Properties

Label 64.2.i.a.29.6
Level $64$
Weight $2$
Character 64.29
Analytic conductor $0.511$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [64,2,Mod(5,64)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(64, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("64.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.i (of order \(16\), degree \(8\), 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: \(0.511042572936\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 29.6
Character \(\chi\) \(=\) 64.29
Dual form 64.2.i.a.53.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.468362 - 1.33441i) q^{2} +(-2.98137 - 0.593031i) q^{3} +(-1.56127 - 1.24997i) q^{4} +(0.914126 - 1.36809i) q^{5} +(-2.18770 + 3.70060i) q^{6} +(2.65574 - 1.10004i) q^{7} +(-2.39921 + 1.49793i) q^{8} +(5.76522 + 2.38803i) q^{9} +O(q^{10})\) \(q+(0.468362 - 1.33441i) q^{2} +(-2.98137 - 0.593031i) q^{3} +(-1.56127 - 1.24997i) q^{4} +(0.914126 - 1.36809i) q^{5} +(-2.18770 + 3.70060i) q^{6} +(2.65574 - 1.10004i) q^{7} +(-2.39921 + 1.49793i) q^{8} +(5.76522 + 2.38803i) q^{9} +(-1.39744 - 1.86057i) q^{10} +(0.246413 + 1.23880i) q^{11} +(3.91346 + 4.65250i) q^{12} +(0.319413 + 0.478036i) q^{13} +(-0.224055 - 4.05906i) q^{14} +(-3.53666 + 3.53666i) q^{15} +(0.875149 + 3.90309i) q^{16} +(-3.38390 - 3.38390i) q^{17} +(5.88682 - 6.57468i) q^{18} +(4.19561 - 2.80342i) q^{19} +(-3.13727 + 0.993326i) q^{20} +(-8.57011 + 1.70470i) q^{21} +(1.76847 + 0.251393i) q^{22} +(0.178010 - 0.429755i) q^{23} +(8.04124 - 3.04308i) q^{24} +(0.877384 + 2.11819i) q^{25} +(0.787494 - 0.202333i) q^{26} +(-8.18962 - 5.47213i) q^{27} +(-5.52137 - 1.60213i) q^{28} +(-1.02242 + 5.14005i) q^{29} +(3.06290 + 6.37578i) q^{30} +10.0065i q^{31} +(5.61819 + 0.660257i) q^{32} -3.83945i q^{33} +(-6.10038 + 2.93060i) q^{34} +(0.922728 - 4.63887i) q^{35} +(-6.01612 - 10.9347i) q^{36} +(0.447703 + 0.299146i) q^{37} +(-1.77583 - 6.91166i) q^{38} +(-0.668798 - 1.61462i) q^{39} +(-0.143878 + 4.65162i) q^{40} +(2.44115 - 5.89346i) q^{41} +(-1.73915 + 12.2344i) q^{42} +(3.80641 - 0.757142i) q^{43} +(1.16375 - 2.24212i) q^{44} +(8.53718 - 5.70436i) q^{45} +(-0.490094 - 0.438819i) q^{46} +(-5.99084 - 5.99084i) q^{47} +(-0.294489 - 12.1555i) q^{48} +(0.893127 - 0.893127i) q^{49} +(3.23746 - 0.178704i) q^{50} +(8.08188 + 12.0954i) q^{51} +(0.0988389 - 1.14560i) q^{52} +(0.810472 + 4.07452i) q^{53} +(-11.1378 + 8.36533i) q^{54} +(1.92004 + 0.795307i) q^{55} +(-4.72389 + 6.61736i) q^{56} +(-14.1712 + 5.86989i) q^{57} +(6.38004 + 3.77172i) q^{58} +(-1.03615 + 1.55070i) q^{59} +(9.94242 - 1.10097i) q^{60} +(-6.47490 - 1.28794i) q^{61} +(13.3528 + 4.68668i) q^{62} +17.9379 q^{63} +(3.51240 - 7.18770i) q^{64} +0.945978 