Properties

Label 847.2.u.a.23.14
Level $847$
Weight $2$
Character 847.23
Analytic conductor $6.763$
Analytic rank $0$
Dimension $1720$
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] = [847,2,Mod(23,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([22, 42]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.u (of order \(33\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(1720\)
Relative dimension: \(86\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 23.14
Character \(\chi\) \(=\) 847.23
Dual form 847.2.u.a.221.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24481 - 1.74809i) q^{2} +(-0.628335 - 1.08831i) q^{3} +(-0.852131 + 2.46207i) q^{4} +(-0.293339 + 0.279699i) q^{5} +(-1.12030 + 2.45312i) q^{6} +(-2.19146 - 1.48239i) q^{7} +(1.24649 - 0.366003i) q^{8} +(0.710390 - 1.23043i) q^{9} +O(q^{10})\) \(q+(-1.24481 - 1.74809i) q^{2} +(-0.628335 - 1.08831i) q^{3} +(-0.852131 + 2.46207i) q^{4} +(-0.293339 + 0.279699i) q^{5} +(-1.12030 + 2.45312i) q^{6} +(-2.19146 - 1.48239i) q^{7} +(1.24649 - 0.366003i) q^{8} +(0.710390 - 1.23043i) q^{9} +(0.854089 + 0.164612i) q^{10} +(3.09374 + 1.19532i) q^{11} +(3.21491 - 0.619624i) q^{12} +(3.59831 + 4.15268i) q^{13} +(0.136603 + 5.67617i) q^{14} +(0.488714 + 0.143499i) q^{15} +(1.90446 + 1.49768i) q^{16} +(-0.352001 + 7.38942i) q^{17} +(-3.03521 + 0.289827i) q^{18} +(-0.146838 - 3.08250i) q^{19} +(-0.438674 - 0.960562i) q^{20} +(-0.236324 + 3.31643i) q^{21} +(-1.76159 - 6.89607i) q^{22} +(3.53620 + 2.78090i) q^{23} +(-1.18154 - 1.12660i) q^{24} +(-0.230093 + 4.83024i) q^{25} +(2.78003 - 11.4595i) q^{26} -5.55546 q^{27} +(5.51717 - 4.13235i) q^{28} +(-0.856029 + 0.550136i) q^{29} +(-0.357505 - 1.03294i) q^{30} +(-7.04246 - 1.35732i) q^{31} +(0.371025 - 7.78877i) q^{32} +(-0.643029 - 4.11800i) q^{33} +(13.3555 - 8.58308i) q^{34} +(1.05747 - 0.178106i) q^{35} +(2.42407 + 2.79752i) q^{36} +(2.80748 + 8.11167i) q^{37} +(-5.20570 + 4.09381i) q^{38} +(2.25844 - 6.52534i) q^{39} +(-0.263275 + 0.456006i) q^{40} +(1.61591 - 3.53834i) q^{41} +(6.09159 - 3.71520i) q^{42} +(5.34677 - 1.56995i) q^{43} +(-5.57923 + 6.59843i) q^{44} +(0.135765 + 0.559629i) q^{45} +(0.459366 - 9.64329i) q^{46} +(5.44065 + 0.519519i) q^{47} +(0.433302 - 3.01368i) q^{48} +(2.60504 + 6.49721i) q^{49} +(8.73012 - 5.61051i) q^{50} +(8.26314 - 4.25994i) q^{51} +(-13.2904 + 5.32068i) q^{52} +(9.02675 - 7.09872i) q^{53} +(6.91549 + 9.71144i) q^{54} +(-1.24184 + 0.514680i) q^{55} +(-3.27421 - 1.04571i) q^{56} +(-3.26245 + 2.09665i) q^{57} +(2.02728 + 0.811600i) q^{58} +(8.32784 - 11.6948i) q^{59} +(-0.769753 + 1.08097i) q^{60} +(-11.2529 - 1.07452i) q^{61} +(6.39380 + 14.0005i) q^{62} +(-3.38078 + 1.64337i) q^{63} +(-10.0009 + 6.42721i) q^{64} +(-2.21702 - 0.211700i) q^{65} +(-6.39818 + 6.25019i) q^{66} +(-4.81608 + 0.459880i) q^{67} +(-17.8933 - 7.16341i) q^{68} +(0.804557 - 5.59582i) q^{69} +(-1.62769 - 1.62684i) q^{70} +(-0.914053 + 0.587426i) q^{71} +(0.435154 - 1.79373i) q^{72} +(-2.24988 + 0.900715i) q^{73} +(10.6852 - 15.0052i) q^{74} +(5.40137 - 2.78460i) q^{75} +(7.71446 + 2.26517i) q^{76} +(-5.00789 - 7.20563i) q^{77} +(-14.2182 + 4.17484i) q^{78} +(-4.58634 + 4.37307i) q^{79} +(-0.977551 + 0.0933448i) q^{80} +(1.35952 + 2.35476i) q^{81} +(-8.19683 + 1.57981i) q^{82} +(0.368618 + 2.56380i) q^{83} +(-7.96390 - 3.40788i) q^{84} +(-1.96355 - 2.26606i) q^{85} +(-9.40013 - 7.39234i) q^{86} +(1.13659 + 0.585953i) q^{87} +(4.29381 + 0.357637i) q^{88} +(6.85556 - 3.53429i) q^{89} +(0.809281 - 0.933960i) q^{90} +(-1.72969 - 14.4345i) q^{91} +(-9.86008 + 6.33669i) q^{92} +(2.94784 + 8.51722i) q^{93} +(-5.86440 - 10.1574i) q^{94} +(0.905244 + 0.863148i) q^{95} +(-8.70971 + 4.49017i) q^{96} +(0.991779 - 0.291212i) q^{97} +(8.11494 - 12.6416i) q^{98} +(3.66852 - 2.95749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1720 q - 11 q^{2} - 20 q^{3} + 73 q^{4} - 7 q^{5} + 8 q^{6} - 24 q^{7} - 32 q^{8} - 844 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1720 q - 11 q^{2} - 20 q^{3} + 73 q^{4} - 7 q^{5} + 8 q^{6} - 24 q^{7} - 32 q^{8} - 844 q^{9} - 39 q^{10} - 22 q^{11} + 49 q^{12} - 28 q^{13} - 8 q^{14} - 26 q^{15} + 61 q^{16} - 17 q^{17} - 2 q^{18} - 13 q^{19} - 76 q^{20} + 13 q^{21} - 132 q^{22} + 23 q^{23} - 36 q^{24} + 75 q^{25} + 7 q^{26} + 28 q^{27} - 38 q^{28} - 20 q^{29} + 51 q^{30} - 5 q^{31} - 23 q^{32} + 59 q^{33} + 4 q^{34} - 16 q^{35} - 18 q^{36} - 52 q^{37} - 13 q^{38} - 46 q^{39} + 110 q^{40} - 52 q^{41} + 33 q^{42} - 48 q^{43} - 4 q^{44} + 60 q^{45} - 45 q^{46} - 19 q^{47} - 2 q^{48} - 92 q^{49} - 68 q^{50} + 127 q^{51} - 75 q^{52} - 97 q^{53} - 213 q^{54} - 60 q^{55} - 18 q^{56} - 18 q^{57} + 54 q^{58} - 7 q^{59} - 20 q^{60} - 23 q^{61} - 64 q^{62} + 125 q^{63} - 412 q^{64} + 19 q^{65} - 46 q^{66} + 7 q^{67} - 27 q^{68} - 6 q^{69} - 40 q^{70} - 24 q^{71} - 11 q^{72} - 25 q^{73} + 29 q^{74} + 81 q^{75} + 184 q^{76} - 284 q^{77} + 2 q^{78} - 55 q^{79} + 7 q^{80} - 772 q^{81} + 27 q^{82} + 8 q^{83} - q^{84} - 232 q^{85} - 37 q^{86} - 38 q^{87} + 23 q^{88} - 126 q^{89} + 448 q^{90} + 17 q^{91} + 416 q^{92} + 2 q^{93} + 144 q^{94} + 69 q^{95} - 47 q^{96} - 62 q^{97} + 96 q^{98} + 330 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24481 1.74809i −0.880213 1.23609i −0.970726 0.240190i \(-0.922790\pi\)
0.0905132 0.995895i \(-0.471149\pi\)
\(3\) −0.628335 1.08831i −0.362769 0.628335i 0.625646 0.780107i \(-0.284835\pi\)
−0.988416 + 0.151772i \(0.951502\pi\)
\(4\) −0.852131 + 2.46207i −0.426065 + 1.23104i
\(5\) −0.293339 + 0.279699i −0.131185 + 0.125085i −0.752832 0.658213i \(-0.771313\pi\)
0.621646 + 0.783298i \(0.286464\pi\)
\(6\) −1.12030 + 2.45312i −0.457362 + 1.00148i
\(7\) −2.19146 1.48239i −0.828296 0.560291i
\(8\) 1.24649 0.366003i 0.440702 0.129402i
\(9\) 0.710390 1.23043i 0.236797 0.410144i
\(10\) 0.854089 + 0.164612i 0.270087 + 0.0520550i
\(11\) 3.09374 + 1.19532i 0.932797 + 0.360402i
\(12\) 3.21491 0.619624i 0.928066 0.178870i
\(13\) 3.59831 + 4.15268i 0.997993 + 1.15174i 0.988413 + 0.151791i \(0.0485040\pi\)
0.00957997 + 0.999954i \(0.496951\pi\)
\(14\) 0.136603 + 5.67617i 0.0365087 + 1.51702i
\(15\) 0.488714 + 0.143499i 0.126185 + 0.0370513i
\(16\) 1.90446 + 1.49768i 0.476114 + 0.374420i
\(17\) −0.352001 + 7.38942i −0.0853729 + 1.79220i 0.398611 + 0.917120i \(0.369493\pi\)
−0.483983 + 0.875077i \(0.660810\pi\)
\(18\) −3.03521 + 0.289827i −0.715405 + 0.0683129i
\(19\) −0.146838 3.08250i −0.0336868 0.707174i −0.951034 0.309086i \(-0.899977\pi\)
0.917347 0.398088i \(-0.130326\pi\)
\(20\) −0.438674 0.960562i −0.0980905 0.214788i
\(21\) −0.236324 + 3.31643i −0.0515701 + 0.723704i
\(22\) −1.76159 6.89607i −0.375572 1.47025i
\(23\) 3.53620 + 2.78090i 0.737349 + 0.579858i 0.914625 0.404303i \(-0.132486\pi\)
−0.177276 + 0.984161i \(0.556728\pi\)
\(24\) −1.18154 1.12660i −0.241181 0.229965i
\(25\) −0.230093 + 4.83024i −0.0460186 + 0.966049i
\(26\) 2.78003 11.4595i 0.545210 2.24738i
\(27\) −5.55546 −1.06915
\(28\) 5.51717 4.13235i 1.04265 0.780941i
\(29\) −0.856029 + 0.550136i −0.158961 + 0.102158i −0.617703 0.786412i \(-0.711937\pi\)
0.458742 + 0.888569i \(0.348300\pi\)
\(30\) −0.357505 1.03294i −0.0652713 0.188589i
\(31\) −7.04246 1.35732i −1.26486 0.243782i −0.487661 0.873033i \(-0.662150\pi\)
−0.777203 + 0.629251i \(0.783362\pi\)
\(32\) 0.371025 7.78877i 0.0655886 1.37687i
\(33\) −0.643029 4.11800i −0.111937 0.716852i
\(34\) 13.3555 8.58308i 2.29046 1.47199i
\(35\) 1.05747 0.178106i 0.178744 0.0301054i
\(36\) 2.42407 + 2.79752i 0.404011 + 0.466253i
\(37\) 2.80748 + 8.11167i 0.461546 + 1.33355i 0.900428 + 0.435006i \(0.143254\pi\)
−0.438881 + 0.898545i \(0.644625\pi\)
\(38\) −5.20570 + 4.09381i −0.844476 + 0.664103i
\(39\) 2.25844 6.52534i 0.361640 1.04489i
\(40\) −0.263275 + 0.456006i −0.0416274 + 0.0721008i
\(41\) 1.61591 3.53834i 0.252362 0.552596i −0.740473 0.672086i \(-0.765399\pi\)
0.992835 + 0.119490i \(0.0381258\pi\)
\(42\) 6.09159 3.71520i 0.939952 0.573268i
\(43\) 5.34677 1.56995i 0.815375 0.239416i 0.152652 0.988280i \(-0.451219\pi\)
0.662724 + 0.748864i \(0.269400\pi\)
\(44\) −5.57923 + 6.59843i −0.841100 + 0.994751i
\(45\) 0.135765 + 0.559629i 0.0202386 + 0.0834246i
