0.390857\pi\)
0.336202 + 0.941790i \(0.390857\pi\)
\(168\) −24.4441 + 3.40794i −1.88590 + 0.262928i
\(169\) −1.00000 −0.0769231
\(170\) −5.55186 + 10.7315i −0.425808 + 0.823071i
\(171\) −4.11619 −0.314773
\(172\) −8.80111 12.4343i −0.671078 0.948104i
\(173\) 3.41141i 0.259365i 0.991556 + 0.129682i \(0.0413958\pi\)
−0.991556 + 0.129682i \(0.958604\pi\)
\(174\) 10.5484 + 5.45713i 0.799674 + 0.413704i
\(175\) 24.5779 1.85791
\(176\) 1.59634 + 13.1701i 0.120329 + 0.992734i
\(177\) −19.3382 −1.45355
\(178\) −12.3076 6.36720i −0.922490 0.477242i
\(179\) 20.2599i 1.51429i 0.653245 + 0.757146i \(0.273407\pi\)
−0.653245 + 0.757146i \(0.726593\pi\)
\(180\) 3.27790 + 4.63103i 0.244320 + 0.345177i
\(181\) −0.387206 −0.0287808 −0.0143904 0.999896i \(-0.504581\pi\)
−0.0143904 + 0.999896i \(0.504581\pi\)
\(182\) −2.88099 + 5.56884i −0.213553 + 0.412790i
\(183\) −4.33504 −0.320455
\(184\) 0.120500 0.0167999i 0.00888339 0.00123851i
\(185\) 5.84231 0.429536
\(186\) 16.8293 + 8.70651i 1.23399 + 0.638392i
\(187\) 3.87040 + 7.82136i 0.283032 + 0.571955i
\(188\) −19.3781 + 13.7160i −1.41329 + 1.00035i
\(189\) 18.5542i 1.34962i
\(190\) 19.2161 + 9.94128i 1.39408 + 0.721216i
\(191\) 9.65674i 0.698737i 0.936985 + 0.349369i \(0.113604\pi\)
−0.936985 + 0.349369i \(0.886396\pi\)
\(192\) 4.30665 + 15.1449i 0.310805 + 1.09299i
\(193\) 15.6944i 1.12971i −0.825191 0.564854i \(-0.808932\pi\)
0.825191 0.564854i \(-0.191068\pi\)
\(194\) −13.4212 6.94333i −0.963585 0.498502i
\(195\) 6.39082 0.457656
\(196\) 14.6236 + 20.6603i 1.04454 + 1.47574i
\(197\) 2.74588i 0.195636i 0.995204 + 0.0978178i \(0.0311862\pi\)
−0.995204 + 0.0978178i \(0.968814\pi\)
\(198\) 4.09717 + 0.0733643i 0.291173 + 0.00521377i
\(199\) 21.4785i 1.52257i 0.648417 + 0.761285i \(0.275431\pi\)
−0.648417 + 0.761285i \(0.724569\pi\)
\(200\) −2.16511 15.5296i −0.153096 1.09811i
\(201\) 6.59532 0.465198
\(202\) 9.21681 17.8157i 0.648492 1.25351i
\(203\) 18.9172i 1.32773i
\(204\) 5.98367 + 8.45376i 0.418940 + 0.591882i
\(205\) 4.87112i 0.340213i
\(206\) 1.70236 3.29060i 0.118609 0.229267i
\(207\) 0.0375807i 0.00261204i
\(208\) 3.77249 + 1.32979i 0.261575 + 0.0922046i
\(209\) 14.0051 6.93043i 0.968753 0.479388i
\(210\) 18.4119 35.5894i 1.27054 2.45590i
\(211\) −16.8319 −1.15876 −0.579378 0.815059i \(-0.696705\pi\)
−0.579378 + 0.815059i \(0.696705\pi\)
\(212\) −12.0664 17.0475i −0.828724 1.17083i
\(213\) −28.8278 −1.97525
\(214\) −15.1183 7.82132i −1.03347 0.534655i
\(215\) 24.7329 1.68677
\(216\) −11.7235 + 1.63447i −0.797685 + 0.111212i
\(217\) 30.1813i 2.04884i
\(218\) −10.8130 + 20.9012i −0.732352 + 1.41561i
\(219\) 13.8738 0.937502
\(220\) −18.9501 10.2378i −1.27762 0.690235i
\(221\) 2.63117 0.176992
\(222\) 2.30114 4.44802i 0.154443 0.298532i
\(223\) 8.72379i 0.584188i 0.956390 + 0.292094i \(0.0943520\pi\)
−0.956390 + 0.292094i \(0.905648\pi\)
\(224\) 18.2739 17.1772i 1.22098 1.14770i
\(225\) −4.84327 −0.322884
\(226\) 24.0612 + 12.4479i 1.60053 + 0.828019i
\(227\) −11.1722 −0.741522 −0.370761 0.928728i \(-0.620903\pi\)
−0.370761 + 0.928728i \(0.620903\pi\)
\(228\) 15.1375 10.7145i 1.00251 0.709584i
\(229\) −14.1298 −0.933724 −0.466862 0.884330i \(-0.654616\pi\)
−0.466862 + 0.884330i \(0.654616\pi\)
\(230\) −0.0907637 + 0.175443i −0.00598478 + 0.0115684i
\(231\) −12.8356 25.9383i −0.844520 1.70662i
\(232\) −11.9529 + 1.66646i −0.784749 + 0.109408i
\(233\) 5.12682i 0.335869i 0.985798 + 0.167935i \(0.0537098\pi\)
−0.985798 + 0.167935i \(0.946290\pi\)
\(234\) 0.567722 1.09739i 0.0371131 0.0717383i
\(235\) 38.5449i 2.51439i
\(236\) 16.0397 11.3531i 1.04410 0.739022i
\(237\) 3.92948i 0.255247i
\(238\) 7.58037 14.6526i 0.491363 0.949785i
\(239\) −10.5322 −0.681274 −0.340637 0.940195i \(-0.610643\pi\)
−0.340637 + 0.940195i \(0.610643\pi\)
\(240\) −24.1093 8.49847i −1.55625 0.548574i
\(241\) 18.8992i 1.21740i 0.793399 + 0.608702i \(0.208310\pi\)
−0.793399 + 0.608702i \(0.791690\pi\)
\(242\) −14.0639 + 6.64879i −0.904062 + 0.427400i
\(243\) 8.81476i 0.565467i
\(244\) 3.59561 2.54501i 0.230185 0.162928i
\(245\) −41.0954 −2.62549
\(246\) 3.70860 + 1.91861i 0.236452 + 0.122326i
\(247\) 4.71143i 0.299781i
\(248\) −19.0702 + 2.65873i −1.21096 + 0.168829i
\(249\) 24.2783i 1.53858i
\(250\) 2.21735 + 1.14712i 0.140237 + 0.0725505i
\(251\) 26.8996i 1.69789i −0.528484 0.848943i \(-0.677239\pi\)
0.528484 0.848943i \(-0.322761\pi\)
\(252\) −4.47556 6.32310i −0.281934 0.398318i
\(253\) 0.0632747 + 0.127866i 0.00397805 + 0.00803889i
\(254\) −0.161463 0.0835313i −0.0101311 0.00524122i
\(255\) −16.8153 −1.05302
\(256\) −12.4633 10.0333i −0.778956 0.627079i
\(257\) −1.07645 −0.0671468 −0.0335734 0.999436i \(-0.510689\pi\)
−0.0335734 + 0.999436i \(0.510689\pi\)
\(258\) 9.74169 18.8303i 0.606491 1.17232i
\(259\) −7.97696 −0.495664
\(260\) −5.30073 + 3.75191i −0.328737 + 0.232684i
\(261\) 3.72780i 0.230745i
\(262\) −17.5830 9.09640i −1.08628 0.561977i
\(263\) 14.9965 0.924723 0.462362 0.886691i \(-0.347002\pi\)
0.462362 + 0.886691i \(0.347002\pi\)
\(264\) −15.2585 + 10.3952i −0.939097 + 0.639779i
\(265\) 33.9091 2.08302
\(266\) −26.2372 13.5736i −1.60871 0.832250i
\(267\) 19.2848i 1.18021i
\(268\) −5.47035 + 3.87197i −0.334155 + 0.236519i
\(269\) 2.55255 0.155632 0.0778160 0.996968i \(-0.475205\pi\)