q^{65} +(-5.12339 - 1.79826i) q^{66} +(6.01983 + 1.19742i) q^{67} +(1.05342 + 9.51296i) q^{68} +(-0.785572 + 1.17569i) q^{69} +(-5.75795 - 3.40396i) q^{70} +(-4.20400 + 1.74136i) q^{71} +(-17.4091 + 2.90652i) q^{72} +(-0.911379 - 0.377506i) q^{73} +(0.608868 - 0.457308i) q^{74} +(-1.35965 - 6.83542i) q^{75} +(-10.0547 - 0.867487i) q^{76} +(2.01715 + 3.01887i) q^{77} +(-2.46780 + 0.136220i) q^{78} +(0.152459 - 0.152459i) q^{79} +(6.13976 + 2.37064i) q^{80} +(7.93360 + 7.93360i) q^{81} +(-6.72092 - 6.01776i) q^{82} +(-5.16472 + 3.45096i) q^{83} +(15.5111 + 8.05087i) q^{84} +(-7.72277 + 1.53615i) q^{85} +(0.772445 - 5.43391i) q^{86} +(6.09641 - 14.7180i) q^{87} +(-2.44684 - 2.60303i) q^{88} +(1.48745 + 3.59102i) q^{89} +(-3.61343 - 14.0638i) q^{90} +(1.37414 + 0.918171i) q^{91} +(-0.815104 + 0.448458i) q^{92} +(5.93418 - 29.8331i) q^{93} +(-10.8001 + 5.18832i) q^{94} -8.30263i q^{95} +(-16.3583 - 5.30023i) q^{96} -13.7742i q^{97} +(-0.773486 - 1.61010i) q^{98} +(-1.53767 + 7.73041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(63\)
\(\chi(n)\) \(e\left(\frac{11}{16}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.468362 1.33441i 0.331182 0.943567i
\(3\) −2.98137 0.593031i −1.72129 0.342386i −0.767088 0.641542i \(-0.778295\pi\)
−0.954204 + 0.299155i \(0.903295\pi\)
\(4\) −1.56127 1.24997i −0.780637 0.624985i
\(5\) 0.914126 1.36809i 0.408810 0.611827i −0.568744 0.822515i \(-0.692570\pi\)
0.977553 + 0.210688i \(0.0675704\pi\)
\(6\) −2.18770 + 3.70060i −0.893126 + 1.51076i
\(7\) 2.65574 1.10004i 1.00378 0.415778i 0.180596 0.983557i \(-0.442197\pi\)
0.823181 + 0.567779i \(0.192197\pi\)
\(8\) −2.39921 + 1.49793i −0.848248 + 0.529599i
\(9\) 5.76522 + 2.38803i 1.92174 + 0.796011i
\(10\) −1.39744 1.86057i −0.441909 0.588365i
\(11\) 0.246413 + 1.23880i 0.0742963 + 0.373513i 0.999989 0.00476447i \(-0.00151658\pi\)
−0.925692 + 0.378277i \(0.876517\pi\)
\(12\) 3.91346 + 4.65250i 1.12972 + 1.34306i
\(13\) 0.319413 + 0.478036i 0.0885893 + 0.132583i 0.873117 0.487510i \(-0.162095\pi\)
−0.784528 + 0.620093i \(0.787095\pi\)
\(14\) −0.224055 4.05906i −0.0598813 1.08483i
\(15\) −3.53666 + 3.53666i −0.913162 + 0.913162i
\(16\) 0.875149 + 3.90309i 0.218787 + 0.975773i
\(17\) −3.38390 3.38390i −0.820715 0.820715i 0.165495 0.986211i \(-0.447078\pi\)
−0.986211 + 0.165495i \(0.947078\pi\)
\(18\) 5.88682 6.57468i 1.38754 1.54967i
\(19\) 4.19561 2.80342i 0.962539 0.643148i 0.0282261 0.999602i \(-0.491014\pi\)
0.934313 + 0.356453i \(0.116014\pi\)
\(20\) −3.13727 + 0.993326i −0.701514 + 0.222115i
\(21\) −8.57011 + 1.70470i −1.87015 + 0.371996i
\(22\) 1.76847 + 0.251393i 0.377040 + 0.0535972i
\(23\) 0.178010 0.429755i 0.0371177 0.0896101i −0.904234 0.427038i \(-0.859557\pi\)