\(46\) 0.459366 9.64329i 0.0677299 1.42183i
\(47\) 5.44065 + 0.519519i 0.793601 + 0.0757797i 0.483978 0.875080i \(-0.339191\pi\)
0.309622 + 0.950860i \(0.399797\pi\)
\(48\) 0.433302 3.01368i 0.0625417 0.434987i
\(49\) 2.60504 + 6.49721i 0.372148 + 0.928173i
\(50\) 8.73012 5.61051i 1.23463 0.793445i
\(51\) 8.26314 4.25994i 1.15707 0.596512i
\(52\) −13.2904 + 5.32068i −1.84305 + 0.737845i
\(53\) 9.02675 7.09872i 1.23992 0.975084i 0.239929 0.970790i \(-0.422876\pi\)
0.999991 0.00429317i \(-0.00136656\pi\)
\(54\) 6.91549 + 9.71144i 0.941079 + 1.32156i
\(55\) −1.24184 + 0.514680i −0.167450 + 0.0693994i
\(56\) −3.27421 1.04571i −0.437534 0.139738i
\(57\) −3.26245 + 2.09665i −0.432122 + 0.277708i
\(58\) 2.02728 + 0.811600i 0.266195 + 0.106568i
\(59\) 8.32784 11.6948i 1.08419 1.52253i 0.252258 0.967660i \(-0.418827\pi\)
0.831934 0.554874i \(-0.187234\pi\)
\(60\) −0.769753 + 1.08097i −0.0993747 + 0.139552i
\(61\) −11.2529 1.07452i −1.44079 0.137578i −0.654791 0.755810i \(-0.727243\pi\)
−0.785996 + 0.618232i \(0.787849\pi\)
\(62\) 6.39380 + 14.0005i 0.812013 + 1.77806i
\(63\) −3.38078 + 1.64337i −0.425938 + 0.207046i
\(64\) −10.0009 + 6.42721i −1.25012 + 0.803401i
\(65\) −2.21702 0.211700i −0.274988 0.0262582i
\(66\) −6.39818 + 6.25019i −0.787562 + 0.769346i
\(67\) −4.81608 + 0.459880i −0.588378 + 0.0561833i −0.384999 0.922917i \(-0.625798\pi\)
−0.203379 + 0.979100i \(0.565192\pi\)
\(68\) −17.8933 7.16341i −2.16988 0.868691i
\(69\) 0.804557 5.59582i 0.0968573 0.673657i
\(70\) −1.62769 1.62684i −0.194546 0.194444i
\(71\) −0.914053 + 0.587426i −0.108478 + 0.0697146i −0.593755 0.804646i \(-0.702355\pi\)
0.485277 + 0.874361i \(0.338719\pi\)
\(72\) 0.435154 1.79373i 0.0512834 0.211393i
\(73\) −2.24988 + 0.900715i −0.263328 + 0.105421i −0.499570 0.866274i \(-0.666509\pi\)
0.236242 + 0.971694i \(0.424084\pi\)
\(74\) 10.6852 15.0052i 1.24212 1.74432i
\(75\) 5.40137 2.78460i 0.623696 0.321538i
\(76\) 7.71446 + 2.26517i 0.884909 + 0.259833i
\(77\) −5.00789 7.20563i −0.570702 0.821157i
\(78\) −14.2182 + 4.17484i −1.60990 + 0.472708i
\(79\) −4.58634 + 4.37307i −0.516004 + 0.492008i −0.902743 0.430181i \(-0.858450\pi\)
0.386739 + 0.922189i \(0.373601\pi\)
\(80\) −0.977551 + 0.0933448i −0.109294 + 0.0104363i
\(81\) 1.35952 + 2.35476i 0.151058 + 0.261640i
\(82\) −8.19683 + 1.57981i −0.905189 + 0.174461i
\(83\) 0.368618 + 2.56380i 0.0404611 + 0.281413i 1.00000 0.000163017i \(-5.18899e-5\pi\)
−0.959539 + 0.281576i \(0.909143\pi\)
\(84\) −7.96390 3.40788i −0.868932 0.371830i
\(85\) −1.96355 2.26606i −0.212977 0.245789i
\(86\) −9.40013 7.39234i −1.01364 0.797137i
\(87\) 1.13659 + 0.585953i 0.121855 + 0.0628208i
\(88\) 4.29381 + 0.357637i 0.457722 + 0.0381243i
\(89\) 6.85556 3.53429i 0.726688 0.374634i −0.0548471 0.998495i \(-0.517467\pi\)
0.781535 + 0.623861i \(0.214437\pi\)
\(90\) 0.809281 0.933960i 0.0853057 0.0984480i
\(91\) −1.72969 14.4345i −0.181321 1.51315i
\(92\) −9.86008 + 6.33669i −1.02798 + 0.660646i
\(93\) 2.94784 + 8.51722i 0.305677 + 0.883195i
\(94\) −5.86440 10.1574i −0.604867 1.04766i
\(95\) 0.905244 + 0.863148i 0.0928761 + 0.0885572i
\(96\) −8.70971 + 4.49017i −0.888931 + 0.458276i
\(97\) 0.991779 0.291212i 0.100700 0.0295681i −0.230994 0.972955i \(-0.574198\pi\)
0.331694 + 0.943387i \(0.392380\pi\)
\(98\) 8.11494 12.6416i 0.819732 1.27700i
\(99\) 3.66852 2.95749i 0.368700 0.297239i
\(100\) −11.6963 4.68250i −1.16963 0.468250i
\(101\) −4.64367 + 6.52112i −0.462062 + 0.648876i −0.978209 0.207625i \(-0.933427\pi\)
0.516146 + 0.856501i \(0.327366\pi\)
\(102\) −17.7328 9.14189i −1.75581 0.905182i
\(103\) 10.7759 + 15.1327i 1.06178 + 1.49107i 0.859091 + 0.511822i \(0.171029\pi\)
0.202691 + 0.979243i \(0.435031\pi\)
\(104\) 6.00517 + 3.85929i 0.588855 + 0.378434i
\(105\) −0.858277 1.03894i −0.0837592 0.101390i
\(106\) −23.6458 6.94302i −2.29668 0.674366i
\(107\) −8.67017 + 8.26699i −0.838177 + 0.799200i −0.981697 0.190447i \(-0.939006\pi\)
0.143520 + 0.989647i \(0.454158\pi\)
\(108\) 4.73398 13.6779i 0.455528 1.31616i
\(109\) 1.57919 4.56277i 0.151259 0.437034i −0.843760 0.536721i \(-0.819663\pi\)
0.995019 + 0.0996866i \(0.0317840\pi\)
\(110\) 2.44556 + 1.53018i 0.233175 + 0.145897i
\(111\) 7.06396 8.15225i 0.670482 0.773777i
\(112\) −1.95340 6.10526i −0.184579 0.576893i
\(113\) 12.2911 3.60900i 1.15625 0.339506i 0.353277 0.935519i \(-0.385067\pi\)
0.802975 + 0.596012i \(0.203249\pi\)
\(114\) 7.72625 + 3.09312i 0.723629 + 0.289697i
\(115\) −1.81512 + 0.173323i −0.169261 + 0.0161625i
\(116\) −0.625026 2.57639i −0.0580322 0.239212i
\(117\) 7.66579 1.47746i 0.708703 0.136591i
\(118\) −30.8101 −2.83630
\(119\) 11.7254 15.6718i 1.07487 1.43664i
\(120\) 0.661699 0.0604046
\(121\) 8.14243 + 7.39600i 0.740221 + 0.672364i
\(122\) 12.1293 + 21.0086i 1.09814 + 1.90203i
\(123\) −4.86614 + 0.464660i −0.438765 + 0.0418970i
\(124\) 9.34293 16.1824i 0.839020 1.45322i
\(125\) −2.61064 3.01284i −0.233502 0.269476i
\(126\) 7.08118 + 3.86421i 0.630842 + 0.344252i
\(127\) −1.32435 + 2.89993i −0.117517 + 0.257327i −0.959245 0.282575i \(-0.908811\pi\)
0.841728 + 0.539902i \(0.181539\pi\)
\(128\) 9.20649 + 3.68572i 0.813746 + 0.325775i
\(129\) −5.06816 4.83248i −0.446227 0.425476i
\(130\) 2.38970 + 4.13908i 0.209591 + 0.363022i
\(131\) 4.74609 + 13.7129i 0.414668 + 1.19810i 0.938198 + 0.346098i \(0.112493\pi\)
−0.523530 + 0.852007i \(0.675385\pi\)
\(132\) 10.6868 + 1.92589i 0.930162 + 0.167627i
\(133\) −4.24768 + 6.97286i −0.368321 + 0.604624i
\(134\) 6.79901 + 7.84648i 0.587345 + 0.677833i
\(135\) 1.62964 1.55385i 0.140257 0.133735i
\(136\) 2.26579 + 9.33970i 0.194290 + 0.800872i
\(137\) −7.43873 + 2.97802i −0.635534 + 0.254429i −0.666979 0.745076i \(-0.732413\pi\)
0.0314458 + 0.999505i \(0.489989\pi\)
\(138\) −10.7835 + 5.55928i −0.917953 + 0.473238i
\(139\) −6.01747 + 13.1764i −0.510395 + 1.11761i 0.462554 + 0.886591i \(0.346933\pi\)
−0.972949 + 0.231018i \(0.925794\pi\)
\(140\) −0.462590 + 2.75532i −0.0390960 + 0.232867i
\(141\) −2.85315 6.24754i −0.240279 0.526138i
\(142\) 2.16469 + 0.866613i 0.181657 + 0.0727245i
\(143\) 6.16847 + 17.1484i 0.515833 + 1.43402i
\(144\) 3.19570 1.27937i 0.266308 0.106614i
\(145\) 0.0972347 0.400807i 0.00807490 0.0332852i
\(146\) 4.37520 + 2.81177i 0.362094 + 0.232704i
\(147\) 5.43414 6.91751i 0.448200 0.570546i
\(148\) −22.3639 −1.83830
\(149\) 4.31515 + 12.4678i 0.353511 + 1.02140i 0.971872 + 0.235509i \(0.0756757\pi\)
−0.618361 + 0.785894i \(0.712203\pi\)
\(150\) −11.5914 5.97578i −0.946433 0.487920i
\(151\) 1.29838 + 0.250241i 0.105660 + 0.0203643i 0.241807 0.970324i \(-0.422260\pi\)
−0.136147 + 0.990689i \(0.543472\pi\)
\(152\) −1.31124 3.78857i −0.106355 0.307294i
\(153\) 8.84212 + 5.68249i 0.714843 + 0.459402i
\(154\) −6.36221 + 17.7239i −0.512682 + 1.42823i
\(155\) 2.44547 1.57161i 0.196425 0.126235i
\(156\) 14.1414 + 11.1209i 1.13222 + 0.890384i
\(157\) 0.434827 1.25635i 0.0347030 0.100268i −0.926319 0.376741i \(-0.877045\pi\)
0.961022 + 0.276474i \(0.0891658\pi\)
\(158\) 13.3536 + 2.57370i 1.06236 + 0.204753i
\(159\) −13.3974 5.36352i −1.06248 0.425354i
\(160\) 2.06967 + 2.38853i 0.163622 + 0.188830i
\(161\) −3.62708 11.3363i −0.285854 0.893424i
\(162\) 2.42398 5.30778i 0.190446 0.417019i
\(163\) 5.82119 5.55050i 0.455951 0.434748i −0.426973 0.904264i \(-0.640420\pi\)
0.882924 + 0.469516i \(0.155572\pi\)
\(164\) 7.33469 + 6.99361i 0.572743 + 0.546109i
\(165\) 1.34042 + 1.02812i 0.104352 + 0.0800388i
\(166\) 4.02288 3.83581i 0.312236 0.297717i
\(167\) 1.00337 + 0.644828i 0.0776433 + 0.0498983i 0.578886 0.815408i \(-0.303487\pi\)
−0.501243 + 0.865306i \(0.667124\pi\)
\(168\) 0.919248 + 4.22040i 0.0709215 + 0.325611i
\(169\) −2.44676 + 17.0176i −0.188212 + 1.30904i
\(170\) −1.51703 + 6.25328i −0.116351 + 0.479605i
\(171\) −3.89712 2.00910i −0.298020 0.153640i
\(172\) −0.690813 + 14.5019i −0.0526740 + 1.10576i
\(173\) −6.26831 4.92945i −0.476570 0.374779i 0.350787 0.936455i \(-0.385914\pi\)
−0.827357 + 0.561676i \(0.810157\pi\)
\(174\) −0.390539 2.71626i −0.0296067 0.205919i
\(175\) 7.66455 10.2442i 0.579385 0.774390i
\(176\) 4.10168 + 6.90986i 0.309176 + 0.520850i
\(177\) −17.9602 1.71499i −1.34997 0.128907i