0.0778160 + 0.996968i \(0.475205\pi\)
\(270\) 8.83044 17.0689i 0.537404 1.03878i
\(271\) −1.38884 −0.0843660 −0.0421830 0.999110i \(-0.513431\pi\)
−0.0421830 + 0.999110i \(0.513431\pi\)
\(272\) −9.92606 3.49892i −0.601856 0.212153i
\(273\) −8.72587 −0.528114
\(274\) −2.02999 1.05019i −0.122636 0.0634446i
\(275\) 16.4789 8.15461i 0.993717 0.491741i
\(276\) 0.0978231 + 0.138205i 0.00588826 + 0.00831897i
\(277\) 3.21600i 0.193230i 0.995322 + 0.0966152i \(0.0308016\pi\)
−0.995322 + 0.0966152i \(0.969198\pi\)
\(278\) −9.07151 4.69306i −0.544073 0.281471i
\(279\) 5.94747i 0.356066i
\(280\) 5.62247 + 40.3281i 0.336007 + 2.41007i
\(281\) 19.1473i 1.14223i 0.820870 + 0.571115i \(0.193489\pi\)
−0.820870 + 0.571115i \(0.806511\pi\)
\(282\) −29.3460 15.1819i −1.74753 0.904068i
\(283\) 18.9770 1.12807 0.564033 0.825752i \(-0.309249\pi\)
0.564033 + 0.825752i \(0.309249\pi\)
\(284\) 23.9106 16.9242i 1.41883 1.00427i
\(285\) 30.1099i 1.78356i
\(286\) −0.0839736 + 4.68966i −0.00496546 + 0.277306i
\(287\) 6.65091i 0.392591i
\(288\) −3.60102 + 3.38492i −0.212192 + 0.199458i
\(289\) 10.0769 0.592761
\(290\) 9.00324 17.4029i 0.528689 1.02194i
\(291\) 21.0298i 1.23279i
\(292\) −11.5073 + 8.14500i −0.673414 + 0.476650i
\(293\) 25.4147i 1.48474i 0.669989 + 0.742371i \(0.266299\pi\)
−0.669989 + 0.742371i \(0.733701\pi\)
\(294\) −16.1864 + 31.2878i −0.944013 + 1.82474i
\(295\) 31.9045i 1.85755i
\(296\) 0.702705 + 5.04027i 0.0408439 + 0.292960i
\(297\) −6.15603 12.4402i −0.357209 0.721852i
\(298\) 3.51724 6.79869i 0.203748 0.393837i
\(299\) 0.0430153 0.00248764
\(300\) 17.8114 12.6071i 1.02834 0.727869i
\(301\) −33.7698 −1.94646
\(302\) 6.15225 + 3.18281i 0.354022 + 0.183150i
\(303\) 27.9157 1.60371
\(304\) −6.26524 + 17.7738i −0.359336 + 1.01940i
\(305\) 7.15201i 0.409523i
\(306\) −1.49377 + 2.88741i −0.0853934 + 0.165062i
\(307\) −7.51797 −0.429073 −0.214537 0.976716i \(-0.568824\pi\)
−0.214537 + 0.976716i \(0.568824\pi\)
\(308\) 25.8741 + 13.9785i 1.47431 + 0.796499i
\(309\) 5.15608 0.293319
\(310\) 14.3641 27.7653i 0.815827 1.57696i
\(311\) 15.5561i 0.882106i −0.897481 0.441053i \(-0.854605\pi\)
0.897481 0.441053i \(-0.145395\pi\)
\(312\) 0.768678 + 5.51348i 0.0435178 + 0.312139i
\(313\) 14.5247 0.820982 0.410491 0.911865i \(-0.365357\pi\)
0.410491 + 0.911865i \(0.365357\pi\)
\(314\) 23.9807 + 12.4062i 1.35331 + 0.700123i
\(315\) 12.5772 0.708648
\(316\) −2.30692 3.25923i −0.129774 0.183346i
\(317\) −18.6400 −1.04693 −0.523464 0.852048i \(-0.675361\pi\)
−0.523464 + 0.852048i \(0.675361\pi\)
\(318\) 13.3559 25.8165i 0.748964 1.44772i
\(319\) −6.27649 12.6836i −0.351416 0.710146i
\(320\) 24.9862 7.10516i 1.39677 0.397191i
\(321\) 23.6890i 1.32219i
\(322\) 0.123927 0.239545i 0.00690616 0.0133493i
\(323\) 12.3966i 0.689765i
\(324\) −12.5457 17.7247i −0.696984 0.984703i
\(325\) 5.54365i 0.307507i
\(326\) 1.95144 3.77206i 0.108080 0.208915i
\(327\) −32.7503 −1.81110
\(328\) −4.20240 + 0.585891i −0.232039 + 0.0323504i
\(329\) 52.6283i 2.90149i
\(330\) 0.536660 29.9708i 0.0295421 1.64984i
\(331\) 3.68073i 0.202311i 0.994871 + 0.101156i \(0.0322540\pi\)
−0.994871 + 0.101156i \(0.967746\pi\)
\(332\) 14.2533 + 20.1372i 0.782251 + 1.10517i
\(333\) 1.57192 0.0861409
\(334\) −10.9145 5.64654i −0.597217 0.308965i
\(335\) 10.8810i 0.594495i
\(336\) 32.9182 + 11.6036i 1.79584 + 0.633029i
\(337\) 1.56649i 0.0853321i 0.999089 + 0.0426660i \(0.0135851\pi\)
−0.999089 + 0.0426660i \(0.986415\pi\)
\(338\) 1.25608 + 0.649821i 0.0683217 + 0.0353456i
\(339\) 37.7018i 2.04768i
\(340\) 13.9471 9.87193i 0.756390 0.535381i
\(341\) −10.0138 20.2359i −0.542275 1.09584i
\(342\) 5.17026 + 2.67478i 0.279576 + 0.144636i
\(343\) 25.0761 1.35398
\(344\) 2.97484 + 21.3376i 0.160393 + 1.15044i
\(345\) −0.274903 −0.0148003
\(346\) 2.21681 4.28500i 0.119176 0.230363i
\(347\) 2.65428 0.142489 0.0712446 0.997459i \(-0.477303\pi\)
0.0712446 + 0.997459i \(0.477303\pi\)
\(348\) −9.70349 13.7092i −0.520162 0.734888i
\(349\) 24.6358i 1.31873i 0.751825 + 0.659363i \(0.229174\pi\)
−0.751825 + 0.659363i \(0.770826\pi\)
\(350\) −30.8717 15.9712i −1.65016 0.853696i
\(351\) −4.18498 −0.223378
\(352\) 6.55308 17.5800i 0.349280 0.937018i
\(353\) −13.5304 −0.720152 −0.360076 0.932923i \(-0.617249\pi\)
−0.360076 + 0.932923i \(0.617249\pi\)
\(354\) 24.2903 + 12.5664i 1.29102 + 0.667896i
\(355\) 47.5604i 2.52425i
\(356\) 11.3217 + 15.9954i 0.600050 + 0.847755i
\(357\) 22.9593 1.21513
\(358\) 13.1653 25.4480i 0.695806 1.34497i
\(359\) 14.1427 0.746426 0.373213 0.927746i \(-0.378256\pi\)
0.373213 + 0.927746i \(0.378256\pi\)
\(360\) −1.10795 7.94699i −0.0583943 0.418843i
\(361\) 3.19761 0.168296
\(362\) 0.486361 + 0.251614i 0.0255626 + 0.0132246i
\(363\) −17.2120 13.1324i −0.903395 0.689273i
\(364\) 7.23749 5.12277i 0.379348 0.268506i
\(365\) 22.8891i 1.19807i
\(366\) 5.44515 + 2.81700i 0.284623 + 0.147247i
\(367\) 2.81256i 0.146814i 0.997302 + 0.0734072i \(0.0233873\pi\)
−0.997302 + 0.0734072i \(0.976613\pi\)
\(368\) −0.162275 0.0572015i −0.00845915 0.00298184i
\(369\) 1.31062i 0.0682279i
\(370\) −7.33841 3.79646i −0.381506 0.197368i
\(371\) −46.2987 −2.40371
\(372\) −15.4813 21.8721i −0.802669 1.13402i
\(373\) 37.0235i 1.91700i 0.285090 + 0.958501i \(0.407977\pi\)