0.941351 + 0.337428i \(0.109557\pi\)
\(24\) 8.04124 3.04308i 1.64141 0.621166i
\(25\) 0.877384 + 2.11819i 0.175477 + 0.423638i
\(26\) 0.787494 0.202333i 0.154440 0.0396807i
\(27\) −8.18962 5.47213i −1.57609 1.05311i
\(28\) −5.52137 1.60213i −1.04344 0.302774i
\(29\) −1.02242 + 5.14005i −0.189858 + 0.954483i 0.761914 + 0.647678i \(0.224260\pi\)
−0.951773 + 0.306805i \(0.900740\pi\)
\(30\) 3.06290 + 6.37578i 0.559206 + 1.16405i
\(31\) 10.0065i 1.79722i 0.438743 + 0.898612i \(0.355424\pi\)
−0.438743 + 0.898612i \(0.644576\pi\)
\(32\) 5.61819 + 0.660257i 0.993165 + 0.116718i
\(33\) 3.83945i 0.668363i
\(34\) −6.10038 + 2.93060i −1.04621 + 0.502593i
\(35\) 0.922728 4.63887i 0.155969 0.784111i
\(36\) −6.01612 10.9347i −1.00269 1.82245i
\(37\) 0.447703 + 0.299146i 0.0736019 + 0.0491792i 0.591827 0.806065i \(-0.298407\pi\)
−0.518225 + 0.855244i \(0.673407\pi\)
\(38\) −1.77583 6.91166i −0.288077 1.12122i
\(39\) −0.668798 1.61462i −0.107093 0.258546i
\(40\) −0.143878 + 4.65162i −0.0227491 + 0.735486i
\(41\) 2.44115 5.89346i 0.381244 0.920404i −0.610482 0.792030i \(-0.709024\pi\)
0.991726 0.128374i \(-0.0409757\pi\)
\(42\) −1.73915 + 12.2344i −0.268357 + 1.88781i
\(43\) 3.80641 0.757142i 0.580472 0.115463i 0.103883 0.994589i \(-0.466873\pi\)
0.476589 + 0.879126i \(0.341873\pi\)
\(44\) 1.16375 2.24212i 0.175441 0.338012i
\(45\) 8.53718 5.70436i 1.27265 0.850355i
\(46\) −0.490094 0.438819i −0.0722604 0.0647003i
\(47\) −5.99084 5.99084i −0.873854 0.873854i 0.119036 0.992890i \(-0.462020\pi\)
−0.992890 + 0.119036i \(0.962020\pi\)
\(48\) −0.294489 12.1555i −0.0425058 1.75450i
\(49\) 0.893127 0.893127i 0.127590 0.127590i
\(50\) 3.23746 0.178704i 0.457846 0.0252726i
\(51\) 8.08188 + 12.0954i 1.13169 + 1.69369i
\(52\) 0.0988389 1.14560i 0.0137065 0.158866i
\(53\) 0.810472 + 4.07452i 0.111327 + 0.559678i 0.995679 + 0.0928581i \(0.0296003\pi\)
−0.884353 + 0.466820i \(0.845400\pi\)
\(54\) −11.1378 + 8.36533i −1.51566 + 1.13838i
\(55\) 1.92004 + 0.795307i 0.258898 + 0.107239i
\(56\) −4.72389 + 6.61736i −0.631256 + 0.884282i
\(57\) −14.1712 + 5.86989i −1.87702 + 0.777486i
\(58\) 6.38004 + 3.77172i 0.837740 + 0.495252i
\(59\) −1.03615 + 1.55070i −0.134895 + 0.201884i −0.892767 0.450519i \(-0.851239\pi\)
0.757872 + 0.652403i \(0.226239\pi\)
\(60\) 9.94242 1.10097i 1.28356 0.142135i
\(61\) −6.47490 1.28794i −0.829026 0.164903i −0.237702 0.971338i \(-0.576394\pi\)
−0.591323 + 0.806435i \(0.701394\pi\)
\(62\) 13.3528 + 4.68668i 1.69580 + 0.595209i
\(63\) 17.9379 2.25996
\(64\) 3.51240 7.18770i 0.439050 0.898463i
\(65\) 0.945978 0.117334
\(66\) −5.12339 1.79826i −0.630645 0.221350i
\(67\) 6.01983 + 1.19742i 0.735439 + 0.146288i 0.548579 0.836099i \(-0.315169\pi\)