\(178\) −14.7121 7.58462i −1.10272 0.568491i
\(179\) 16.3782 12.8800i 1.22417 0.962695i 0.224237 0.974535i \(-0.428011\pi\)
0.999930 + 0.0118393i \(0.00376864\pi\)
\(180\) −1.49354 0.142615i −0.111322 0.0106299i
\(181\) −1.16336 2.54741i −0.0864720 0.189347i 0.861456 0.507832i \(-0.169553\pi\)
−0.947928 + 0.318485i \(0.896826\pi\)
\(182\) −23.0797 + 20.9919i −1.71078 + 1.55602i
\(183\) 5.90118 + 12.9218i 0.436228 + 0.955206i
\(184\) 5.42567 + 2.17211i 0.399986 + 0.160130i
\(185\) −3.09237 1.59423i −0.227355 0.117210i
\(186\) 11.2194 15.7554i 0.822644 1.15524i
\(187\) −9.92171 + 22.4402i −0.725547 + 1.64099i
\(188\) −5.91524 + 12.9526i −0.431413 + 0.944663i
\(189\) 12.1746 + 8.23537i 0.885572 + 0.599035i
\(190\) 0.382005 2.65690i 0.0277135 0.192752i
\(191\) 21.7556 11.2158i 1.57418 0.811545i 0.574204 0.818712i \(-0.305312\pi\)
0.999974 + 0.00716725i \(0.00228143\pi\)
\(192\) 13.2787 + 6.84566i 0.958309 + 0.494043i
\(193\) 14.3289 + 13.6626i 1.03142 + 0.983455i 0.999871 0.0160470i \(-0.00510815\pi\)
0.0315469 + 0.999502i \(0.489957\pi\)
\(194\) −1.74364 1.37121i −0.125186 0.0984474i
\(195\) 1.16264 + 2.54582i 0.0832583 + 0.182310i
\(196\) −18.2164 + 0.877305i −1.30117 + 0.0626646i
\(197\) −13.6783 4.01630i −0.974536 0.286150i −0.244569 0.969632i \(-0.578646\pi\)
−0.729967 + 0.683482i \(0.760465\pi\)
\(198\) −9.73657 2.73139i −0.691948 0.194111i
\(199\) −5.64960 5.38688i −0.400490 0.381866i 0.462894 0.886413i \(-0.346811\pi\)
−0.863384 + 0.504547i \(0.831659\pi\)
\(200\) 1.48108 + 6.10508i 0.104728 + 0.431694i
\(201\) 3.52660 + 4.95242i 0.248748 + 0.349317i
\(202\) 17.1800 1.20878
\(203\) 2.69147 + 0.0633648i 0.188904 + 0.00444734i
\(204\) 3.44701 + 23.9745i 0.241339 + 1.67855i
\(205\) 0.515660 + 1.48990i 0.0360153 + 0.104059i
\(206\) 13.0393 37.6745i 0.908490 2.62491i
\(207\) 5.93380 2.37553i 0.412427 0.165111i
\(208\) 0.633448 + 13.2977i 0.0439217 + 0.922030i
\(209\) 3.23029 9.71196i 0.223444 0.671791i
\(210\) −0.747766 + 2.79362i −0.0516008 + 0.192778i
\(211\) 12.0571 13.9146i 0.830042 0.957920i −0.169577 0.985517i \(-0.554240\pi\)
0.999619 + 0.0275973i \(0.00878559\pi\)
\(212\) 9.78557 + 28.2735i 0.672075 + 1.94183i
\(213\) 1.21363 + 0.625671i 0.0831567 + 0.0428702i
\(214\) 25.2441 + 4.86541i 1.72565 + 0.332593i
\(215\) −1.12931 + 1.95601i −0.0770180 + 0.133399i
\(216\) −6.92485 + 2.03332i −0.471176 + 0.138350i
\(217\) 13.4212 + 13.4142i 0.911092 + 0.910616i
\(218\) −9.94192 + 2.91921i −0.673352 + 0.197714i
\(219\) 2.39393 + 1.88261i 0.161767 + 0.127215i
\(220\) −0.208965 3.49608i −0.0140884 0.235706i
\(221\) −31.9525 + 25.1277i −2.14936 + 1.69027i
\(222\) −23.0441 2.20045i −1.54662 0.147684i
\(223\) −0.700251 + 0.450024i −0.0468923 + 0.0301358i −0.563877 0.825859i \(-0.690691\pi\)
0.516985 + 0.855995i \(0.327054\pi\)
\(224\) −12.3591 + 16.5188i −0.825777 + 1.10371i
\(225\) 5.77983 + 3.71447i 0.385322 + 0.247631i
\(226\) −21.6090 16.9935i −1.43741 1.13039i
\(227\) 4.01268 + 16.5405i 0.266331 + 1.09783i 0.935107 + 0.354366i \(0.115303\pi\)
−0.668776 + 0.743464i \(0.733181\pi\)
\(228\) −2.38206 9.81899i −0.157756 0.650279i
\(229\) 3.71966 0.716906i 0.245802 0.0473745i −0.0648619 0.997894i \(-0.520661\pi\)
0.310664 + 0.950520i \(0.399449\pi\)
\(230\) 2.56246 + 2.95724i 0.168964 + 0.194995i
\(231\) −4.69531 + 9.97767i −0.308929 + 0.656483i
\(232\) −0.865683 + 0.999051i −0.0568349 + 0.0655909i
\(233\) 10.8328 18.7630i 0.709682 1.22921i −0.255293 0.966864i \(-0.582172\pi\)
0.964975 0.262342i \(-0.0844948\pi\)
\(234\) −12.1252 11.5613i −0.792648 0.755788i
\(235\) −1.74127 + 1.36935i −0.113588 + 0.0893263i
\(236\) 21.6970 + 30.4692i 1.41236 + 1.98338i
\(237\) 7.64100 + 2.24360i 0.496336 + 0.145738i
\(238\) −41.9917 0.988601i −2.72192 0.0640815i
\(239\) 1.76709 0.114304 0.0571519 0.998365i \(-0.481798\pi\)
0.0571519 + 0.998365i \(0.481798\pi\)
\(240\) 0.715817 + 1.00522i 0.0462058 + 0.0648870i
\(241\) −10.9950 19.0440i −0.708253 1.22673i −0.965505 0.260385i \(-0.916150\pi\)
0.257252 0.966344i \(-0.417183\pi\)
\(242\) 2.79311 23.4403i 0.179548 1.50680i
\(243\) −6.62473 + 11.4744i −0.424976 + 0.736081i
\(244\) 12.2345 26.7898i 0.783233 1.71504i
\(245\) −2.58142 1.17726i −0.164921 0.0752126i
\(246\) 6.86968 + 7.92803i 0.437995 + 0.505473i
\(247\) 12.2723 11.7016i 0.780865 0.744553i
\(248\) −9.27517 + 0.885671i −0.588974 + 0.0562402i
\(249\) 2.55858 2.01209i 0.162144 0.127511i
\(250\) −2.01696 + 8.31403i −0.127564 + 0.525825i
\(251\) 17.9869 1.13532 0.567662 0.823262i \(-0.307848\pi\)
0.567662 + 0.823262i \(0.307848\pi\)
\(252\) −1.16524 9.72408i −0.0734029 0.612560i
\(253\) 7.61603 + 12.8303i 0.478815 + 0.806632i
\(254\) 6.71791 1.29477i 0.421519 0.0812411i
\(255\) −1.23240 + 3.56080i −0.0771761 + 0.222986i
\(256\) 0.588122 + 2.42427i 0.0367576 + 0.151517i
\(257\) −16.5324 + 15.7636i −1.03126 + 0.983305i −0.999869 0.0162021i \(-0.994842\pi\)
−0.0313919 + 0.999507i \(0.509994\pi\)
\(258\) −2.13872 + 14.8751i −0.133151 + 0.926084i
\(259\) 5.87218 21.9382i 0.364880 1.36318i
\(260\) 2.41042 5.27807i 0.149488 0.327332i
\(261\) 0.0687908 + 1.44410i 0.00425805 + 0.0893874i
\(262\) 18.0635 25.3666i 1.11596 1.56715i
\(263\) 1.60226 1.26003i 0.0987997 0.0776970i −0.567537 0.823348i \(-0.692104\pi\)
0.666337 + 0.745651i \(0.267861\pi\)
\(264\) −2.30873 4.89771i −0.142093 0.301433i
\(265\) −0.662401 + 4.60710i −0.0406910 + 0.283012i
\(266\) 17.4767 1.25455i 1.07157 0.0769216i
\(267\) −8.15398 5.24025i −0.499016 0.320698i
\(268\) 2.97168 12.2494i 0.181524 0.748252i
\(269\) 0.433056 + 0.750075i 0.0264039 + 0.0457329i 0.878925 0.476959i \(-0.158261\pi\)
−0.852522 + 0.522692i \(0.824928\pi\)
\(270\) −4.74486 0.914497i −0.288763 0.0556545i
\(271\) −0.776883 16.3088i −0.0471923 0.990688i −0.890989 0.454025i \(-0.849988\pi\)
0.843797 0.536663i \(-0.180315\pi\)
\(272\) −11.7374 + 13.5456i −0.711682 + 0.821325i
\(273\) −14.6224 + 10.9522i −0.884988 + 0.662855i
\(274\) 14.4656 + 9.29650i 0.873901 + 0.561622i
\(275\) −6.48553 + 14.6685i −0.391092 + 0.884542i
\(276\) 13.0917 + 6.74924i 0.788028 + 0.406257i
\(277\) −29.5817 + 11.8427i −1.77739 + 0.711561i −0.781212 + 0.624266i \(0.785398\pi\)
−0.996182 + 0.0872959i \(0.972177\pi\)
\(278\) 30.5241 5.88305i 1.83072 0.352842i
\(279\) −6.67299 + 7.70104i −0.399502 + 0.461049i
\(280\) 1.25294 0.609044i 0.0748773 0.0363973i
\(281\) 13.2785 + 15.3242i 0.792128 + 0.914164i 0.997922 0.0644311i \(-0.0205233\pi\)
−0.205794 + 0.978595i \(0.565978\pi\)
\(282\) −7.36962 + 12.7646i −0.438854 + 0.760118i
\(283\) −28.4420 + 2.71588i −1.69070 + 0.161442i −0.895547 0.444967i \(-0.853215\pi\)
−0.795153 + 0.606409i \(0.792609\pi\)
\(284\) −0.667392 2.75103i −0.0396024 0.163243i
\(285\) 0.370575 1.52753i 0.0219510 0.0904831i
\(286\) 22.2984 32.1295i 1.31853 1.89986i
\(287\) −8.78641 + 5.35875i −0.518645 + 0.316317i
\(288\) −9.31999 5.98959i −0.549186 0.352940i
\(289\) −37.5566 3.58622i −2.20921 0.210954i
\(290\) −0.821684 + 0.328953i −0.0482510 + 0.0193168i
\(291\) −0.940098 0.896382i −0.0551095 0.0525468i
\(292\) −0.300434 6.30689i −0.0175816 0.369083i
\(293\) 8.20836 + 5.27519i 0.479538 + 0.308180i 0.757986 0.652271i \(-0.226184\pi\)
−0.278448 + 0.960451i \(0.589820\pi\)
\(294\) −18.8569 0.888379i −1.09976 0.0518113i
\(295\) 0.828139 + 5.75983i 0.0482161 + 0.335350i
\(296\) 6.46840 + 9.08360i 0.375968 + 0.527974i
\(297\) −17.1871 6.64055i −0.997299 0.385324i
\(298\) 16.4233 23.0633i 0.951377 1.33602i
\(299\) 1.17619 + 24.6913i 0.0680208 + 1.42793i
\(300\) 2.25321 + 15.6714i 0.130089 + 0.904788i
\(301\) −14.0446 4.48551i −0.809515 0.258540i
\(302\) −1.17878 2.58118i −0.0678314 0.148530i
\(303\) 10.0148 + 0.956294i 0.575333 + 0.0549377i
\(304\) 4.33695 6.09040i 0.248741 0.349308i
\(305\) 3.60146 2.83222i 0.206219 0.162172i
\(306\) −1.07326 22.5304i −0.0613540 1.28798i
\(307\) −7.51389 16.4531i −0.428840 0.939029i −0.993513 0.113715i \(-0.963725\pi\)
0.564673 0.825315i \(-0.309002\pi\)
\(308\) 22.0081 6.18964i 1.25403 0.352687i
\(309\) 9.69811 21.2359i 0.551706 1.20807i
\(310\) −5.79146 2.31855i −0.328933 0.131685i
\(311\) −11.2976 + 4.52290i −0.640631 + 0.256470i −0.669155 0.743123i \(-0.733344\pi\)
0.0285238 + 0.999593i \(0.490919\pi\)