−0.285090 + 0.958501i \(0.592023\pi\)
\(374\) 0.220949 12.3393i 0.0114250 0.638051i
\(375\) 3.47439i 0.179416i
\(376\) 33.2534 4.63612i 1.71491 0.239090i
\(377\) −4.26688 −0.219755
\(378\) −12.0569 + 23.3055i −0.620139 + 1.19870i
\(379\) 9.88028i 0.507516i 0.967268 + 0.253758i \(0.0816667\pi\)
−0.967268 + 0.253758i \(0.918333\pi\)
\(380\) −17.6769 24.9740i −0.906806 1.28114i
\(381\) 0.252998i 0.0129615i
\(382\) 6.27515 12.1296i 0.321064 0.620606i
\(383\) 8.45161i 0.431857i 0.976409 + 0.215929i \(0.0692779\pi\)
−0.976409 + 0.215929i \(0.930722\pi\)
\(384\) 4.43196 21.8217i 0.226168 1.11358i
\(385\) −42.7934 + 21.1763i −2.18095 + 1.07925i
\(386\) −10.1985 + 19.7134i −0.519092 + 1.00339i
\(387\) 6.65461 0.338273
\(388\) 12.3462 + 17.4427i 0.626781 + 0.885521i
\(389\) 21.0938 1.06950 0.534749 0.845011i \(-0.320406\pi\)
0.534749 + 0.845011i \(0.320406\pi\)
\(390\) −8.02737 4.15288i −0.406481 0.210289i
\(391\) −0.113181 −0.00572379
\(392\) −4.94289 35.4537i −0.249654 1.79068i
\(393\) 27.5510i 1.38976i
\(394\) 1.78433 3.44904i 0.0898931 0.173760i
\(395\) 6.48291 0.326191
\(396\) −5.09869 2.75458i −0.256219 0.138423i
\(397\) −2.44016 −0.122468 −0.0612342 0.998123i \(-0.519504\pi\)
−0.0612342 + 0.998123i \(0.519504\pi\)
\(398\) 13.9572 26.9787i 0.699610 1.35232i
\(399\) 41.1114i 2.05814i
\(400\) −7.37192 + 20.9134i −0.368596 + 1.04567i
\(401\) −6.63786 −0.331479 −0.165739 0.986170i \(-0.553001\pi\)
−0.165739 + 0.986170i \(0.553001\pi\)
\(402\) −8.28424 4.28577i −0.413180 0.213755i
\(403\) −6.80753 −0.339107
\(404\) −23.1541 + 16.3887i −1.15196 + 0.815368i
\(405\) 35.2560 1.75189
\(406\) −12.2928 + 23.7615i −0.610082 + 1.17927i
\(407\) −5.34838 + 2.64665i −0.265110 + 0.131190i
\(408\) −2.02252 14.5069i −0.100130 0.718199i
\(409\) 3.66960i 0.181450i 0.995876 + 0.0907251i \(0.0289185\pi\)
−0.995876 + 0.0907251i \(0.971082\pi\)
\(410\) 3.16535 6.11850i 0.156326 0.302171i
\(411\) 3.18080i 0.156898i
\(412\) −4.27660 + 3.02703i −0.210693 + 0.149131i
\(413\) 43.5616i 2.14353i
\(414\) −0.0244207 + 0.0472044i −0.00120021 + 0.00231997i
\(415\) −40.0547 −1.96621
\(416\) −3.87441 4.12176i −0.189959 0.202086i
\(417\) 14.2142i 0.696074i
\(418\) −22.0950 0.395636i −1.08070 0.0193512i
\(419\) 27.2616i 1.33182i 0.746033 + 0.665909i \(0.231956\pi\)
−0.746033 + 0.665909i \(0.768044\pi\)
\(420\) −46.2535 + 32.7387i −2.25694 + 1.59749i
\(421\) 15.5302 0.756894 0.378447 0.925623i \(-0.376458\pi\)
0.378447 + 0.925623i \(0.376458\pi\)
\(422\) 21.1422 + 10.9377i 1.02919 + 0.532440i
\(423\) 10.3708i 0.504247i
\(424\) 4.07854 + 29.2540i 0.198071 + 1.42070i
\(425\) 14.5863i 0.707540i
\(426\) 36.2099 + 18.7329i 1.75438 + 0.907611i
\(427\) 9.76518i 0.472570i
\(428\) 13.9073 + 19.6484i 0.672237 + 0.949741i
\(429\) −5.85051 + 2.89513i −0.282465 + 0.139778i
\(430\) −31.0665 16.0720i −1.49816 0.775059i
\(431\) −9.83196 −0.473589 −0.236794 0.971560i \(-0.576097\pi\)
−0.236794 + 0.971560i \(0.576097\pi\)
\(432\) 15.7878 + 5.56516i 0.759590 + 0.267754i
\(433\) −0.171638 −0.00824838 −0.00412419 0.999991i \(-0.501313\pi\)
−0.00412419 + 0.999991i \(0.501313\pi\)
\(434\) −19.6124 + 37.9101i −0.941426 + 1.81974i
\(435\) 27.2688 1.30744
\(436\) 27.1641 19.2270i 1.30092 0.920807i
\(437\) 0.202664i 0.00969473i
\(438\) −17.4265 9.01546i −0.832672 0.430775i
\(439\) −14.2897 −0.682009 −0.341005 0.940062i \(-0.610767\pi\)
−0.341005 + 0.940062i \(0.610767\pi\)
\(440\) 17.1501 + 25.1737i 0.817599 + 1.20011i
\(441\) −11.0571 −0.526527
\(442\) −3.30496 1.70979i −0.157201 0.0813264i
\(443\) 23.0592i 1.09558i −0.836617 0.547788i \(-0.815470\pi\)
0.836617 0.547788i \(-0.184530\pi\)
\(444\) −5.78083 + 4.09174i −0.274346 + 0.194185i
\(445\) −31.8164 −1.50824
\(446\) 5.66890 10.9578i 0.268430 0.518865i
\(447\) 10.6529 0.503866
\(448\) −34.1156 + 9.70122i −1.61181 + 0.458339i
\(449\) −10.1080 −0.477024 −0.238512 0.971139i \(-0.576660\pi\)
−0.238512 + 0.971139i \(0.576660\pi\)
\(450\) 6.08352 + 3.14725i 0.286780 + 0.148363i
\(451\) −2.20668 4.45929i −0.103909 0.209980i
\(452\) −22.1339 31.2710i −1.04109 1.47086i
\(453\) 9.64002i 0.452928i
\(454\) 14.0331 + 7.25990i 0.658607 + 0.340724i
\(455\) 14.3961i 0.674897i
\(456\) −25.9764 + 3.62158i −1.21646 + 0.169596i
\(457\) 23.7906i 1.11288i −0.830888 0.556440i \(-0.812167\pi\)
0.830888 0.556440i \(-0.187833\pi\)
\(458\) 17.7481 + 9.18184i 0.829317 + 0.429039i
\(459\) 11.0114 0.513968
\(460\) 0.228013 0.161390i 0.0106311 0.00752484i
\(461\) 16.8140i 0.783104i −0.920156 0.391552i \(-0.871938\pi\)
0.920156 0.391552i \(-0.128062\pi\)
\(462\) −0.732742 + 40.9214i −0.0340903 + 1.90384i
\(463\) 19.1240i 0.888769i 0.895836 + 0.444385i \(0.146578\pi\)
−0.895836 + 0.444385i \(0.853422\pi\)
\(464\) 16.0967 + 5.67407i 0.747272 + 0.263412i
\(465\) 43.5057 2.01753
\(466\) 3.33152 6.43969i 0.154329 0.298313i
\(467\) 6.90045i 0.319315i −0.987172 0.159657i \(-0.948961\pi\)
0.987172 0.159657i \(-0.0510390\pi\)
\(468\) −1.42621 + 1.00948i −0.0659264 + 0.0466634i
\(469\) 14.8567i 0.686020i
\(470\) −25.0473 + 48.4154i −1.15534 + 2.23324i
\(471\) 37.5756i 1.73139i
\(472\) −27.5246 + 3.83742i −1.26692 + 0.176632i
\(473\) −22.6419 + 11.2044i −1.04108 + 0.515177i
\(474\) 2.55346 4.93574i 0.117284 0.226706i