0.186860 + 0.982387i \(0.440169\pi\)
\(68\) 1.05342 + 9.51296i 0.127746 + 1.15362i
\(69\) −0.785572 + 1.17569i −0.0945718 + 0.141537i
\(70\) −5.75795 3.40396i −0.688207 0.406851i
\(71\) −4.20400 + 1.74136i −0.498924 + 0.206661i −0.617931 0.786232i \(-0.712029\pi\)
0.119007 + 0.992893i \(0.462029\pi\)
\(72\) −17.4091 + 2.90652i −2.05168 + 0.342537i
\(73\) −0.911379 0.377506i −0.106669 0.0441837i 0.328711 0.944431i \(-0.393386\pi\)
−0.435380 + 0.900247i \(0.643386\pi\)
\(74\) 0.608868 0.457308i 0.0707795 0.0531610i
\(75\) −1.35965 6.83542i −0.156999 0.789286i
\(76\) −10.0547 0.867487i −1.15335 0.0995076i
\(77\) 2.01715 + 3.01887i 0.229875 + 0.344033i
\(78\) −2.46780 + 0.136220i −0.279423 + 0.0154238i
\(79\) 0.152459 0.152459i 0.0171530 0.0171530i −0.698478 0.715631i \(-0.746139\pi\)
0.715631 + 0.698478i \(0.246139\pi\)
\(80\) 6.13976 + 2.37064i 0.686446 + 0.265045i
\(81\) 7.93360 + 7.93360i 0.881511 + 0.881511i
\(82\) −6.72092 6.01776i −0.742201 0.664550i
\(83\) −5.16472 + 3.45096i −0.566902 + 0.378792i −0.805741 0.592267i \(-0.798233\pi\)
0.238840 + 0.971059i \(0.423233\pi\)
\(84\) 15.5111 + 8.05087i 1.69240 + 0.878422i
\(85\) −7.72277 + 1.53615i −0.837652 + 0.166619i
\(86\) 0.772445 5.43391i 0.0832949 0.585954i
\(87\) 6.09641 14.7180i 0.653604 1.57794i
\(88\) −2.44684 2.60303i −0.260834 0.277484i
\(89\) 1.48745 + 3.59102i 0.157669 + 0.380648i 0.982898 0.184151i \(-0.0589537\pi\)
−0.825228 + 0.564799i \(0.808954\pi\)
\(90\) −3.61343 14.0638i −0.380889 1.48245i
\(91\) 1.37414 + 0.918171i 0.144049 + 0.0962505i
\(92\) −0.815104 + 0.448458i −0.0849805 + 0.0467549i
\(93\) 5.93418 29.8331i 0.615345 3.09355i
\(94\) −10.8001 + 5.18832i −1.11394 + 0.535135i
\(95\) 8.30263i 0.851832i
\(96\) −16.3583 5.30023i −1.66957 0.540952i
\(97\) 13.7742i 1.39856i −0.714849 0.699279i \(-0.753505\pi\)
0.714849 0.699279i \(-0.246495\pi\)
\(98\) −0.773486 1.61010i −0.0781339 0.162645i
\(99\) −1.53767 + 7.73041i −0.154542 + 0.776936i
\(100\) 1.27784 4.40378i 0.127784 0.440378i
\(101\) 3.34129 + 2.23258i 0.332470 + 0.222150i 0.710589 0.703608i \(-0.248429\pi\)
−0.378118 + 0.925757i \(0.623429\pi\)
\(102\) 19.9254 5.11948i 1.97291 0.506904i
\(103\) 3.02140 + 7.29430i 0.297707 + 0.718728i 0.999977 + 0.00681740i \(0.00217006\pi\)
−0.702270 + 0.711911i \(0.747830\pi\)
\(104\) −1.48240 0.668448i −0.145362 0.0655467i
\(105\) −5.50198 + 13.2830i −0.536938 + 1.29628i
\(106\) 5.81665 + 0.826852i 0.564963 + 0.0803110i
\(107\) −5.40913 + 1.07594i −0.522920 + 0.104015i −0.449490 0.893285i \(-0.648394\pi\)
−0.0734296 + 0.997300i \(0.523394\pi\)
\(108\) 5.94624 + 18.7803i 0.572177 + 1.80713i
\(109\) −3.62995 + 2.42545i −0.347686 + 0.232316i −0.717134 0.696935i \(-0.754547\pi\)
0.369448 + 0.929251i \(0.379547\pi\)