\(312\) 0.426836 8.96040i 0.0241648 0.507283i
\(313\) −0.410096 8.60898i −0.0231800 0.486608i −0.980372 0.197155i \(-0.936830\pi\)
0.957192 0.289453i \(-0.0934733\pi\)
\(314\) −2.73749 + 0.803800i −0.154486 + 0.0453610i
\(315\) 0.532066 1.42766i 0.0299785 0.0804398i
\(316\) −6.85864 15.0183i −0.385828 0.844846i
\(317\) 22.6487 11.6762i 1.27208 0.655801i 0.315956 0.948774i \(-0.397675\pi\)
0.956121 + 0.292973i \(0.0946446\pi\)
\(318\) 7.30131 + 30.0964i 0.409437 + 1.68772i
\(319\) −3.30592 + 0.678751i −0.185096 + 0.0380028i
\(320\) 1.13599 4.68260i 0.0635036 0.261765i
\(321\) 14.4448 + 4.24138i 0.806230 + 0.236731i
\(322\) −15.3018 + 20.4520i −0.852736 + 1.13974i
\(323\) 22.8296 1.27027
\(324\) −6.95607 + 1.34067i −0.386448 + 0.0744818i
\(325\) −20.8864 + 16.4252i −1.15857 + 0.911108i
\(326\) −16.9490 3.26666i −0.938720 0.180923i
\(327\) −5.95796 + 1.14830i −0.329476 + 0.0635013i
\(328\) 0.719172 5.00195i 0.0397096 0.276186i
\(329\) −11.1529 9.20368i −0.614877 0.507415i
\(330\) 0.128669 3.62299i 0.00708299 0.199439i
\(331\) 2.39751 1.23600i 0.131779 0.0679368i −0.391076 0.920358i \(-0.627897\pi\)
0.522855 + 0.852421i \(0.324867\pi\)
\(332\) −6.62636 1.27713i −0.363669 0.0700914i
\(333\) 11.9753 + 2.30804i 0.656241 + 0.126480i
\(334\) −0.121789 2.55667i −0.00666402 0.139895i
\(335\) 1.28412 1.48195i 0.0701589 0.0809677i
\(336\) −5.41702 + 5.96205i −0.295522 + 0.325256i
\(337\) 10.7441 3.15476i 0.585270 0.171851i 0.0243254 0.999704i \(-0.492256\pi\)
0.560945 + 0.827853i \(0.310438\pi\)
\(338\) 32.7940 16.9065i 1.78376 0.919591i
\(339\) −11.6507 11.1089i −0.632777 0.603351i
\(340\) 7.25241 2.90343i 0.393317 0.157460i
\(341\) −20.1651 12.6172i −1.09200 0.683259i
\(342\) 1.33907 + 9.31346i 0.0724088 + 0.503614i
\(343\) 3.92257 18.1001i 0.211799 0.977313i
\(344\) 6.09011 3.91388i 0.328357 0.211022i
\(345\) 1.32913 + 1.86651i 0.0715581 + 0.100489i
\(346\) −0.814277 + 17.0938i −0.0437758 + 0.918967i
\(347\) 18.3651 7.35228i 0.985891 0.394691i 0.178005 0.984030i \(-0.443036\pi\)
0.807886 + 0.589338i \(0.200611\pi\)
\(348\) −2.41118 + 2.29906i −0.129253 + 0.123242i
\(349\) 28.2078 + 8.28257i 1.50993 + 0.443356i 0.928839 0.370483i \(-0.120808\pi\)
0.581091 + 0.813838i \(0.302626\pi\)
\(350\) −27.4487 0.646219i −1.46720 0.0345419i
\(351\) −19.9903 23.0700i −1.06700 1.23139i
\(352\) 10.4579 23.6529i 0.557409 1.26071i
\(353\) −13.0651 2.51809i −0.695384 0.134024i −0.170702 0.985323i \(-0.554604\pi\)
−0.524682 + 0.851298i \(0.675816\pi\)
\(354\) 19.3591 + 33.5309i 1.02892 + 1.78215i
\(355\) 0.103825 0.427974i 0.00551048 0.0227145i
\(356\) 2.85983 + 19.8906i 0.151571 + 1.05420i
\(357\) −24.4233 2.91368i −1.29262 0.154208i
\(358\) −42.9031 12.5975i −2.26750 0.665798i
\(359\) −12.6649 + 2.44096i −0.668429 + 0.128829i −0.512166 0.858886i \(-0.671157\pi\)
−0.156263 + 0.987715i \(0.549945\pi\)
\(360\) 0.374056 + 0.647884i 0.0197145 + 0.0341465i
\(361\) 9.43372 0.900811i 0.496512 0.0474111i
\(362\) −3.00493 + 5.20469i −0.157936 + 0.273552i
\(363\) 2.93296 13.5086i 0.153940 0.709020i
\(364\) 37.0128 + 8.04151i 1.94000 + 0.421489i
\(365\) 0.408049 0.893503i 0.0213583 0.0467681i
\(366\) 15.2426 26.4009i 0.796743 1.38000i
\(367\) 0.228456 0.660081i 0.0119253 0.0344560i −0.938881 0.344242i \(-0.888136\pi\)
0.950806 + 0.309786i \(0.100257\pi\)
\(368\) 2.56964 + 10.5922i 0.133952 + 0.552157i
\(369\) −3.20577 4.50187i −0.166886 0.234358i
\(370\) 1.06256 + 7.39024i 0.0552397 + 0.384200i
\(371\) −30.3049 + 2.17541i −1.57335 + 0.112942i
\(372\) −23.4819 −1.21748
\(373\) 9.39924 + 27.1573i 0.486674 + 1.40615i 0.874772 + 0.484534i \(0.161011\pi\)
−0.388098 + 0.921618i \(0.626868\pi\)
\(374\) 51.5780 10.5897i 2.66704 0.547580i
\(375\) −1.63854 + 4.73425i −0.0846138 + 0.244475i
\(376\) 6.97188 1.34372i 0.359547 0.0692971i
\(377\) −5.36480 1.57525i −0.276301 0.0811293i
\(378\) −0.758894 31.5337i −0.0390333 1.62192i
\(379\) 4.47333 31.1127i 0.229779 1.59815i −0.469256 0.883062i \(-0.655478\pi\)
0.699035 0.715088i \(-0.253613\pi\)
\(380\) −2.89652 + 1.49326i −0.148588 + 0.0766026i
\(381\) 3.98816 0.380823i 0.204319 0.0195101i
\(382\) −46.6877 24.0692i −2.38875 1.23149i
\(383\) −9.16795 0.875433i −0.468460 0.0447325i −0.141843 0.989889i \(-0.545303\pi\)
−0.326617 + 0.945157i \(0.605909\pi\)
\(384\) −1.77356 12.3354i −0.0905065 0.629486i
\(385\) 3.48441 + 0.712995i 0.177582 + 0.0363376i
\(386\) 6.04667 42.0555i 0.307768 2.14057i
\(387\) 1.86657 7.69413i 0.0948833 0.391114i
\(388\) −0.128140 + 2.68998i −0.00650530 + 0.136563i
\(389\) 18.0717 + 17.2313i 0.916270 + 0.873661i 0.992352 0.123440i \(-0.0393927\pi\)
−0.0760823 + 0.997102i \(0.524241\pi\)
\(390\) 3.00306 5.20146i 0.152066 0.263386i
\(391\) −21.7940 + 25.1516i −1.10217 + 1.27197i
\(392\) 5.62516 + 7.14528i 0.284114 + 0.360891i
\(393\) 11.9418 13.7815i 0.602382 0.695186i
\(394\) 10.0060 + 28.9103i 0.504093 + 1.45648i
\(395\) 0.122214 2.56559i 0.00614925 0.129089i
\(396\) 4.15550 + 11.5523i 0.208822 + 0.580526i
\(397\) 1.32754 + 27.8685i 0.0666274 + 1.39868i 0.746517 + 0.665367i \(0.231725\pi\)
−0.679889 + 0.733315i \(0.737972\pi\)
\(398\) −2.38408 + 16.5816i −0.119503 + 0.831163i
\(399\) 10.2576 + 0.241492i 0.513522 + 0.0120897i
\(400\) −7.67236 + 8.85438i −0.383618 + 0.442719i
\(401\) 16.4645 + 6.59140i 0.822199 + 0.329159i 0.744336 0.667805i \(-0.232766\pi\)
0.0778632 + 0.996964i \(0.475190\pi\)
\(402\) 4.26733 12.3296i 0.212835 0.614946i
\(403\) −19.7045 34.1291i −0.981549 1.70009i
\(404\) −12.0984 16.9899i −0.601920 0.845279i
\(405\) −1.05742 0.310487i −0.0525438 0.0154282i
\(406\) −3.23960 4.78381i −0.160779 0.237417i
\(407\) −1.01043 + 28.4512i −0.0500853 + 1.41027i
\(408\) 8.74079 8.33433i 0.432734 0.412611i
\(409\) 0.524593 11.0126i 0.0259395 0.544536i −0.948074 0.318048i \(-0.896973\pi\)
0.974014 0.226488i \(-0.0727244\pi\)
\(410\) 1.96258 2.75606i 0.0969251 0.136112i
\(411\) 7.91501 + 6.22444i 0.390419 + 0.307029i
\(412\) −46.4402 + 13.6361i −2.28794 + 0.671801i
\(413\) −35.5864 + 13.2837i −1.75109 + 0.653646i
\(414\) −11.5391 7.41572i −0.567115 0.364463i
\(415\) −0.825220 0.648960i −0.0405085 0.0318562i
\(416\) 33.6793 26.4857i 1.65126 1.29857i
\(417\) 18.1210 1.73034i 0.887389 0.0847353i
\(418\) −20.9985 + 6.44270i −1.02707 + 0.315123i
\(419\) −3.22377 7.05907i −0.157491 0.344858i 0.814394 0.580312i \(-0.197069\pi\)
−0.971885 + 0.235454i \(0.924342\pi\)
\(420\) 3.28930 1.22783i 0.160502 0.0599118i
\(421\) 3.79780 + 26.4143i 0.185094 + 1.28735i 0.844495 + 0.535564i \(0.179901\pi\)
−0.659401 + 0.751791i \(0.729190\pi\)
\(422\) −39.3327 3.75581i −1.91468 0.182830i
\(423\) 4.50422 6.32529i 0.219003 0.307546i
\(424\) 8.65363 12.1523i 0.420258 0.590169i
\(425\) −35.6117 3.40051i −1.72742 0.164949i
\(426\) −0.417011 2.90038i −0.0202043 0.140524i
\(427\) 23.0675 + 19.0360i 1.11631 + 0.921215i
\(428\) −12.9658 28.3911i −0.626725 1.37234i
\(429\) 14.7869 17.4881i 0.713918 0.844336i
\(430\) 4.82506 0.460737i 0.232685 0.0222187i
\(431\) −1.75373 + 1.37915i −0.0844741 + 0.0664312i −0.659503 0.751702i \(-0.729233\pi\)
0.575029 + 0.818133i \(0.304991\pi\)
\(432\) −10.5801 8.32031i −0.509037 0.400311i
\(433\) −12.8570 8.26270i −0.617868 0.397080i 0.193932 0.981015i \(-0.437876\pi\)
−0.811800 + 0.583935i \(0.801512\pi\)
\(434\) 6.74237 40.1596i 0.323644 1.92772i
\(435\) −0.497297 + 0.146020i −0.0238436 + 0.00700110i
\(436\) 9.88819 + 7.77616i 0.473558 + 0.372410i
\(437\) 8.05288 11.3087i 0.385222 0.540968i
\(438\) 0.310981 6.52830i 0.0148593 0.311934i
\(439\) −7.76829 + 7.40705i −0.370760 + 0.353519i −0.852437 0.522830i \(-0.824876\pi\)
0.481677 + 0.876349i \(0.340028\pi\)
\(440\) −1.35958 + 1.09606i −0.0648152 + 0.0522528i
\(441\) 9.84497 + 1.41024i 0.468808 + 0.0671542i
\(442\) 83.7002 + 24.5766i 3.98121 + 1.16899i
\(443\) −2.65912 3.73421i −0.126339 0.177418i 0.746562 0.665316i \(-0.231703\pi\)
−0.872901 + 0.487898i \(0.837764\pi\)
\(444\) 14.0520 + 24.3388i 0.666878 + 1.15507i
\(445\) −1.02247 + 2.95424i −0.0484698 + 0.140044i
\(446\) 1.65836 + 0.663908i 0.0785257 + 0.0314369i
\(447\) 10.8575 12.5302i 0.513540 0.592657i
\(448\) 31.4443 + 0.740287i 1.48561 + 0.0349753i
\(449\) 0.824421 5.73397i 0.0389068 0.270603i −0.961077 0.276280i \(-0.910898\pi\)