\(475\) 26.1186 1.19840
\(476\) −19.0431 + 13.4789i −0.872838 + 0.617804i
\(477\) 9.12353 0.417738
\(478\) 13.2293 + 6.84407i 0.605095 + 0.313040i
\(479\) −16.3169 −0.745537 −0.372769 0.927924i \(-0.621591\pi\)
−0.372769 + 0.927924i \(0.621591\pi\)
\(480\) 24.7606 + 26.3414i 1.13016 + 1.20232i
\(481\) 1.79924i 0.0820383i
\(482\) 12.2811 23.7389i 0.559388 1.08128i
\(483\) 0.375346 0.0170788
\(484\) 21.9859 + 0.787616i 0.999359 + 0.0358007i
\(485\) −34.6952 −1.57543
\(486\) 5.72801 11.0720i 0.259828 0.502237i
\(487\) 38.1232i 1.72753i −0.503899 0.863763i \(-0.668102\pi\)
0.503899 0.863763i \(-0.331898\pi\)
\(488\) −6.17017 + 0.860233i −0.279311 + 0.0389409i
\(489\) 5.91048 0.267281
\(490\) 51.6190 + 26.7046i 2.33191 + 1.20639i
\(491\) 23.0861 1.04186 0.520931 0.853599i \(-0.325585\pi\)
0.520931 + 0.853599i \(0.325585\pi\)
\(492\) −3.41154 4.81985i −0.153804 0.217296i
\(493\) 11.2269 0.505633
\(494\) −3.06159 + 5.91793i −0.137747 + 0.266260i
\(495\) 8.43278 4.17297i 0.379025 0.187561i
\(496\) 25.6813 + 9.05262i 1.15313 + 0.406475i
\(497\) 64.9379i 2.91286i
\(498\) −15.7765 + 30.4955i −0.706964 + 1.36653i
\(499\) 20.7554i 0.929138i −0.885537 0.464569i \(-0.846209\pi\)
0.885537 0.464569i \(-0.153791\pi\)
\(500\) −2.03974 2.88176i −0.0912199 0.128876i
\(501\) 17.1021i 0.764066i
\(502\) −17.4799 + 33.7880i −0.780166 + 1.50803i
\(503\) 35.2656 1.57241 0.786207 0.617963i \(-0.212042\pi\)
0.786207 + 0.617963i \(0.212042\pi\)
\(504\) 1.51277 + 10.8506i 0.0673843 + 0.483325i
\(505\) 46.0556i 2.04945i
\(506\) 0.00361215 0.201727i 0.000160580 0.00896788i
\(507\) 1.96816i 0.0874091i
\(508\) 0.148530 + 0.209844i 0.00658994 + 0.00931031i
\(509\) 31.3323 1.38878 0.694389 0.719600i \(-0.255675\pi\)
0.694389 + 0.719600i \(0.255675\pi\)
\(510\) 21.1214 + 10.9269i 0.935270 + 0.483853i
\(511\) 31.2523i 1.38252i
\(512\) 9.13506 + 20.7015i 0.403716 + 0.914884i
\(513\) 19.7173i 0.870539i
\(514\) 1.35210 + 0.699497i 0.0596386 + 0.0308535i
\(515\) 8.50657i 0.374844i
\(516\) −24.4727 + 17.3220i −1.07735 + 0.762559i
\(517\) 17.4614 + 35.2862i 0.767951 + 1.55188i
\(518\) 10.0197 + 5.18359i 0.440240 + 0.227754i
\(519\) 6.71421 0.294721
\(520\) 9.09621 1.26818i 0.398895 0.0556132i
\(521\) −14.0072 −0.613668 −0.306834 0.951763i \(-0.599270\pi\)
−0.306834 + 0.951763i \(0.599270\pi\)
\(522\) 2.42240 4.68241i 0.106026 0.204943i
\(523\) 4.74895 0.207657 0.103829 0.994595i \(-0.466891\pi\)
0.103829 + 0.994595i \(0.466891\pi\)
\(524\) 16.1746 + 22.8516i 0.706591 + 0.998276i
\(525\) 48.3732i 2.11118i
\(526\) −18.8368 9.74503i −0.821322 0.424903i
\(527\) 17.9118 0.780250
\(528\) 25.9209 3.14185i 1.12806 0.136732i
\(529\) 22.9981 0.999920
\(530\) −42.5925 22.0348i −1.85010 0.957131i
\(531\) 8.58417i 0.372521i
\(532\) 24.1356 + 34.0990i 1.04641 + 1.47838i
\(533\) −1.50014 −0.0649784
\(534\) −12.5317 + 24.2233i −0.542299 + 1.04824i
\(535\) −39.0825 −1.68968
\(536\) 9.38728 1.30876i 0.405469 0.0565297i
\(537\) 39.8747 1.72072
\(538\) −3.20621 1.65870i −0.138229 0.0715117i
\(539\) 37.6210 18.6168i 1.62045 0.801881i
\(540\) −22.1835 + 15.7017i −0.954624 + 0.675693i
\(541\) 14.6610i 0.630325i 0.949038 + 0.315163i \(0.102059\pi\)
−0.949038 + 0.315163i \(0.897941\pi\)
\(542\) 1.74449 + 0.902497i 0.0749323 + 0.0387656i
\(543\) 0.762084i 0.0327042i
\(544\) 10.1942 + 10.8451i 0.437074 + 0.464979i
\(545\) 54.0319i 2.31447i
\(546\) 10.9604 + 5.67025i 0.469061 + 0.242664i
\(547\) −36.7535 −1.57147 −0.785733 0.618566i \(-0.787714\pi\)
−0.785733 + 0.618566i \(0.787714\pi\)
\(548\) 1.86738 + 2.63825i 0.0797707 + 0.112701i
\(549\) 1.92431i 0.0821275i
\(550\) −25.9979 0.465520i −1.10855 0.0198499i
\(551\) 20.1031i 0.856421i
\(552\) −0.0330649 0.237164i −0.00140734 0.0100944i
\(553\) −8.85161 −0.376409
\(554\) 2.08982 4.03954i 0.0887880 0.171624i
\(555\) 11.4986i 0.488089i
\(556\) 8.34488 + 11.7897i 0.353902 + 0.499995i
\(557\) 5.32657i 0.225694i −0.993612 0.112847i \(-0.964003\pi\)
0.993612 0.112847i \(-0.0359970\pi\)
\(558\) 3.86479 7.47049i 0.163609 0.316251i
\(559\) 7.61693i 0.322162i
\(560\) 19.1438 54.3089i 0.808973 2.29497i
\(561\) 15.3937 7.61758i 0.649923 0.321615i
\(562\) 12.4423 24.0505i 0.524847 1.01451i
\(563\) −28.2126 −1.18902 −0.594510 0.804088i \(-0.702654\pi\)
−0.594510 + 0.804088i \(0.702654\pi\)
\(564\) 26.9954 + 38.1393i 1.13671 + 1.60595i
\(565\) 62.2009 2.61681
\(566\) −23.8366 12.3317i −1.00193 0.518338i
\(567\) −48.1377 −2.02159
\(568\) −41.0313 + 5.72050i −1.72163 + 0.240027i
\(569\) 44.4460i 1.86327i 0.363391 + 0.931637i \(0.381619\pi\)
−0.363391 + 0.931637i \(0.618381\pi\)
\(570\) 19.5660 37.8204i 0.819531 1.58412i
\(571\) −16.4445 −0.688180 −0.344090 0.938937i \(-0.611813\pi\)
−0.344090 + 0.938937i \(0.611813\pi\)
\(572\) 3.15292 5.83602i 0.131830 0.244016i
\(573\) 19.0060 0.793988
\(574\) −4.32190 + 8.35406i −0.180392 + 0.348692i
\(575\) 0.238462i 0.00994455i
\(576\) 6.72275 1.91170i 0.280115 0.0796543i
\(577\) 37.3254 1.55388 0.776938 0.629577i \(-0.216772\pi\)
0.776938 + 0.629577i \(0.216772\pi\)
\(578\) −12.6574 6.54820i −0.526479 0.272369i
\(579\) −30.8891 −1.28371
\(580\) −22.6176 + 16.0090i −0.939143 + 0.664736i
\(581\) 54.6897 2.26891
\(582\) −13.6656 + 26.4151i −0.566457 + 1.09494i
\(583\) −31.0423 + 15.3613i −1.28564 + 0.636200i