\(110\) 1.96054 2.18962i 0.186930 0.208772i
\(111\) −1.15736 1.15736i −0.109852 0.109852i
\(112\) 6.61775 + 9.40290i 0.625318 + 0.888491i
\(113\) −11.6929 + 11.6929i −1.09998 + 1.09998i −0.105567 + 0.994412i \(0.533666\pi\)
−0.994412 + 0.105567i \(0.966334\pi\)
\(114\) 1.19557 + 21.6593i 0.111975 + 2.02858i
\(115\) −0.425218 0.636384i −0.0396518 0.0593431i
\(116\) 8.02118 6.74702i 0.744748 0.626445i
\(117\) 0.699923 + 3.51875i 0.0647079 + 0.325309i
\(118\) 1.58397 + 2.10893i 0.145816 + 0.194142i
\(119\) −12.7092 5.26432i −1.16505 0.482580i
\(120\) 3.18751 13.7829i 0.290978 1.25820i
\(121\) 8.68876 3.59900i 0.789888 0.327182i
\(122\) −4.75123 + 8.03691i −0.430156 + 0.727628i
\(123\) −10.7730 + 16.1229i −0.971366 + 1.45375i
\(124\) 12.5079 15.6229i 1.12324 1.40298i
\(125\) 11.7687 + 2.34095i 1.05263 + 0.209381i
\(126\) 8.40144 23.9364i 0.748459 2.13243i
\(127\) −21.9517 −1.94790 −0.973949 0.226767i \(-0.927185\pi\)
−0.973949 + 0.226767i \(0.927185\pi\)
\(128\) −7.94623 8.05341i −0.702354 0.711828i
\(129\) −11.7973 −1.03870
\(130\) 0.443060 1.26232i 0.0388590 0.110713i
\(131\) −7.05871 1.40406i −0.616722 0.122674i −0.123164 0.992386i \(-0.539304\pi\)
−0.493558 + 0.869713i \(0.664304\pi\)
\(132\) −4.79920 + 5.99444i −0.417717 + 0.521749i
\(133\) 8.05858 12.0605i 0.698768 1.04578i
\(134\) 4.41730 7.47207i 0.381597 0.645488i
\(135\) −14.9727 + 6.20189i −1.28864 + 0.533774i
\(136\) 13.1875 + 3.04982i 1.13082 + 0.261520i
\(137\) 10.2318 + 4.23815i 0.874161 + 0.362089i 0.774229 0.632905i \(-0.218138\pi\)
0.0999315 + 0.994994i \(0.468138\pi\)
\(138\) 1.20092 + 1.59892i 0.102229 + 0.136109i
\(139\) −0.752410 3.78262i −0.0638186 0.320838i 0.935668 0.352882i \(-0.114798\pi\)
−0.999486 + 0.0320443i \(0.989798\pi\)
\(140\) −7.23907 + 6.08916i −0.611813 + 0.514628i
\(141\) 14.3081 + 21.4136i 1.20496 + 1.80335i
\(142\) 0.354676 + 6.42543i 0.0297638 + 0.539210i
\(143\) −0.513484 + 0.513484i −0.0429397 + 0.0429397i
\(144\) −4.27528 + 24.5921i −0.356273 + 2.04934i
\(145\) 6.09741 + 6.09741i 0.506362 + 0.506362i
\(146\) −0.930601 + 1.03934i −0.0770171 + 0.0860163i
\(147\) −3.19239 + 2.13309i −0.263304 + 0.175934i
\(148\) −0.325064 1.02666i −0.0267201 0.0843912i
\(149\) 21.8201 4.34028i 1.78757 0.355569i 0.813455 0.581628i \(-0.197584\pi\)
0.974114 + 0.226059i \(0.0725841\pi\)
\(150\) −9.75803 1.38713i −0.796740 0.113259i
\(151\) 2.99065 7.22006i 0.243375 0.587560i −0.754239 0.656600i \(-0.771994\pi\)
0.997614 + 0.0690406i \(0.0219938\pi\)
\(152\) −5.86681 + 13.0107i −0.475861 + 1.05531i
\(153\) −11.4281 27.5898i −0.923904 2.23050i
\(154\) 4.97316 1.27776i 0.400748 0.102965i
\(155\) 13.6898 + 9.14722i 1.09959 + 0.734723i
\(156\) −0.974052 + 3.35684i −0.0779865 + 0.268762i