0.999984 + 0.00567756i \(0.00180723\pi\)
\(450\) −0.701556 14.7275i −0.0330717 0.694259i
\(451\) 9.22864 9.01518i 0.434560 0.424508i
\(452\) −1.58804 + 33.3370i −0.0746949 + 1.56804i
\(453\) −0.543475 1.57027i −0.0255347 0.0737776i
\(454\) 23.9192 27.6042i 1.12258 1.29553i
\(455\) 4.54471 + 3.75043i 0.213059 + 0.175823i
\(456\) −3.29924 + 3.80752i −0.154501 + 0.178304i
\(457\) −1.07172 + 1.85628i −0.0501332 + 0.0868332i −0.890003 0.455955i \(-0.849298\pi\)
0.839870 + 0.542788i \(0.182631\pi\)
\(458\) −5.88348 5.60989i −0.274917 0.262133i
\(459\) 1.95553 41.0516i 0.0912764 1.91613i
\(460\) 1.11999 4.61665i 0.0522197 0.215253i
\(461\) 3.90484 27.1588i 0.181867 1.26491i −0.670478 0.741929i \(-0.733911\pi\)
0.852345 0.522981i \(-0.175180\pi\)
\(462\) 23.2866 4.21247i 1.08339 0.195982i
\(463\) −0.936493 6.51345i −0.0435225 0.302706i −0.999943 0.0107117i \(-0.996590\pi\)
0.956420 0.291994i \(-0.0943188\pi\)
\(464\) −2.45420 0.234347i −0.113933 0.0108793i
\(465\) −3.24697 1.67393i −0.150575 0.0776267i
\(466\) −46.2842 + 4.41961i −2.14407 + 0.204734i
\(467\) 1.63928 0.845110i 0.0758570 0.0391070i −0.419881 0.907579i \(-0.637928\pi\)
0.495738 + 0.868472i \(0.334898\pi\)
\(468\) −2.89465 + 20.1327i −0.133805 + 0.930635i
\(469\) 11.2360 + 6.13151i 0.518830 + 0.283127i
\(470\) 4.56128 + 1.33931i 0.210396 + 0.0617779i
\(471\) −1.64051 + 0.316183i −0.0755909 + 0.0145690i
\(472\) 6.10025 17.6255i 0.280787 0.811280i
\(473\) 18.4181 + 1.53407i 0.846866 + 0.0705366i
\(474\) −5.58957 16.1500i −0.256737 0.741794i
\(475\) 14.9230 0.684715
\(476\) 28.5936 + 42.2232i 1.31059 + 1.93530i
\(477\) −2.32197 16.1497i −0.106316 0.739442i
\(478\) −2.19969 3.08904i −0.100612 0.141289i
\(479\) 8.97645 + 37.0014i 0.410144 + 1.69064i 0.684502 + 0.729011i \(0.260020\pi\)
−0.274358 + 0.961628i \(0.588465\pi\)
\(480\) 1.29901 3.75324i 0.0592913 0.171311i
\(481\) −23.5830 + 40.8469i −1.07529 + 1.86246i
\(482\) −19.6038 + 42.9264i −0.892930 + 1.95524i
\(483\) −10.0583 + 11.0704i −0.457671 + 0.503719i
\(484\) −25.1479 + 13.7449i −1.14309 + 0.624767i
\(485\) −0.209476 + 0.362823i −0.00951182 + 0.0164749i
\(486\) 28.3047 2.70277i 1.28393 0.122600i
\(487\) 0.298231 + 0.516552i 0.0135141 + 0.0234072i 0.872703 0.488251i \(-0.162365\pi\)
−0.859189 + 0.511658i \(0.829032\pi\)
\(488\) −14.4199 + 2.77922i −0.652760 + 0.125809i
\(489\) −9.69831 2.84768i −0.438573 0.128777i
\(490\) 1.15541 + 5.97802i 0.0521962 + 0.270060i
\(491\) −4.86348 33.8262i −0.219486 1.52656i −0.739944 0.672669i \(-0.765148\pi\)
0.520458 0.853887i \(-0.325761\pi\)
\(492\) 3.00256 12.3767i 0.135366 0.557986i
\(493\) −3.76387 6.51921i −0.169516 0.293610i
\(494\) −35.7320 6.88678i −1.60766 0.309851i
\(495\) −0.248915 + 1.89363i −0.0111879 + 0.0851123i
\(496\) −11.3792 13.1323i −0.510942 0.589659i
\(497\) 2.87391 + 0.0676598i 0.128912 + 0.00303496i
\(498\) −6.70226 1.96796i −0.300336 0.0881865i
\(499\) −10.6021 + 10.1091i −0.474615 + 0.452544i −0.889235 0.457450i \(-0.848763\pi\)
0.414621 + 0.909994i \(0.363914\pi\)
\(500\) 9.64242 3.86024i 0.431222 0.172635i
\(501\) 0.0713179 1.49715i 0.00318625 0.0668876i
\(502\) −22.3903 31.4427i −0.999326 1.40336i
\(503\) 1.71767 1.10388i 0.0765872 0.0492196i −0.501787 0.864991i \(-0.667324\pi\)
0.578374 + 0.815772i \(0.303687\pi\)
\(504\) −3.61264 + 3.28583i −0.160920 + 0.146362i
\(505\) −0.461777 3.21173i −0.0205488 0.142920i
\(506\) 12.9480 29.2847i 0.575607 1.30186i
\(507\) 20.0577 8.02991i 0.890796 0.356621i
\(508\) −6.01131 5.73178i −0.266709 0.254306i
\(509\) 7.59599 3.91601i 0.336686 0.173574i −0.281590 0.959535i \(-0.590862\pi\)
0.618276 + 0.785961i \(0.287831\pi\)
\(510\) 7.75870 2.27816i 0.343561 0.100879i
\(511\) 6.26574 + 1.36131i 0.277180 + 0.0602209i
\(512\) 16.4941 19.0352i 0.728941 0.841243i
\(513\) 0.815751 + 17.1247i 0.0360163 + 0.756075i
\(514\) 48.1358 + 9.27741i 2.12318 + 0.409209i
\(515\) −7.39358 1.42500i −0.325800 0.0627928i
\(516\) 16.2166 8.36026i 0.713898 0.368040i
\(517\) 16.2110 + 8.11057i 0.712957 + 0.356702i
\(518\) −45.6597 + 17.0438i −2.00617 + 0.748861i
\(519\) −1.42616 + 9.91919i −0.0626017 + 0.435404i
\(520\) −2.84099 + 0.547556i −0.124586 + 0.0240119i
\(521\) −26.9154 5.18753i −1.17919 0.227270i −0.438256 0.898850i \(-0.644404\pi\)
−0.740931 + 0.671581i \(0.765616\pi\)
\(522\) 2.43878 1.91788i 0.106742 0.0839432i
\(523\) −5.36204 + 1.03345i −0.234466 + 0.0451895i −0.305130 0.952311i \(-0.598700\pi\)
0.0706648 + 0.997500i \(0.477488\pi\)
\(524\) −37.8065 −1.65159
\(525\) −15.9648 1.90459i −0.696760 0.0831230i
\(526\) −4.19716 1.23240i −0.183005 0.0537351i
\(527\) 12.5088 51.5619i 0.544891 2.24607i
\(528\) 4.94283 8.80560i 0.215109 0.383215i
\(529\) −0.651131 2.68400i −0.0283100 0.116696i
\(530\) 8.87819 4.57702i 0.385644 0.198813i
\(531\) −8.47366 18.5547i −0.367725 0.805206i
\(532\) −13.5481 16.3999i −0.587384 0.711025i
\(533\) 20.5081 6.02173i 0.888306 0.260830i
\(534\) 0.989730 + 20.7770i 0.0428298 + 0.899109i
\(535\) 0.231037 4.85007i 0.00998861 0.209687i
\(536\) −5.83490 + 2.33594i −0.252029 + 0.100897i
\(537\) −24.3084 9.73162i −1.04899 0.419950i
\(538\) 0.772126 1.69072i 0.0332887 0.0728922i
\(539\) 0.293059 + 23.2145i 0.0126229 + 0.999920i
\(540\) 2.43704 + 5.33637i 0.104873 + 0.229641i
\(541\) −1.35148 28.3711i −0.0581047 1.21977i −0.820114 0.572201i \(-0.806090\pi\)
0.762009 0.647567i \(-0.224213\pi\)
\(542\) −27.5421 + 21.6594i −1.18304 + 0.930350i
\(543\) −2.04138 + 2.86672i −0.0876041 + 0.123023i
\(544\) 57.4239 + 5.48332i 2.46203 + 0.235095i
\(545\) 0.812962 + 1.78014i 0.0348235 + 0.0762528i
\(546\) 37.3475 + 11.9279i 1.59832 + 0.510468i
\(547\) 3.69326 + 25.6872i 0.157912 + 1.09830i 0.902472 + 0.430749i \(0.141750\pi\)
−0.744560 + 0.667556i \(0.767340\pi\)
\(548\) −0.993319 20.8523i −0.0424325 0.890768i
\(549\) −9.31608 + 13.0826i −0.397601 + 0.558352i
\(550\) 33.7150 6.92217i 1.43761 0.295162i
\(551\) 1.82149 + 2.55793i 0.0775982 + 0.108971i
\(552\) −1.04521 7.26962i −0.0444872 0.309416i
\(553\) 16.5334 2.78467i 0.703072 0.118416i
\(554\) 57.5258 + 36.9696i 2.44404 + 1.57069i
\(555\) 0.208033 + 4.36716i 0.00883052 + 0.185375i
\(556\) −27.3136 26.0435i −1.15835 1.10449i
\(557\) 3.33352 1.33454i 0.141246 0.0565462i −0.299963 0.953951i \(-0.596974\pi\)
0.441208 + 0.897405i \(0.354550\pi\)
\(558\) 21.7687 + 2.07866i 0.921543 + 0.0879967i
\(559\) 25.7589 + 16.5542i 1.08948 + 0.700169i
\(560\) 2.28064 + 1.24455i 0.0963747 + 0.0525919i
\(561\) 30.6560 3.30207i 1.29430 0.139414i
\(562\) 10.2589 42.2876i 0.432744 1.78380i
\(563\) −6.18629 25.5002i −0.260721 1.07471i −0.940095 0.340914i \(-0.889264\pi\)
0.679374 0.733793i \(-0.262252\pi\)
\(564\) 17.8131 1.70095i 0.750068 0.0716229i
\(565\) −2.59604 + 4.49647i −0.109216 + 0.189168i
\(566\) 40.1524 + 46.3383i 1.68773 + 1.94775i
\(567\) 0.511331 7.17571i 0.0214739 0.301351i
\(568\) −0.924361 + 1.06677i −0.0387853 + 0.0447606i
\(569\) −13.7845 + 2.65674i −0.577876 + 0.111376i −0.469811 0.882767i \(-0.655678\pi\)
−0.108066 + 0.994144i \(0.534466\pi\)
\(570\) −3.13155 + 1.25369i −0.131166 + 0.0525111i
\(571\) −16.2377 8.37111i −0.679526 0.350320i 0.0836642 0.996494i \(-0.473338\pi\)
−0.763190 + 0.646174i \(0.776368\pi\)
\(572\) −47.4770 + 0.574512i −1.98511 + 0.0240216i
\(573\) −25.8760 16.6295i −1.08099 0.694707i
\(574\) 20.3050 + 8.68881i 0.847513 + 0.362664i
\(575\) −14.2461 + 16.4409i −0.594103 + 0.685631i
\(576\) 0.803679 + 16.8713i 0.0334866 + 0.702971i
\(577\) −9.16257 1.76594i −0.381443 0.0735171i −0.00507434 0.999987i \(-0.501615\pi\)
−0.376369 + 0.926470i \(0.622827\pi\)
\(578\) 40.4817 + 70.1164i 1.68382 + 2.91646i
\(579\) 5.86575 24.1790i 0.243772 1.00484i
\(580\) 0.903958 + 0.580938i 0.0375348 + 0.0241222i
\(581\) 2.99273 6.16490i 0.124159 0.255763i
\(582\) −0.396713 + 2.75920i −0.0164443 + 0.114372i
\(583\) 36.4116 11.1717i 1.50802 0.462686i
\(584\) −2.47479 + 1.94620i −0.102408 + 0.0805343i
\(585\) −1.83544 + 2.57751i −0.0758859 + 0.106567i
\(586\) −0.996331 20.9156i −0.0411580 0.864013i
\(587\) −6.57140 + 14.3894i −0.271231 + 0.593912i −0.995410 0.0956991i \(-0.969491\pi\)
0.724180 + 0.689611i \(0.242219\pi\)
\(588\) 12.4008 + 19.2738i 0.511400 + 0.794840i