\(584\) 19.7469 2.75307i 0.817131 0.113923i
\(585\) 2.83686i 0.117290i
\(586\) 16.5150 31.9229i 0.682228 1.31872i
\(587\) 44.5232i 1.83767i 0.394641 + 0.918835i \(0.370869\pi\)
−0.394641 + 0.918835i \(0.629131\pi\)
\(588\) 40.6629 28.7816i 1.67691 1.18693i
\(589\) 32.0732i 1.32156i
\(590\) 20.7322 40.0745i 0.853531 1.64984i
\(591\) 5.40433 0.222304
\(592\) 2.39262 6.78761i 0.0983361 0.278969i
\(593\) 24.9092i 1.02290i −0.859313 0.511449i \(-0.829109\pi\)
0.859313 0.511449i \(-0.170891\pi\)
\(594\) −0.351428 + 19.6262i −0.0144193 + 0.805271i
\(595\) 37.8785i 1.55287i
\(596\) −8.83586 + 6.25411i −0.361931 + 0.256178i
\(597\) 42.2731 1.73012
\(598\) −0.0540306 0.0279522i −0.00220948 0.00114305i
\(599\) 3.19345i 0.130481i 0.997870 + 0.0652404i \(0.0207814\pi\)
−0.997870 + 0.0652404i \(0.979219\pi\)
\(600\) −30.5648 + 4.26128i −1.24780 + 0.173966i
\(601\) 19.2008i 0.783217i −0.920132 0.391608i \(-0.871919\pi\)
0.920132 0.391608i \(-0.128081\pi\)
\(602\) 42.4175 + 21.9443i 1.72881 + 0.894382i
\(603\) 2.92764i 0.119223i
\(604\) −5.65945 7.99572i −0.230280 0.325341i
\(605\) −21.6660 + 28.3966i −0.880850 + 1.15448i
\(606\) −35.0643 18.1402i −1.42439 0.736894i
\(607\) 32.1463 1.30478 0.652390 0.757884i \(-0.273766\pi\)
0.652390 + 0.757884i \(0.273766\pi\)
\(608\) 19.4194 18.2540i 0.787562 0.740299i
\(609\) −37.2322 −1.50872
\(610\) 4.64752 8.98349i 0.188173 0.363731i
\(611\) 11.8706 0.480232
\(612\) 3.75259 2.65613i 0.151690 0.107368i
\(613\) 2.71563i 0.109683i 0.998495 + 0.0548416i \(0.0174654\pi\)
−0.998495 + 0.0548416i \(0.982535\pi\)
\(614\) 9.44317 + 4.88533i 0.381095 + 0.197156i
\(615\) 9.58714 0.386591
\(616\) −23.4163 34.3716i −0.943471 1.38487i
\(617\) 23.5303 0.947295 0.473647 0.880715i \(-0.342937\pi\)
0.473647 + 0.880715i \(0.342937\pi\)
\(618\) −6.47644 3.35053i −0.260521 0.134778i
\(619\) 25.6100i 1.02935i 0.857385 + 0.514676i \(0.172088\pi\)
−0.857385 + 0.514676i \(0.827912\pi\)
\(620\) −36.0849 + 25.5413i −1.44920 + 1.02576i
\(621\) 0.180018 0.00722389
\(622\) −10.1087 + 19.5397i −0.405321 + 0.783470i
\(623\) 43.4413 1.74044
\(624\) 2.61725 7.42486i 0.104774 0.297232i
\(625\) −21.9862 −0.879447
\(626\) −18.2441 9.43842i −0.729181 0.377235i
\(627\) −13.6402 27.5643i −0.544737 1.10081i
\(628\) −22.0599 31.1663i −0.880284 1.24367i
\(629\) 4.73411i 0.188761i
\(630\) −15.7980 8.17295i −0.629408 0.325618i
\(631\) 2.88055i 0.114673i 0.998355 + 0.0573365i \(0.0182608\pi\)
−0.998355 + 0.0573365i \(0.981739\pi\)
\(632\) 0.779755 + 5.59293i 0.0310170 + 0.222475i
\(633\) 33.1279i 1.31672i
\(634\) 23.4133 + 12.1127i 0.929862 + 0.481056i
\(635\) −0.417399 −0.0165640
\(636\) −33.5522 + 23.7486i −1.33043 + 0.941695i
\(637\) 12.6560i 0.501450i
\(638\) −0.358305 + 20.0102i −0.0141854 + 0.792212i
\(639\) 12.7965i 0.506223i
\(640\) −36.0017 7.31191i −1.42309 0.289029i
\(641\) −4.02107 −0.158823 −0.0794113 0.996842i \(-0.525304\pi\)
−0.0794113 + 0.996842i \(0.525304\pi\)
\(642\) −15.3936 + 29.7553i −0.607538 + 1.17435i
\(643\) 14.7579i 0.581993i −0.956724 0.290997i \(-0.906013\pi\)
0.956724 0.290997i \(-0.0939868\pi\)
\(644\) −0.311323 + 0.220358i −0.0122678 + 0.00868331i
\(645\) 48.6784i 1.91671i
\(646\) 8.05556 15.5711i 0.316942 0.612636i
\(647\) 37.3430i 1.46810i 0.679093 + 0.734052i \(0.262373\pi\)
−0.679093 + 0.734052i \(0.737627\pi\)
\(648\) 4.24054 + 30.4160i 0.166584 + 1.19485i
\(649\) −14.4532 29.2072i −0.567337 1.14648i
\(650\) −3.60238 + 6.96326i −0.141297 + 0.273122i
\(651\) −59.4016 −2.32813
\(652\) −4.90233 + 3.46992i −0.191990 + 0.135893i
\(653\) −22.7622 −0.890753 −0.445377 0.895343i \(-0.646930\pi\)
−0.445377 + 0.895343i \(0.646930\pi\)
\(654\) 41.1369 + 21.2818i 1.60858 + 0.832185i
\(655\) −45.4540 −1.77603
\(656\) 5.65927 + 1.99488i 0.220957 + 0.0778871i
\(657\) 6.15851i 0.240266i
\(658\) 34.1989 66.1053i 1.33321 2.57705i
\(659\) 10.7424 0.418464 0.209232 0.977866i \(-0.432904\pi\)
0.209232 + 0.977866i \(0.432904\pi\)
\(660\) −20.1497 + 37.2969i −0.784327 + 1.45178i
\(661\) −2.43331 −0.0946446 −0.0473223 0.998880i \(-0.515069\pi\)
−0.0473223 + 0.998880i \(0.515069\pi\)
\(662\) 2.39181 4.62329i 0.0929605 0.179689i
\(663\) 5.17857i 0.201119i
\(664\) −4.81772 34.5559i −0.186964 1.34103i
\(665\) −67.8261 −2.63018
\(666\) −1.97446 1.02147i −0.0765088 0.0395811i
\(667\) 0.183541 0.00710674
\(668\) 10.0403 + 14.1850i 0.388471 + 0.548834i
\(669\) 17.1698 0.663824
\(670\) −7.07073 + 13.6675i −0.273166 + 0.528020i
\(671\) −3.23996 6.54735i −0.125077 0.252758i
\(672\) −33.8076 35.9660i −1.30416 1.38742i
\(673\) 7.53854i 0.290589i 0.989388 + 0.145295i \(0.0464130\pi\)
−0.989388 + 0.145295i \(0.953587\pi\)
\(674\) 1.01794 1.96763i 0.0392095 0.0757904i
\(675\) 23.2001i 0.892972i
\(676\) −1.15547 1.63245i −0.0444410 0.0627866i
\(677\) 31.5739i 1.21349i 0.794898 + 0.606743i \(0.207524\pi\)
−0.794898 + 0.606743i \(0.792476\pi\)
\(678\) 24.4994 47.3564i 0.940894 1.81871i
\(679\) 47.3720 1.81797
\(680\) −23.9337 + 3.33679i −0.917815 + 0.127960i
\(681\) 21.9886i 0.842606i
\(682\) −0.571653 + 31.9250i −0.0218897 + 1.22247i
\(683\) 19.3540i 0.740560i 0.928920 + 0.370280i \(0.120738\pi\)
−0.928920 + 0.370280i \(0.879262\pi\)
\(684\) −4.75612 6.71948i −0.181855 0.256926i