\(157\) −4.09955 + 20.6098i −0.327180 + 1.64484i 0.370790 + 0.928717i \(0.379087\pi\)
−0.697970 + 0.716127i \(0.745913\pi\)
\(158\) −0.132036 0.274849i −0.0105042 0.0218658i
\(159\) 12.6283i 1.00149i
\(160\) 6.03902 7.08261i 0.477427 0.559930i
\(161\) 1.33714i 0.105381i
\(162\) 14.3024 6.87083i 1.12370 0.539824i
\(163\) 3.99966 20.1077i 0.313278 1.57495i −0.428015 0.903772i \(-0.640787\pi\)
0.741293 0.671182i \(-0.234213\pi\)
\(164\) −11.1780 + 6.14994i −0.872851 + 0.480229i
\(165\) −5.25270 3.50974i −0.408922 0.273233i
\(166\) 2.18601 + 8.50812i 0.169667 + 0.660359i
\(167\) 5.57052 + 13.4484i 0.431060 + 1.04067i 0.978946 + 0.204118i \(0.0654326\pi\)
−0.547886 + 0.836553i \(0.684567\pi\)
\(168\) 18.0079 16.9274i 1.38934 1.30597i
\(169\) 4.84839 11.7051i 0.372953 0.900389i
\(170\) −1.56720 + 11.0248i −0.120199 + 0.845562i
\(171\) 30.8833 6.14307i 2.36170 0.469772i
\(172\) −6.88925 3.57579i −0.525301 0.272652i
\(173\) −15.4616 + 10.3311i −1.17552 + 0.785459i −0.980727 0.195384i \(-0.937405\pi\)
−0.194796 + 0.980844i \(0.562405\pi\)
\(174\) −16.7845 15.0285i −1.27243 1.13930i
\(175\) 4.66021 + 4.66021i 0.352279 + 0.352279i
\(176\) −4.61951 + 2.04591i −0.348208 + 0.154216i
\(177\) 4.00874 4.00874i 0.301315 0.301315i
\(178\) 5.48854 0.302961i 0.411384 0.0227079i
\(179\) −5.99376 8.97030i −0.447995 0.670472i 0.536896 0.843648i \(-0.319597\pi\)
−0.984891 + 0.173177i \(0.944597\pi\)
\(180\) −20.4591 1.76515i −1.52493 0.131567i
\(181\) 0.698076 + 3.50946i 0.0518876 + 0.260856i 0.998018 0.0629294i \(-0.0200443\pi\)
−0.946130 + 0.323786i \(0.895044\pi\)
\(182\) 1.86881 1.40362i 0.138525 0.104043i
\(183\) 18.5403 + 7.67963i 1.37054 + 0.567694i
\(184\) 0.216660 + 1.29772i 0.0159724 + 0.0956691i
\(185\) 0.818514 0.339039i 0.0601783 0.0249267i
\(186\) −37.0301 21.8913i −2.71518 1.60515i
\(187\) 3.35814 5.02581i 0.245572 0.367524i
\(188\) 1.86497 + 16.8417i 0.136017 + 1.22831i
\(189\) −27.7691 5.52362i −2.01991 0.401784i
\(190\) −11.0791 3.88864i −0.803761 0.282112i
\(191\) −0.722126 −0.0522512 −0.0261256 0.999659i \(-0.508317\pi\)
−0.0261256 + 0.999659i \(0.508317\pi\)
\(192\) −14.7343 + 19.3462i −1.06335 + 1.39619i
\(193\) −5.30778 −0.382063 −0.191031 0.981584i \(-0.561183\pi\)
−0.191031 + 0.981584i \(0.561183\pi\)
\(194\) −18.3804 6.45131i −1.31963 0.463177i
\(195\) −2.82031 0.560994i −0.201966 0.0401736i
\(196\) −2.51080 + 0.278034i −0.179343 + 0.0198595i
\(197\) 8.28629 12.4013i 0.590373 0.883556i −0.409209 0.912441i \(-0.634195\pi\)
0.999583 + 0.0288843i \(0.00919543\pi\)
\(198\) 9.59531 + 5.67251i 0.681909 + 0.403128i
\(199\) −0.443861 + 0.183853i −0.0314644 + 0.0130330i −0.398360 0.917229i \(-0.630421\pi\)
0.366896 + 0.930262i \(0.380421\pi\)