\(589\) −3.14985 + 21.9077i −0.129787 + 0.902691i
\(590\) 9.03782 8.61755i 0.372081 0.354779i
\(591\) 4.22356 + 17.4097i 0.173734 + 0.716141i
\(592\) −6.80198 + 19.6530i −0.279560 + 0.807734i
\(593\) −11.2501 + 2.16827i −0.461984 + 0.0890402i −0.414932 0.909852i \(-0.636195\pi\)
−0.0470520 + 0.998892i \(0.514983\pi\)
\(594\) 9.78644 + 38.3109i 0.401542 + 1.57191i
\(595\) 0.943870 + 7.87675i 0.0386949 + 0.322915i
\(596\) −34.3737 −1.40800
\(597\) −2.31275 + 9.53327i −0.0946544 + 0.390171i
\(598\) 41.6984 32.7920i 1.70517 1.34096i
\(599\) −32.6114 + 3.11402i −1.33247 + 0.127235i −0.736863 0.676042i \(-0.763694\pi\)
−0.595605 + 0.803278i \(0.703088\pi\)
\(600\) 5.71360 5.44790i 0.233257 0.222410i
\(601\) −1.59643 1.84238i −0.0651199 0.0751524i 0.722255 0.691627i \(-0.243106\pi\)
−0.787375 + 0.616475i \(0.788560\pi\)
\(602\) 9.64171 + 30.1347i 0.392967 + 1.22820i
\(603\) −2.85545 + 6.25256i −0.116283 + 0.254624i
\(604\) −1.72250 + 2.98345i −0.0700874 + 0.121395i
\(605\) −4.45715 + 0.107886i −0.181209 + 0.00438621i
\(606\) −10.7948 18.6971i −0.438508 0.759518i
\(607\) 5.36836 + 7.53880i 0.217895 + 0.305991i 0.909026 0.416738i \(-0.136827\pi\)
−0.691132 + 0.722729i \(0.742887\pi\)
\(608\) −24.0634 −0.975899
\(609\) −1.62219 2.96897i −0.0657343 0.120309i
\(610\) −9.43410 2.77010i −0.381976 0.112158i
\(611\) 17.4198 + 24.4627i 0.704729 + 0.989653i
\(612\) −21.5253 + 16.9277i −0.870110 + 0.684262i
\(613\) −9.15330 8.72766i −0.369698 0.352507i 0.482342 0.875983i \(-0.339786\pi\)
−0.852040 + 0.523476i \(0.824635\pi\)
\(614\) −19.4082 + 33.6159i −0.783250 + 1.35663i
\(615\) 1.29747 1.49735i 0.0523189 0.0603792i
\(616\) −8.87959 7.14886i −0.357769 0.288036i
\(617\) −26.9180 31.0650i −1.08368 1.25063i −0.966265 0.257549i \(-0.917085\pi\)
−0.117413 0.993083i \(-0.537460\pi\)
\(618\) −49.1945 + 9.48147i −1.97889 + 0.381401i
\(619\) 7.40633 + 30.5293i 0.297686 + 1.22708i 0.902493 + 0.430705i \(0.141735\pi\)
−0.604807 + 0.796372i \(0.706750\pi\)
\(620\) 1.78555 + 7.36015i 0.0717095 + 0.295591i
\(621\) −19.6452 15.4492i −0.788337 0.619955i
\(622\) 21.9698 + 14.1192i 0.880910 + 0.566126i
\(623\) −20.2629 2.41735i −0.811817 0.0968493i
\(624\) 14.0740 9.04480i 0.563410 0.362082i
\(625\) −22.4606 2.14473i −0.898425 0.0857892i
\(626\) −14.5388 + 11.4334i −0.581086 + 0.456971i
\(627\) −12.5993 + 2.58681i −0.503168 + 0.103307i
\(628\) 2.72270 + 2.14115i 0.108647 + 0.0854413i
\(629\) −60.9288 + 17.8903i −2.42939 + 0.713333i
\(630\) −3.15800 + 0.847070i −0.125818 + 0.0337481i
\(631\) 11.3103 3.32101i 0.450256 0.132207i −0.0487396 0.998812i \(-0.515520\pi\)
0.498996 + 0.866604i \(0.333702\pi\)
\(632\) −4.11629 + 7.12962i −0.163737 + 0.283601i
\(633\) −22.7192 4.37877i −0.903008 0.174041i
\(634\) −48.6043 25.0573i −1.93032 0.995151i
\(635\) −0.422621 1.22108i −0.0167712 0.0484573i
\(636\) 24.6217 28.4150i 0.976314 1.12673i
\(637\) −17.6071 + 34.1969i −0.697618 + 1.35493i
\(638\) 5.30175 + 4.93412i 0.209898 + 0.195344i
\(639\) 0.0734536 + 1.54198i 0.00290578 + 0.0609999i
\(640\) −3.73152 + 1.49387i −0.147501 + 0.0590506i
\(641\) −14.7738 + 42.6860i −0.583529 + 1.68600i 0.135295 + 0.990805i \(0.456802\pi\)
−0.718824 + 0.695192i \(0.755319\pi\)
\(642\) −10.5667 30.5305i −0.417035 1.20494i
\(643\) 2.81502 + 19.5789i 0.111013 + 0.772115i 0.966937 + 0.255014i \(0.0820799\pi\)
−0.855924 + 0.517102i \(0.827011\pi\)
\(644\) 31.0015 + 0.729861i 1.22163 + 0.0287606i
\(645\) 2.83833 0.111759
\(646\) −28.4184 39.9081i −1.11811 1.57016i
\(647\) −2.63651 10.8678i −0.103652 0.427259i 0.896214 0.443621i \(-0.146307\pi\)
−0.999866 + 0.0163627i \(0.994791\pi\)
\(648\) 2.55648 + 2.43760i 0.100428 + 0.0957580i
\(649\) 39.7432 26.2263i 1.56006 1.02947i
\(650\) 54.7123 + 16.0650i 2.14599 + 0.630120i
\(651\) 6.16577 23.0350i 0.241655 0.902814i
\(652\) 8.70530 + 19.0619i 0.340926 + 0.746523i
\(653\) 6.22132 + 4.89250i 0.243459 + 0.191458i 0.732431 0.680841i \(-0.238386\pi\)
−0.488972 + 0.872299i \(0.662628\pi\)
\(654\) 9.42386 + 8.98563i 0.368502 + 0.351366i
\(655\) −5.22770 2.69507i −0.204263 0.105305i
\(656\) 8.37673 4.31851i 0.327056 0.168609i
\(657\) −0.490023 + 3.40818i −0.0191176 + 0.132966i
\(658\) −2.20567 + 30.9530i −0.0859859 + 1.20667i
\(659\) 4.56347 9.99260i 0.177767 0.389256i −0.799683 0.600423i \(-0.794999\pi\)
0.977450 + 0.211167i \(0.0677262\pi\)
\(660\) −3.67351 + 2.42413i −0.142991 + 0.0943591i
\(661\) −17.1403 + 24.0702i −0.666680 + 0.936221i −0.999978 0.00660016i \(-0.997899\pi\)
0.333298 + 0.942822i \(0.391838\pi\)
\(662\) −5.14508 2.65248i −0.199969 0.103091i
\(663\) 47.4235 + 18.9855i 1.84178 + 0.737336i
\(664\) 1.39784 + 3.06084i 0.0542466 + 0.118784i
\(665\) −0.704287 3.23348i −0.0273111 0.125389i
\(666\) −10.8723 23.8069i −0.421291 0.922499i
\(667\) −4.55697 0.435138i −0.176447 0.0168486i
\(668\) −2.44262 + 1.92090i −0.0945077 + 0.0743217i
\(669\) 0.929757 + 0.479323i 0.0359465 + 0.0185317i
\(670\) −4.18907 0.400007i −0.161838 0.0154536i
\(671\) −33.5291 16.7751i −1.29438 0.647595i
\(672\) 25.7432 + 3.07115i 0.993066 + 0.118472i
\(673\) −2.85444 19.8530i −0.110030 0.765279i −0.967886 0.251388i \(-0.919113\pi\)
0.857856 0.513890i \(-0.171796\pi\)
\(674\) −18.8892 14.8546i −0.727584 0.572179i
\(675\) 1.27827 26.8342i 0.0492007 1.03285i
\(676\) −39.8135 20.5253i −1.53129 0.789434i
\(677\) −1.11911 + 4.61304i −0.0430110 + 0.177294i −0.989266 0.146129i \(-0.953318\pi\)
0.946255 + 0.323423i \(0.104834\pi\)
\(678\) −4.91647 + 34.1948i −0.188816 + 1.31324i
\(679\) −2.60514 0.832022i −0.0999760 0.0319301i
\(680\) −3.27694 2.10596i −0.125665 0.0807600i
\(681\) 15.4798 14.7600i 0.593188 0.565604i
\(682\) 3.04572 + 50.9564i 0.116627 + 1.95122i
\(683\) 5.40450 + 5.15318i 0.206797 + 0.197181i 0.786399 0.617719i \(-0.211943\pi\)
−0.579601 + 0.814900i \(0.696792\pi\)
\(684\) 8.26741 7.88296i 0.316112 0.301413i
\(685\) 1.34913 2.95417i 0.0515474 0.112873i
\(686\) −36.5234 + 15.6742i −1.39447 + 0.598442i
\(687\) −3.11741 3.59768i −0.118937 0.137260i
\(688\) 12.5340 + 5.01785i 0.477854 + 0.191304i
\(689\) 61.9597 + 11.9418i 2.36048 + 0.454945i
\(690\) 1.60830 4.64689i 0.0612271 0.176904i
\(691\) 5.77564 + 4.54201i 0.219716 + 0.172786i 0.721950 0.691945i \(-0.243246\pi\)
−0.502234 + 0.864732i \(0.667488\pi\)
\(692\) 17.4781 11.2325i 0.664417 0.426995i
\(693\) −12.4236 + 1.04306i −0.471933 + 0.0396226i
\(694\) −35.7135 22.9517i −1.35567 0.871234i
\(695\) −1.92026 5.54824i −0.0728398 0.210457i
\(696\) 1.63121 + 0.314391i 0.0618310 + 0.0119169i
\(697\) 25.5775 + 13.1861i 0.968817 + 0.499460i
\(698\) −20.6347 59.6200i −0.781034 2.25665i
\(699\) −27.2266 −1.02980
\(700\) 18.6908 + 27.6001i 0.706446 + 1.04318i
\(701\) −18.8292 12.1008i −0.711171 0.457042i 0.134385 0.990929i \(-0.457094\pi\)
−0.845555 + 0.533888i \(0.820731\pi\)
\(702\) −15.4444 + 63.6626i −0.582910 + 2.40279i
\(703\) 24.5920 9.84515i 0.927505 0.371317i
\(704\) −38.6228 + 7.92980i −1.45565 + 0.298866i
\(705\) 2.58437 + 1.03463i 0.0973330 + 0.0389663i
\(706\) 11.8617 + 25.9735i 0.446420 + 0.977524i
\(707\) 19.8433 7.40708i 0.746284 0.278572i
\(708\) 19.5269 42.7579i 0.733866 1.60694i
\(709\) −36.7689 + 18.9557i −1.38088 + 0.711895i −0.979012 0.203801i \(-0.934671\pi\)
−0.401872 + 0.915696i \(0.631640\pi\)
\(710\) −0.877380 + 0.351250i −0.0329275 + 0.0131822i
\(711\) 2.12267 + 8.74977i 0.0796064 + 0.328142i
\(712\) 7.25185 6.91463i 0.271775 0.259137i
\(713\) −21.1290 24.3842i −0.791287 0.913194i
\(714\) 25.3089 + 46.3210i 0.947163 + 1.73352i
\(715\) −6.60584 3.30499i −0.247045 0.123600i
\(716\) 17.7550 + 51.2998i 0.663537 + 1.91716i
\(717\) −1.11033 1.92314i −0.0414659 0.0718211i
\(718\) 20.0324 + 19.1009i 0.747604 + 0.712839i
\(719\) 21.7444 + 8.70514i 0.810929 + 0.324647i 0.739806 0.672821i \(-0.234917\pi\)
0.0711231 + 0.997468i \(0.477342\pi\)
\(720\) −0.579588 + 1.26912i −0.0216000 + 0.0472974i
\(721\) −1.18253 49.1368i −0.0440398 1.82995i
\(722\) −13.3179 15.3696i −0.495640 0.571999i
\(723\) −13.8171 + 23.9320i −0.513865 + 0.890040i
\(724\) 7.26323 0.693554i 0.269936 0.0257757i
\(725\) −2.46033 4.26141i −0.0913742 0.158265i
\(726\) −27.2653 + 11.6886i −1.01191 + 0.433805i