\(685\) −5.24773 −0.200506
\(686\) −31.4975 16.2949i −1.20258 0.622144i
\(687\) 27.8097i 1.06101i
\(688\) 10.1290 28.7348i 0.386163 1.09550i
\(689\) 10.4429i 0.397842i
\(690\) 0.345300 + 0.178638i 0.0131453 + 0.00680062i
\(691\) 6.00107i 0.228292i −0.993464 0.114146i \(-0.963587\pi\)
0.993464 0.114146i \(-0.0364131\pi\)
\(692\) −5.56896 + 3.94177i −0.211700 + 0.149844i
\(693\) −11.5139 + 5.69767i −0.437378 + 0.216437i
\(694\) −3.33399 1.72481i −0.126556 0.0654728i
\(695\) −23.4508 −0.889541
\(696\) 3.27985 + 23.5253i 0.124323 + 0.891725i
\(697\) 3.94714 0.149508
\(698\) 16.0089 30.9445i 0.605944 1.17127i
\(699\) 10.0904 0.381655
\(700\) 28.3989 + 40.1221i 1.07338 + 1.51647i
\(701\) 21.4823i 0.811375i −0.914012 0.405688i \(-0.867032\pi\)
0.914012 0.405688i \(-0.132968\pi\)
\(702\) 5.25667 + 2.71949i 0.198400 + 0.102640i
\(703\) −8.47701 −0.319716
\(704\) −19.6550 + 17.8236i −0.740777 + 0.671751i
\(705\) −75.8626 −2.85715
\(706\) 16.9953 + 8.79236i 0.639626 + 0.330905i
\(707\) 62.8832i 2.36497i
\(708\) −22.3447 31.5687i −0.839765 1.18643i
\(709\) 31.2876 1.17503 0.587515 0.809213i \(-0.300106\pi\)
0.587515 + 0.809213i \(0.300106\pi\)
\(710\) 30.9058 59.7397i 1.15987 2.24199i
\(711\) 1.74428 0.0654157
\(712\) −3.82683 27.4486i −0.143416 1.02868i
\(713\) 0.292828 0.0109665
\(714\) −28.8386 14.9194i −1.07926 0.558344i
\(715\) 4.77642 + 9.65225i 0.178628 + 0.360974i
\(716\) −33.0732 + 23.4096i −1.23600 + 0.874857i
\(717\) 20.7292i 0.774145i
\(718\) −17.7644 9.19025i −0.662962 0.342977i
\(719\) 37.4361i 1.39613i −0.716034 0.698065i \(-0.754044\pi\)
0.716034 0.698065i \(-0.245956\pi\)
\(720\) −3.77244 + 10.7020i −0.140590 + 0.398840i
\(721\) 11.6147i 0.432553i
\(722\) −4.01645 2.07788i −0.149477 0.0773305i
\(723\) 37.1967 1.38336
\(724\) −0.447404 0.632095i −0.0166276 0.0234916i
\(725\) 23.6541i 0.878490i
\(726\) 13.0859 + 27.6800i 0.485663 + 1.02730i
\(727\) 8.13794i 0.301820i −0.988548 0.150910i \(-0.951780\pi\)
0.988548 0.150910i \(-0.0482203\pi\)
\(728\) −12.4197 + 1.73154i −0.460306 + 0.0641750i
\(729\) −15.2242 −0.563860
\(730\) −14.8738 + 28.7505i −0.550505 + 1.06411i
\(731\) 20.0415i 0.741260i
\(732\) −5.00900 7.07674i −0.185138 0.261564i
\(733\) 23.1590i 0.855396i 0.903922 + 0.427698i \(0.140675\pi\)
−0.903922 + 0.427698i \(0.859325\pi\)
\(734\) 1.82766 3.53280i 0.0674602 0.130398i
\(735\) 80.8823i 2.98339i
\(736\) 0.166659 + 0.177299i 0.00614313 + 0.00653533i
\(737\) 4.92927 + 9.96112i 0.181572 + 0.366923i
\(738\) 0.851665 1.64624i 0.0313502 0.0605988i
\(739\) 16.9726 0.624346 0.312173 0.950025i \(-0.398943\pi\)
0.312173 + 0.950025i \(0.398943\pi\)
\(740\) 6.75060 + 9.53729i 0.248157 + 0.350598i
\(741\) −9.27286 −0.340647
\(742\) 58.1548 + 30.0858i 2.13493 + 1.10449i
\(743\) 31.8960 1.17015 0.585075 0.810979i \(-0.301065\pi\)
0.585075 + 0.810979i \(0.301065\pi\)
\(744\) 5.23280 + 37.5332i 0.191844 + 1.37603i
\(745\) 17.5753i 0.643911i
\(746\) 24.0586 46.5044i 0.880848 1.70265i
\(747\) −10.7771 −0.394312
\(748\) −8.29587 + 15.3556i −0.303327 + 0.561455i
\(749\) 53.3623 1.94982
\(750\) 2.25773 4.36410i 0.0824405 0.159354i
\(751\) 29.8967i 1.09095i −0.838129 0.545473i \(-0.816350\pi\)
0.838129 0.545473i \(-0.183650\pi\)
\(752\) −44.7815 15.7854i −1.63301 0.575635i
\(753\) −52.9427 −1.92934
\(754\) 5.35953 + 2.77270i 0.195183 + 0.100976i
\(755\) 15.9042 0.578814
\(756\) 30.2888 21.4387i 1.10159 0.779719i
\(757\) −27.9620 −1.01630 −0.508148 0.861270i \(-0.669670\pi\)
−0.508148 + 0.861270i \(0.669670\pi\)
\(758\) 6.42041 12.4104i 0.233200 0.450766i
\(759\) 0.251662 0.124535i 0.00913474 0.00452033i
\(760\) 5.97492 + 42.8562i 0.216733 + 1.55456i
\(761\) 16.1869i 0.586775i −0.955994 0.293387i \(-0.905217\pi\)
0.955994 0.293387i \(-0.0947825\pi\)
\(762\) −0.164403 + 0.317785i −0.00595570 + 0.0115121i
\(763\) 73.7738i 2.67079i
\(764\) −15.7642 + 11.1580i −0.570327 + 0.403684i
\(765\) 7.46426i 0.269871i
\(766\) 5.49203 10.6159i 0.198435 0.383568i
\(767\) −9.82553 −0.354779
\(768\) −19.7471 + 24.5298i −0.712561 + 0.885142i
\(769\) 2.32712i 0.0839181i −0.999119 0.0419591i \(-0.986640\pi\)
0.999119 0.0419591i \(-0.0133599\pi\)
\(770\) 67.5126 + 1.20889i 2.43299 + 0.0435653i
\(771\) 2.11862i 0.0763002i
\(772\) 25.6204 18.1344i 0.922097 0.652670i
\(773\) 24.0481 0.864949 0.432475 0.901646i \(-0.357641\pi\)
0.432475 + 0.901646i \(0.357641\pi\)
\(774\) −8.35871 4.32430i −0.300448 0.155434i
\(775\) 37.7386i 1.35561i
\(776\) −4.17309 29.9322i −0.149805 1.07450i
\(777\) 15.6999i 0.563232i
\(778\) −26.4955 13.7072i −0.949908 0.491426i
\(779\) 7.06783i 0.253231i
\(780\) 7.38437 + 10.4327i 0.264403 + 0.373550i
\(781\) −21.5455 43.5395i −0.770960 1.55797i
\(782\) 0.142164 + 0.0735471i 0.00508377 + 0.00263004i
\(783\) −17.8568 −0.638150
\(784\) −16.8299 + 47.7447i −0.601068 + 1.70517i
\(785\) 61.9928 2.21262
\(786\) −17.9032 + 34.6062i −0.638585 + 1.23436i
\(787\) 43.5633 1.55287 0.776433 0.630200i \(-0.217027\pi\)
0.776433 + 0.630200i \(0.217027\pi\)
\(788\) −4.48251 + 3.17277i −0.159683 + 0.113025i
\(789\) 29.5155i 1.05078i
\(790\) −8.14304 4.21273i −0.289716 0.149882i
\(791\) −84.9276 −3.01968
\(792\) 4.61438 + 6.77320i 0.163965 + 0.240675i
\(793\) −2.20258 −0.0782161
\(794\) 3.06504 + 1.58567i 0.108774 + 0.0562733i
\(795\) 66.7386i 2.36697i
\(796\) −35.0626 + 24.8177i −1.24276 + 0.879639i
\(797\) −31.4745 −1.11488 −0.557442 0.830216i \(-0.688217\pi\)
−0.557442 + 0.830216i \(0.688217\pi\)
\(798\) −26.7150 + 51.6391i −0.945701 + 1.82800i
\(799\) −31.2335 −1.10496
\(800\) 22.8496 21.4784i 0.807856 0.759376i
\(801\) −8.56046 −0.302469
\(802\) 8.33767 + 4.31342i 0.294413 + 0.152312i
\(803\) 10.3691 + 20.9540i 0.365917 + 0.739450i
\(804\) 7.62067 + 10.7665i 0.268760 + 0.379707i
\(805\) 0.619251i 0.0218257i
\(806\) 8.55080 + 4.42368i 0.301189 + 0.155817i
\(807\) 5.02384i 0.176848i
\(808\) 39.7330 5.53950i 1.39780 0.194879i
\(809\) 42.0775i 1.47937i 0.672955 + 0.739683i \(0.265025\pi\)
−0.672955 + 0.739683i \(0.734975\pi\)
\(810\) −44.2843 22.9101i −1.55599 0.804978i
\(811\) −0.451090 −0.0158399 −0.00791996 0.999969i \(-0.502521\pi\)
−0.00791996 + 0.999969i \(0.502521\pi\)
\(812\) 30.8815 21.8582i 1.08373 0.767074i
\(813\) 2.73346i 0.0958667i
\(814\) 8.43784 + 0.151089i 0.295746 + 0.00529566i
\(815\) 9.75119i 0.341569i
\(816\) −6.88643 + 19.5361i −0.241073 + 0.683900i
\(817\) −35.8867 −1.25552
\(818\) 2.38458 4.60931i 0.0833750 0.161161i
\(819\) 3.87338i 0.135347i
\(820\) −7.95186 + 5.62841i −0.277691 + 0.196553i
\(821\) 2.42693i 0.0847004i 0.999103 + 0.0423502i \(0.0134845\pi\)
−0.999103 + 0.0423502i \(0.986515\pi\)
\(822\) −2.06695 + 3.99534i −0.0720932 + 0.139354i
\(823\) 10.9604i 0.382056i −0.981585 0.191028i \(-0.938818\pi\)
0.981585 0.191028i \(-0.0611821\pi\)
\(824\) 7.33878 1.02316i 0.255658 0.0356434i
\(825\) −16.0496 32.4332i −0.558775 1.12918i
\(826\) −28.3072 + 54.7168i −0.984935 + 1.90384i
\(827\) −37.0988 −1.29005 −0.645026 0.764161i \(-0.723153\pi\)
−0.645026 + 0.764161i \(0.723153\pi\)
\(828\) 0.0613487 0.0434233i 0.00213202 0.00150906i
\(829\) −30.3272 −1.05331 −0.526653 0.850080i \(-0.676553\pi\)
−0.526653 + 0.850080i \(0.676553\pi\)
\(830\) 50.3118 + 26.0284i 1.74635 + 0.903458i
\(831\) 6.32960 0.219571
\(832\) 2.18816 + 7.69493i 0.0758607 + 0.266774i
\(833\) 33.3002i 1.15378i
\(834\) −9.23670 + 17.8542i −0.319841 + 0.618240i
\(835\) −28.2153 −0.976430
\(836\) 27.4960 + 14.8548i 0.950970 + 0.513763i
\(837\) −28.4894 −0.984738
\(838\) 17.7152 34.2428i 0.611961 1.18290i
\(839\) 24.2451i 0.837035i 0.908209 + 0.418517i \(0.137450\pi\)
−0.908209 + 0.418517i \(0.862550\pi\)
\(840\) 79.3723 11.0659i 2.73860 0.381811i
\(841\) 10.7938 0.372199
\(842\) −19.5071 10.0918i −0.672260 0.347787i
\(843\) 37.6849 1.29794
\(844\) −19.4487 27.4773i −0.669452 0.945806i
\(845\) 3.24710 0.111704
\(846\) −6.73918 + 13.0266i −0.231698 + 0.447863i
\(847\) 29.5823 38.7720i 1.01646 1.33222i
\(848\) 13.8869 39.3956i 0.476878 1.35285i
\(849\) 37.3498i 1.28184i
\(850\) 9.47848 18.3215i 0.325109 0.628424i
\(851\) 0.0773949i 0.00265306i
\(852\) −33.3095 47.0599i −1.14117 1.61225i
\(853\) 44.5598i 1.52570i −0.646577 0.762849i \(-0.723800\pi\)
0.646577 0.762849i \(-0.276200\pi\)
\(854\) −6.34562 + 12.2658i −0.217143 + 0.419728i
\(855\) 13.3657 0.457096
\(856\) −4.70079 33.7172i −0.160670 1.15243i
\(857\) 27.6364i 0.944041i −0.881588 0.472020i \(-0.843525\pi\)
0.881588 0.472020i \(-0.156475\pi\)
\(858\) 9.23002 + 0.165274i 0.315108 + 0.00564235i
\(859\) 10.5383i 0.359562i −0.983707 0.179781i \(-0.942461\pi\)
0.983707 0.179781i \(-0.0575389\pi\)
\(860\) 28.5781 + 40.3753i 0.974504 + 1.37679i
\(861\) −13.0901 −0.446108
\(862\) 12.3497 + 6.38901i 0.420633 + 0.217610i
\(863\) 32.2287i 1.09708i 0.836126 + 0.548538i \(0.184815\pi\)
−0.836126 + 0.548538i \(0.815185\pi\)
\(864\) −16.2143 17.2495i −0.551623 0.586840i
\(865\) 11.0772i 0.376636i
\(866\) 0.215590 + 0.111534i 0.00732606 + 0.00379007i
\(867\) 19.8330i 0.673565i
\(868\) 49.2695 34.8735i 1.67231 1.18368i
\(869\) −5.93482 + 2.93685i −0.201325 + 0.0996257i
\(870\) −34.2518 17.7198i −1.16124 0.600759i
\(871\) 3.35101 0.113544
\(872\) −46.6143 + 6.49887i −1.57856 + 0.220080i
\(873\) −9.33505 −0.315943
\(874\) 0.131695 0.254562i 0.00445465 0.00861068i
\(875\) −7.82646 −0.264582
\(876\) 16.0307 + 22.6482i 0.541626 + 0.765213i
\(877\) 55.7387i 1.88216i 0.338182 + 0.941081i \(0.390188\pi\)
−0.338182 + 0.941081i \(0.609812\pi\)
\(878\) 17.9490 + 9.28573i 0.605748 + 0.313378i
\(879\) 50.0202 1.68714
\(880\) −5.18347 42.7646i −0.174735 1.44160i
\(881\) 56.2426 1.89486 0.947431 0.319960i \(-0.103670\pi\)
0.947431 + 0.319960i \(0.103670\pi\)
\(882\) 13.8885 + 7.18510i 0.467651 + 0.241935i
\(883\) 21.5284i 0.724488i −0.932083 0.362244i \(-0.882011\pi\)
0.932083 0.362244i \(-0.117989\pi\)
\(884\) 3.04023 + 4.29526i 0.102254 + 0.144465i
\(885\) 62.7932 2.11077
\(886\) −14.9843 + 28.9642i −0.503409 + 0.973070i
\(887\) 16.2054 0.544126 0.272063 0.962279i \(-0.412294\pi\)
0.272063 + 0.962279i \(0.412294\pi\)
\(888\) 9.92007 1.38304i 0.332896 0.0464117i
\(889\) 0.569907 0.0191141
\(890\) 39.9639 + 20.6749i 1.33959 + 0.693025i
\(891\) −32.2753 + 15.9715i −1.08126 + 0.535064i
\(892\) −14.2412 + 10.0800i −0.476829 + 0.337505i
\(893\) 55.9274i 1.87154i
\(894\) −13.3809 6.92249i −0.447525 0.231523i
\(895\) 65.7858i 2.19898i
\(896\) 49.1559 + 9.98351i 1.64218 + 0.333526i
\(897\) 0.0846611i 0.00282675i
\(898\) 12.6964 + 6.56836i 0.423684 + 0.219189i
\(899\) −29.0469 −0.968768