\(727\) 23.3500 0.866004 0.433002 0.901393i \(-0.357454\pi\)
0.433002 + 0.901393i \(0.357454\pi\)
\(728\) −7.43914 17.3595i −0.275713 0.643386i
\(729\) 24.8073 0.918789
\(730\) −2.06987 + 0.398934i −0.0766092 + 0.0147652i
\(731\) 9.71898 + 40.0622i 0.359470 + 1.48175i
\(732\) −36.8429 + 3.51807i −1.36175 + 0.130032i
\(733\) 40.7242 + 16.3035i 1.50418 + 0.602184i 0.969983 0.243173i \(-0.0781883\pi\)
0.534201 + 0.845358i \(0.320613\pi\)
\(734\) −1.43827 + 0.422313i −0.0530874 + 0.0155879i
\(735\) 0.340771 + 3.54910i 0.0125695 + 0.130910i
\(736\) 22.9718 26.5109i 0.846753 0.977205i
\(737\) −15.4494 4.33400i −0.569086 0.159645i
\(738\) −3.87910 + 11.2079i −0.142792 + 0.412570i
\(739\) −13.6739 + 39.5080i −0.503001 + 1.45333i 0.352641 + 0.935759i \(0.385284\pi\)
−0.855642 + 0.517568i \(0.826837\pi\)
\(740\) 6.56020 6.25514i 0.241158 0.229943i
\(741\) −20.4460 6.00349i −0.751103 0.220544i
\(742\) 41.5266 + 50.2677i 1.52449 + 1.84538i
\(743\) −36.3519 23.3620i −1.33362 0.857067i −0.337188 0.941437i \(-0.609476\pi\)
−0.996434 + 0.0843704i \(0.973112\pi\)
\(744\) 6.79180 + 9.53774i 0.248999 + 0.349671i
\(745\) −4.75303 2.45036i −0.174138 0.0897742i
\(746\) 35.7731 50.2363i 1.30975 1.83928i
\(747\) 3.41644 + 1.36774i 0.125001 + 0.0500428i
\(748\) −46.7947 43.5499i −1.71098 1.59234i
\(749\) 31.2553 5.26424i 1.14204 0.192351i
\(750\) 10.3156 3.02892i 0.376671 0.110601i
\(751\) −0.0128501 + 0.00662469i −0.000468907 + 0.000241738i −0.458461 0.888715i \(-0.651599\pi\)
0.457992 + 0.888956i \(0.348569\pi\)
\(752\) 9.58341 + 9.13776i 0.349471 + 0.333220i
\(753\) −11.3018 19.5753i −0.411861 0.713363i
\(754\) 3.92448 + 11.3390i 0.142921 + 0.412943i
\(755\) −0.450857 + 0.289748i −0.0164084 + 0.0105450i
\(756\) −30.6504 + 22.9571i −1.11474 + 0.834942i
\(757\) −25.1381 + 29.0110i −0.913661 + 1.05442i 0.0846548 + 0.996410i \(0.473021\pi\)
−0.998316 + 0.0580108i \(0.981524\pi\)
\(758\) −59.9561 + 30.9095i −2.17770 + 1.12268i
\(759\) 9.17787 16.3503i 0.333136 0.593478i
\(760\) 1.44430 + 0.744586i 0.0523901 + 0.0270090i
\(761\) −1.32458 1.04166i −0.0480161 0.0377603i 0.593863 0.804567i \(-0.297602\pi\)
−0.641879 + 0.766806i \(0.721845\pi\)
\(762\) −5.63020 6.49760i −0.203961 0.235383i
\(763\) −10.2246 + 7.65818i −0.370154 + 0.277245i
\(764\) 9.07544 + 63.1211i 0.328338 + 2.28364i
\(765\) −4.18313 + 0.806231i −0.151241 + 0.0291494i
\(766\) 9.88201 + 17.1161i 0.357051 + 0.618431i
\(767\) 78.5309 7.49879i 2.83559 0.270766i
\(768\) 2.26882 2.16331i 0.0818689 0.0780618i
\(769\) 34.9263 10.2553i 1.25947 0.369815i 0.417175 0.908826i \(-0.363020\pi\)
0.842299 + 0.539011i \(0.181202\pi\)
\(770\) −3.09105 6.97861i −0.111394 0.251492i
\(771\) 27.5435 + 8.08750i 0.991955 + 0.291264i
\(772\) −45.8484 + 23.6365i −1.65012 + 0.850696i
\(773\) −0.595997 + 0.836960i −0.0214365 + 0.0301034i −0.825155 0.564906i \(-0.808912\pi\)
0.803719 + 0.595010i \(0.202852\pi\)
\(774\) −15.7735 + 6.31477i −0.566968 + 0.226980i
\(775\) 8.17662 33.7045i 0.293713 1.21070i
\(776\) 1.12966 0.725989i 0.0405525 0.0260615i
\(777\) −27.5652 + 7.39381i −0.988898 + 0.265252i
\(778\) 7.62608 53.0405i 0.273408 1.90160i
\(779\) −11.1442 4.46147i −0.399283 0.159849i
\(780\) −7.25872 + 0.693124i −0.259904 + 0.0248178i
\(781\) −3.53000 + 0.724758i −0.126313 + 0.0259339i
\(782\) 71.0966 + 6.78890i 2.54241 + 0.242771i
\(783\) 4.75564 3.05626i 0.169953 0.109222i
\(784\) −4.76958 + 16.2752i −0.170342 + 0.581256i
\(785\) 0.223848 + 0.490158i 0.00798946 + 0.0174945i
\(786\) −38.9565 3.71990i −1.38953 0.132684i
\(787\) 24.1514 33.9159i 0.860904 1.20897i −0.115563 0.993300i \(-0.536867\pi\)
0.976466 0.215670i \(-0.0691935\pi\)
\(788\) 21.5441 30.2544i 0.767476 1.07777i
\(789\) −2.37806 0.952032i −0.0846612 0.0338932i
\(790\) −4.63700 + 2.98002i −0.164977 + 0.106024i
\(791\) −32.2855 10.3113i −1.14794 0.366626i
\(792\) 3.49033 5.02919i 0.124024 0.178704i
\(793\) −36.0293 50.5961i −1.27944 1.79672i
\(794\) 47.0641 37.0116i 1.67024 1.31349i
\(795\) 5.43016 2.17391i 0.192588 0.0771005i
\(796\) 18.0771 9.31938i 0.640725 0.330317i
\(797\) 2.56367 1.64757i 0.0908097 0.0583599i −0.494448 0.869207i \(-0.664630\pi\)
0.585258 + 0.810847i \(0.300993\pi\)
\(798\) −12.3466 18.2318i −0.437064 0.645398i
\(799\) −5.75406 + 40.0204i −0.203564 + 1.41582i
\(800\) 37.5363 + 3.58428i 1.32711 + 0.126724i
\(801\) 0.521424 10.9460i 0.0184236 0.386759i
\(802\) −8.97283 36.9865i −0.316842 1.30604i
\(803\) −8.03718 + 0.0972568i −0.283626 + 0.00343212i
\(804\) −15.1983 + 4.46264i −0.536004 + 0.157385i
\(805\) 4.23471 + 2.31089i 0.149254 + 0.0814481i
\(806\) −35.1325 + 76.9294i −1.23749 + 2.70972i
\(807\) 0.544209 0.942597i 0.0191571 0.0331810i
\(808\) −3.40155 + 9.82813i −0.119666 + 0.345753i
\(809\) 35.5196 27.9329i 1.24880 0.982069i 0.248894 0.968531i \(-0.419933\pi\)
0.999908 0.0135383i \(-0.00430951\pi\)
\(810\) 0.773529 + 2.23497i 0.0271791 + 0.0785287i
\(811\) 18.0488 + 20.8295i 0.633780 + 0.731421i 0.978262 0.207372i \(-0.0664910\pi\)
−0.344482 + 0.938793i \(0.611946\pi\)
\(812\) −2.44950 + 6.57261i −0.0859605 + 0.230653i
\(813\) −17.2608 + 11.0929i −0.605364 + 0.389044i
\(814\) 50.9931 33.6500i 1.78731 1.17943i
\(815\) −0.155119 + 3.25636i −0.00543360 + 0.114065i
\(816\) 22.1168 + 4.26267i 0.774244 + 0.149223i
\(817\) −5.62449 16.2509i −0.196776 0.568547i
\(818\) −19.9040 + 12.7915i −0.695926 + 0.447244i
\(819\) −18.9895 8.12590i −0.663546 0.283942i
\(820\) −4.10765 −0.143446
\(821\) −0.863889 + 3.56100i −0.0301499 + 0.124280i −0.984898 0.173137i \(-0.944610\pi\)
0.954748 + 0.297416i \(0.0961249\pi\)
\(822\) 1.02819 21.5844i 0.0358623 0.752842i
\(823\) 0.0469377 + 0.0447550i 0.00163614 + 0.00156006i 0.690897 0.722954i \(-0.257216\pi\)
−0.689260 + 0.724514i \(0.742064\pi\)
\(824\) 18.9707 + 14.9187i 0.660876 + 0.519719i
\(825\) 20.0389 2.15846i 0.697665 0.0751481i
\(826\) 67.5193 + 45.6726i 2.34930 + 1.58915i
\(827\) 21.6239 + 47.3498i 0.751938 + 1.64652i 0.762850 + 0.646575i \(0.223799\pi\)
−0.0109120 + 0.999940i \(0.503473\pi\)
\(828\) 0.792360 + 16.6337i 0.0275364 + 0.578061i
\(829\) −20.6160 + 1.96859i −0.716025 + 0.0683721i −0.446708 0.894680i \(-0.647404\pi\)
−0.269316 + 0.963052i \(0.586798\pi\)
\(830\) −0.107199 + 2.25039i −0.00372094 + 0.0781122i
\(831\) 31.4758 + 24.7528i 1.09188 + 0.858666i
\(832\) −62.6766 18.4035i −2.17292 0.638027i
\(833\) −48.9276 + 16.9627i −1.69524 + 0.587722i
\(834\) −25.5820 29.5231i −0.885831 1.02230i
\(835\) −0.474686 + 0.0914883i −0.0164272 + 0.00316608i
\(836\) 21.1589 + 16.2291i 0.731796 + 0.561294i
\(837\) 39.1241 + 7.54056i 1.35233 + 0.260640i
\(838\) −8.32690 + 14.4226i −0.287648 + 0.498221i
\(839\) −31.7504 + 9.32274i −1.09614 + 0.321857i −0.779319 0.626627i \(-0.784435\pi\)
−0.316825 + 0.948484i \(0.602617\pi\)
\(840\) −1.45009 0.980897i −0.0500329 0.0338442i
\(841\) −11.6169 + 25.4375i −0.400583 + 0.877154i
\(842\) 41.4470 39.5197i 1.42836 1.36194i
\(843\) 8.33410 24.0798i 0.287042 0.829352i
\(844\) 23.9845 + 41.5424i 0.825581 + 1.42995i
\(845\) −4.04206 5.67628i −0.139051 0.195270i
\(846\) −16.6641 −0.572922
\(847\) −6.88008 28.2783i −0.236402 0.971655i
\(848\) 27.8227 0.955434
\(849\) 20.8268 + 29.2471i 0.714774 + 1.00376i
\(850\) 38.3854 + 66.4854i 1.31661 + 2.28043i
\(851\) −12.6300 + 36.4918i −0.432949 + 1.25092i
\(852\) −2.57462 + 2.45489i −0.0882050 + 0.0841033i
\(853\) 12.8290 28.0916i 0.439256 0.961837i −0.552478 0.833528i \(-0.686318\pi\)
0.991734 0.128310i \(-0.0409552\pi\)
\(854\) 4.56198 64.0201i 0.156108 2.19072i
\(855\) 1.70512 0.500669i 0.0583140 0.0171225i
\(856\) −7.78156 + 13.4781i −0.265968 + 0.460671i
\(857\) −18.1977 3.50733i −0.621623 0.119808i −0.131291 0.991344i \(-0.541912\pi\)
−0.490332 + 0.871536i \(0.663124\pi\)
\(858\) −48.9777 4.07942i −1.67207 0.139269i
\(859\) 47.2266 9.10219i 1.61135 0.310563i 0.697492 0.716592i \(-0.254299\pi\)
0.913860 + 0.406029i \(0.133087\pi\)
\(860\) −3.85353 4.44721i −0.131404 0.151649i
\(861\) 11.3528 + 6.19523i 0.386902 + 0.211133i
\(862\) 4.59393 + 1.34890i 0.156470 + 0.0459437i
\(863\) −20.1546 15.8497i −0.686070 0.539531i 0.213155 0.977018i \(-0.431626\pi\)
−0.899225 + 0.437487i \(0.855869\pi\)
\(864\) −2.06122 + 43.2702i −0.0701240 + 1.47208i