\(900\) −5.59623 7.90639i −0.186541 0.263546i
\(901\) 27.4770i 0.915392i
\(902\) −0.125972 + 7.03517i −0.00419442 + 0.234246i
\(903\) 66.4643i 2.21179i
\(904\) 7.48143 + 53.6619i 0.248829 + 1.78477i
\(905\) 1.25730 0.0417939
\(906\) 6.26428 12.1086i 0.208117 0.402282i
\(907\) 43.5176i 1.44498i 0.691383 + 0.722488i \(0.257002\pi\)
−0.691383 + 0.722488i \(0.742998\pi\)
\(908\) −12.9091 18.2380i −0.428402 0.605250i
\(909\) 12.3917i 0.411005i
\(910\) 9.35485 18.0826i 0.310110 0.599431i
\(911\) 12.0795i 0.400213i 0.979774 + 0.200107i \(0.0641288\pi\)
−0.979774 + 0.200107i \(0.935871\pi\)
\(912\) 34.9817 + 12.3310i 1.15836 + 0.408320i
\(913\) 36.6683 18.1453i 1.21354 0.600523i
\(914\) −15.4596 + 29.8829i −0.511360 + 0.988439i
\(915\) 14.0763 0.465348
\(916\) −16.3265 23.0662i −0.539443 0.762130i
\(917\) 62.0617 2.04946
\(918\) −13.8312 7.15544i −0.456497 0.236165i
\(919\) −22.3771 −0.738151 −0.369075 0.929399i \(-0.620326\pi\)
−0.369075 + 0.929399i \(0.620326\pi\)
\(920\) −0.391276 + 0.0545510i −0.0129000 + 0.00179849i
\(921\) 14.7966i 0.487564i
\(922\) −10.9261 + 21.1197i −0.359831 + 0.695539i
\(923\) −14.6471 −0.482114
\(924\) 27.5119 50.9243i 0.905076 1.67529i
\(925\) −9.97437 −0.327955
\(926\) 12.4272 24.0213i 0.408383 0.789388i
\(927\) 2.28876i 0.0751729i
\(928\) −16.5316 17.5871i −0.542677 0.577323i
\(929\) −26.1944 −0.859409 −0.429704 0.902970i \(-0.641382\pi\)
−0.429704 + 0.902970i \(0.641382\pi\)
\(930\) −54.6466 28.2709i −1.79193 0.927039i
\(931\) 59.6280 1.95423
\(932\) −8.36929 + 5.92387i −0.274145 + 0.194043i
\(933\) −30.6169 −1.00235
\(934\) −4.48406 + 8.66751i −0.146723 + 0.283610i
\(935\) −12.5676 25.3967i −0.411004 0.830562i
\(936\) 2.44741 0.341213i 0.0799961 0.0111529i
\(937\) 42.0828i 1.37478i 0.726287 + 0.687392i \(0.241244\pi\)
−0.726287 + 0.687392i \(0.758756\pi\)
\(938\) 9.65420 18.6612i 0.315221 0.609310i
\(939\) 28.5869i 0.932897i
\(940\) 62.9227 44.5373i 2.05231 1.45265i
\(941\) 7.83575i 0.255438i −0.991810 0.127719i \(-0.959234\pi\)
0.991810 0.127719i \(-0.0407656\pi\)
\(942\) 24.4174 47.1979i 0.795562 1.53779i
\(943\) 0.0645292 0.00210136
\(944\) 37.0667 + 13.0659i 1.20642 + 0.425260i
\(945\) 60.2472i 1.95984i
\(946\) 35.7209 + 0.639621i 1.16139 + 0.0207959i
\(947\) 46.2314i 1.50232i 0.660120 + 0.751160i \(0.270505\pi\)
−0.660120 + 0.751160i \(0.729495\pi\)
\(948\) −6.41468 + 4.54038i −0.208339 + 0.147465i
\(949\) 7.04910 0.228823
\(950\) −32.8070 16.9724i −1.06440 0.550657i
\(951\) 36.6866i 1.18964i
\(952\) 32.6785 4.55597i 1.05912 0.147660i
\(953\) 38.0378i 1.23217i 0.787682 + 0.616083i \(0.211281\pi\)
−0.787682 + 0.616083i \(0.788719\pi\)
\(954\) −11.4599 5.92866i −0.371027 0.191947i
\(955\) 31.3564i 1.01467i
\(956\) −12.1697 17.1934i −0.393595 0.556073i
\(957\) −24.9634 + 12.3532i −0.806952 + 0.399321i
\(958\) 20.4953 + 10.6030i 0.662172 + 0.342569i
\(959\) 7.16513 0.231374
\(960\) −13.9841 49.1769i −0.451335 1.58718i
\(961\) −15.3425 −0.494920
\(962\) 1.16918 2.25999i 0.0376960 0.0728649i
\(963\) −10.5155 −0.338857
\(964\) −30.8520 + 21.8374i −0.993677 + 0.703335i
\(965\) 50.9613i 1.64050i
\(966\) −0.471464 0.243908i −0.0151691 0.00784760i
\(967\) 23.8027 0.765443 0.382722 0.923864i \(-0.374987\pi\)
0.382722 + 0.923864i \(0.374987\pi\)
\(968\) −27.1042 15.2762i −0.871162 0.490995i
\(969\) 24.3985 0.783793
\(970\) 43.5799 + 22.5457i 1.39927 + 0.723898i
\(971\) 4.14136i 0.132903i −0.997790 0.0664513i \(-0.978832\pi\)
0.997790 0.0664513i \(-0.0211677\pi\)
\(972\) −14.3897 + 10.1852i −0.461549 + 0.326689i
\(973\) 32.0192 1.02649
\(974\) −24.7732 + 47.8857i −0.793785 + 1.53436i
\(975\) −10.9108 −0.349425
\(976\) 8.30922 + 2.92898i 0.265972 + 0.0937545i
\(977\) −45.5445 −1.45710 −0.728549 0.684994i \(-0.759805\pi\)
−0.728549 + 0.684994i \(0.759805\pi\)
\(978\) −7.42403 3.84075i −0.237394 0.122814i
\(979\) 29.1265 14.4133i 0.930887 0.460650i
\(980\) −47.4843 67.0862i −1.51683 2.14299i
\(981\) 14.5377i 0.464154i
\(982\) −28.9980 15.0018i −0.925363 0.478728i
\(983\) 16.6727i 0.531778i 0.964004 + 0.265889i \(0.0856654\pi\)
−0.964004 + 0.265889i \(0.914335\pi\)
\(984\) 1.15313 + 8.27101i 0.0367604 + 0.263670i
\(985\) 8.91613i 0.284092i
\(986\) −14.1018 7.29546i −0.449094 0.232335i
\(987\) 103.581 3.29702
\(988\) 7.69119 5.44390i 0.244689 0.173194i
\(989\) 0.327645i 0.0104185i
\(990\) −13.3039 0.238221i −0.422826 0.00757117i
\(991\) 18.8655i 0.599283i 0.954052 + 0.299641i \(0.0968670\pi\)
−0.954052 + 0.299641i \(0.903133\pi\)
\(992\) −26.3752 28.0591i −0.837413 0.890876i
\(993\) 7.24427 0.229890
\(994\) −42.1980 + 81.5671i −1.33844 + 2.58715i
\(995\) 69.7428i 2.21100i
\(996\) 39.6332 28.0528i 1.25582 0.888886i
\(997\) 56.3280i 1.78393i −0.452109 0.891963i \(-0.649328\pi\)
0.452109 0.891963i \(-0.350672\pi\)
\(998\) −13.4873 + 26.0704i −0.426932 + 0.825243i
\(999\) 7.52979i 0.238232i
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 572.2.e.b.131.11 64
4.3 odd 2 inner 572.2.e.b.131.53 yes 64
11.10 odd 2 inner 572.2.e.b.131.54 yes 64
44.43 even 2 inner 572.2.e.b.131.12 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.e.b.131.11 64 1.1 even 1 trivial
572.2.e.b.131.12 yes 64 44.43 even 2 inner
572.2.e.b.131.53 yes 64 4.3 odd 2 inner
572.2.e.b.131.54 yes 64 11.10 odd 2 inner