\(865\) 3.21750 0.307234i 0.109398 0.0104463i
\(866\) 1.56058 + 32.7607i 0.0530308 + 1.11325i
\(867\) 19.6952 + 43.1265i 0.668884 + 1.46465i
\(868\) −44.4634 + 21.6133i −1.50919 + 0.733605i
\(869\) −19.4161 + 8.04699i −0.658647 + 0.272975i
\(870\) 0.874295 + 0.687553i 0.0296414 + 0.0233102i
\(871\) −19.2395 18.3448i −0.651906 0.621591i
\(872\) 0.298460 6.26546i 0.0101071 0.212175i
\(873\) 0.346233 1.42719i 0.0117182 0.0483031i
\(874\) −29.7929 −1.00776
\(875\) 1.25492 + 10.4725i 0.0424240 + 0.354035i
\(876\) −6.67506 + 4.28980i −0.225529 + 0.144939i
\(877\) 0.976754 + 2.82214i 0.0329826 + 0.0952970i 0.960290 0.279003i \(-0.0900041\pi\)
−0.927307 + 0.374300i \(0.877883\pi\)
\(878\) 22.6182 + 4.35931i 0.763328 + 0.147119i
\(879\) 0.583435 12.2478i 0.0196788 0.413109i
\(880\) −3.13586 0.879700i −0.105710 0.0296547i
\(881\) −26.6093 + 17.1007i −0.896489 + 0.576139i −0.905747 0.423819i \(-0.860689\pi\)
0.00925799 + 0.999957i \(0.497053\pi\)
\(882\) −9.78989 18.9654i −0.329643 0.638597i
\(883\) −33.7371 38.9347i −1.13535 1.31026i −0.944453 0.328647i \(-0.893407\pi\)
−0.190893 0.981611i \(-0.561138\pi\)
\(884\) −34.6385 100.081i −1.16502 3.36610i
\(885\) 5.74812 4.52037i 0.193221 0.151951i
\(886\) −3.21764 + 9.29675i −0.108099 + 0.312331i
\(887\) −12.0415 + 20.8565i −0.404314 + 0.700292i −0.994241 0.107164i \(-0.965823\pi\)
0.589928 + 0.807456i \(0.299156\pi\)
\(888\) 5.82143 12.7472i 0.195354 0.427767i
\(889\) 7.20111 4.39189i 0.241517 0.147299i
\(890\) 6.43705 1.89009i 0.215770 0.0633559i
\(891\) 1.39131 + 8.91006i 0.0466107 + 0.298498i
\(892\) −0.511286 2.10755i −0.0171191 0.0705659i
\(893\) 0.802526 16.8471i 0.0268555 0.563767i
\(894\) −35.4193 3.38213i −1.18460 0.113116i
\(895\) −1.20187 + 8.35918i −0.0401740 + 0.279416i
\(896\) −14.7120 21.7247i −0.491494 0.725773i
\(897\) 26.1327 16.7944i 0.872544 0.560750i
\(898\) −11.0497 + 5.69654i −0.368735 + 0.190096i
\(899\) 6.77527 2.71241i 0.225968 0.0904638i
\(900\) −14.0705 + 11.0651i −0.469016 + 0.368838i
\(901\) 49.2780 + 69.2012i 1.64169 + 2.30543i
\(902\) −27.2472 4.91031i −0.907234 0.163495i
\(903\) 3.94307 + 18.1032i 0.131217 + 0.602437i
\(904\) 13.9999 8.99719i 0.465630 0.299242i
\(905\) 1.05377 + 0.421864i 0.0350283 + 0.0140232i
\(906\) −2.06845 + 2.90472i −0.0687195 + 0.0965030i
\(907\) 31.3095 43.9680i 1.03961 1.45993i 0.158306 0.987390i \(-0.449397\pi\)
0.881308 0.472543i \(-0.156664\pi\)
\(908\) −44.1432 4.21516i −1.46494 0.139885i
\(909\) 4.72498 + 10.3463i 0.156718 + 0.343164i
\(910\) 0.898793 12.6131i 0.0297947 0.418121i
\(911\) 14.2293 9.14463i 0.471439 0.302975i −0.283264 0.959042i \(-0.591417\pi\)
0.754703 + 0.656067i \(0.227781\pi\)
\(912\) −9.35329 0.893131i −0.309718 0.0295745i
\(913\) −1.92414 + 8.37233i −0.0636799 + 0.277084i
\(914\) 4.57904 0.437245i 0.151461 0.0144628i
\(915\) −5.34525 2.13992i −0.176709 0.0707434i
\(916\) −1.40457 + 9.76897i −0.0464082 + 0.322776i
\(917\) 9.92703 37.0870i 0.327820 1.22472i
\(918\) −74.1962 + 47.6830i −2.44884 + 1.57377i
\(919\) 4.28376 17.6579i 0.141308 0.582481i −0.856490 0.516163i \(-0.827360\pi\)
0.997799 0.0663176i \(-0.0211250\pi\)
\(920\) −2.19910 + 0.880387i −0.0725022 + 0.0290255i
\(921\) −13.1848 + 18.5155i −0.434455 + 0.610106i
\(922\) −52.3367 + 26.9815i −1.72362 + 0.888587i
\(923\) −5.72844 1.68202i −0.188554 0.0553644i
\(924\) −20.5647 20.0625i −0.676529 0.660007i
\(925\) −39.8273 + 11.6944i −1.30951 + 0.384508i
\(926\) −10.2203 + 9.74508i −0.335861 + 0.320243i
\(927\) 26.2748 2.50894i 0.862978 0.0824044i
\(928\) 3.96728 + 6.87153i 0.130232 + 0.225569i
\(929\) −4.38261 + 0.844680i −0.143789 + 0.0277130i −0.260638 0.965437i \(-0.583933\pi\)
0.116849 + 0.993150i \(0.462721\pi\)
\(930\) 1.11568 + 7.75972i 0.0365846 + 0.254451i
\(931\) 19.6451 8.98406i 0.643844 0.294441i
\(932\) 36.9649 + 42.6597i 1.21082 + 1.39737i
\(933\) 12.0210 + 9.45343i 0.393550 + 0.309491i
\(934\) −3.51792 1.81361i −0.115110 0.0593433i
\(935\) −3.36606 9.35767i −0.110082 0.306029i
\(936\) 9.01461 4.64735i 0.294652 0.151903i
\(937\) 26.8836 31.0253i 0.878248 1.01355i −0.121532 0.992587i \(-0.538781\pi\)
0.999780 0.0209646i \(-0.00667371\pi\)
\(938\) −3.26825 27.2741i −0.106712 0.890530i
\(939\) −9.11154 + 5.85563i −0.297344 + 0.191091i
\(940\) −1.88764 5.45398i −0.0615681 0.177889i
\(941\) −14.3050 24.7769i −0.466329 0.807705i 0.532932 0.846158i \(-0.321090\pi\)
−0.999260 + 0.0384531i \(0.987757\pi\)
\(942\) 2.59484 + 2.47418i 0.0845445 + 0.0806131i
\(943\) 15.5540 8.01862i 0.506507 0.261122i
\(944\) 33.3751 9.79981i 1.08627 0.318957i
\(945\) −5.87471 + 0.989461i −0.191104 + 0.0321872i
\(946\) −20.2453 34.1061i −0.658233 1.10889i
\(947\) −27.7451 11.1075i −0.901594 0.360944i −0.125893 0.992044i \(-0.540180\pi\)
−0.775702 + 0.631100i \(0.782604\pi\)
\(948\) −12.0350 + 16.9008i −0.390880 + 0.548914i
\(949\) −11.8361 6.10196i −0.384218 0.198078i
\(950\) −18.5763 26.0868i −0.602695 0.846366i
\(951\) −26.9383 17.3122i −0.873533 0.561386i
\(952\) 8.87969 23.8264i 0.287792 0.772218i
\(953\) 11.3402 + 3.32979i 0.367346 + 0.107863i 0.460195 0.887818i \(-0.347779\pi\)
−0.0928494 + 0.995680i \(0.529597\pi\)
\(954\) −25.3406 + 24.1623i −0.820434 + 0.782282i
\(955\) −3.24473 + 9.37503i −0.104997 + 0.303369i
\(956\) −1.50580 + 4.35071i −0.0487009 + 0.140712i
\(957\) 2.81591 + 3.17137i 0.0910256 + 0.102516i
\(958\) 53.5078 61.7513i 1.72876 1.99509i
\(959\) 20.7163 + 4.50088i 0.668964 + 0.145341i
\(960\) −5.80989 + 1.70594i −0.187513 + 0.0550589i
\(961\) 18.9745 + 7.59626i 0.612082 + 0.245041i
\(962\) 100.760 9.62144i 3.24864 0.310208i
\(963\) 4.01277 + 16.5408i 0.129310 + 0.533021i
\(964\) 56.2568 10.8426i 1.81191 0.349217i
\(965\) −8.02465 −0.258322
\(966\) 31.8727 + 3.80239i 1.02549 + 0.122340i
\(967\) −37.9262 −1.21962 −0.609812 0.792546i \(-0.708755\pi\)
−0.609812 + 0.792546i \(0.708755\pi\)
\(968\) 12.8564 + 6.23891i 0.413222 + 0.200526i
\(969\) −14.3446 24.8456i −0.460816 0.798156i
\(970\) 0.895005 0.0854626i 0.0287369 0.00274404i
\(971\) 14.2714 24.7188i 0.457991 0.793264i −0.540864 0.841110i \(-0.681903\pi\)
0.998855 + 0.0478466i \(0.0152359\pi\)
\(972\) −22.6056 26.0882i −0.725074 0.836779i
\(973\) 32.7197 19.9554i 1.04894 0.639741i
\(974\) 0.531738 1.16434i 0.0170380 0.0373080i
\(975\) 30.9994 + 12.4103i 0.992774 + 0.397447i
\(976\) −19.8214 18.8996i −0.634466 0.604962i
\(977\) −16.8128 29.1207i −0.537890 0.931653i −0.999017 0.0443188i \(-0.985888\pi\)
0.461128 0.887334i \(-0.347445\pi\)
\(978\) 7.09454 + 20.4983i 0.226858 + 0.655464i
\(979\) 25.4339 2.73958i 0.812871 0.0875574i
\(980\) 5.09822 5.35246i 0.162857 0.170978i
\(981\) −4.49234 5.18444i −0.143429 0.165526i
\(982\) −53.0771 + 50.6090i −1.69376 + 1.61500i
\(983\) 7.50816 + 30.9490i 0.239473 + 0.987121i 0.956884 + 0.290471i \(0.0938120\pi\)
−0.717411 + 0.696650i \(0.754673\pi\)
\(984\) −5.89554 + 2.36022i −0.187943 + 0.0752410i
\(985\) 5.13573 2.64765i 0.163638 0.0843612i
\(986\) −6.71086 + 14.6947i −0.213717 + 0.467976i
\(987\) −3.00870 + 17.9207i −0.0957681 + 0.570424i
\(988\) 18.3525 + 40.1864i 0.583872 + 1.27850i
\(989\) 23.2732 + 9.31717i 0.740044 + 0.296269i
\(990\) 3.62008 1.92208i 0.115054 0.0610877i
\(991\) −23.8929 + 9.56529i −0.758985 + 0.303852i −0.718685 0.695336i \(-0.755256\pi\)
−0.0402998 + 0.999188i \(0.512831\pi\)
\(992\) −13.1848 + 54.3486i −0.418618 + 1.72557i
\(993\) −2.85159 1.83261i −0.0904925 0.0581560i
\(994\) −3.45919 5.10807i −0.109719 0.162018i
\(995\) 3.16395 0.100304
\(996\) 2.77367 + 8.01398i 0.0878870 + 0.253933i
\(997\) −38.4897 19.8428i −1.21898 0.628429i −0.275963 0.961168i \(-0.588997\pi\)
−0.943019 + 0.332739i \(0.892027\pi\)
\(998\) 30.8691 + 5.94954i 0.977145 + 0.188329i
\(999\) −15.5968 45.0641i −0.493462 1.42576i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 847.2.u.a.23.14 1720
7.4 even 3 inner 847.2.u.a.144.73 yes 1720
121.100 even 11 inner 847.2.u.a.100.73 yes 1720
847.221 even 33 inner 847.2.u.a.221.14 yes 1720
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.u.a.23.14 1720 1.1 even 1 trivial
847.2.u.a.100.73 yes 1720 121.100 even 11 inner
847.2.u.a.144.73 yes 1720 7.4 even 3 inner
847.2.u.a.221.14 yes 1720 847.221 even 33 inner