\(200\) −5.27793 3.76772i −0.373206 0.266418i
\(201\) −17.2372 7.13989i −1.21582 0.503609i
\(202\) 4.54409 3.41297i 0.319721 0.240136i
\(203\) 2.93900 + 14.7753i 0.206277 + 1.03703i
\(204\) 2.50085 28.9863i 0.175094 2.02945i
\(205\) −5.83124 8.72707i −0.407272 0.609525i
\(206\) 11.1487 0.615393i 0.776764 0.0428765i
\(207\) 2.05254 2.05254i 0.142661 0.142661i
\(208\) −1.58628 + 1.66505i −0.109989 + 0.115451i
\(209\) 4.50673 + 4.50673i 0.311737 + 0.311737i
\(210\) 15.1479 + 13.5631i 1.04531 + 0.935943i
\(211\) −12.2014 + 8.15273i −0.839980 + 0.561257i −0.899475 0.436972i \(-0.856051\pi\)
0.0594948 + 0.998229i \(0.481051\pi\)
\(212\) 3.82766 7.37450i 0.262884 0.506483i
\(213\) 13.5664 2.69852i 0.929551 0.184899i
\(214\) −1.09769 + 7.72190i −0.0750365 + 0.527858i
\(215\) 2.44370 5.89962i 0.166659 0.402351i
\(216\) 27.8455 + 0.861281i 1.89465 + 0.0586028i
\(217\) 11.0076 + 26.5748i 0.747246 + 1.80401i
\(218\) 1.53641 + 5.97982i 0.104059 + 0.405004i
\(219\) 2.49328 + 1.66596i 0.168480 + 0.112575i
\(220\) −2.00360 3.64168i −0.135083 0.245522i
\(221\) 0.536762 2.69848i 0.0361065 0.181520i
\(222\) −2.08646 + 1.00233i −0.140034 + 0.0672718i
\(223\) 20.5439i 1.37572i 0.725843 + 0.687860i \(0.241450\pi\)
−0.725843 + 0.687860i \(0.758550\pi\)
\(224\) 15.6468 4.42679i 1.04544 0.295777i
\(225\) 14.3071i 0.953804i
\(226\) 10.1266 + 21.0796i 0.673610 + 1.40220i
\(227\) 3.83215 19.2655i 0.254348 1.27870i −0.616582 0.787290i \(-0.711483\pi\)
0.870931 0.491406i \(-0.163517\pi\)
\(228\) 29.4623 + 8.54903i 1.95119 + 0.566174i
\(229\) −18.1422 12.1223i −1.19887 0.801061i −0.214425 0.976740i \(-0.568788\pi\)
−0.984447 + 0.175680i \(0.943788\pi\)
\(230\) −1.04835 + 0.269355i −0.0691261 + 0.0177607i
\(231\) −4.22357 10.1966i −0.277891 0.670887i
\(232\) −5.24644 13.8636i −0.344446 0.910187i
\(233\) −1.49754 + 3.61539i −0.0981074 + 0.236852i −0.965312 0.261100i \(-0.915915\pi\)
0.867204 + 0.497953i \(0.165915\pi\)
\(234\) 5.02326 + 0.714070i 0.328381 + 0.0466802i
\(235\) −13.6724 + 2.71960i −0.891887 + 0.177407i
\(236\) 3.55604 1.12592i 0.231478 0.0732910i
\(237\) −0.544950 + 0.364124i −0.0353983 + 0.0236524i
\(238\) −12.9772 + 14.4936i −0.841190 + 0.939481i
\(239\) 4.87803 + 4.87803i 0.315534 + 0.315534i 0.847049 0.531515i \(-0.178377\pi\)
−0.531515 + 0.847049i \(0.678377\pi\)
\(240\) −16.8990 10.7088i −1.09083 0.691250i
\(241\) 1.70539 1.70539i 0.109854 0.109854i −0.650043 0.759897i \(-0.725249\pi\)
0.759897 + 0.650043i \(0.225249\pi\)
\(242\) −0.733039 13.2800i −0.0471215 0.853669i
\(243\) −2.53170 3.78895i −0.162409 0.243062i
\(244\) 8.49920 + 10.1042i 0.544106 + 0.646858i
\(245\) −0.405444 2.03831i −0.0259029 0.130223i
\(246\) 16.4688 + 21.9269i 1.05001 + 1.39801i
\(247\) 2.68027 + 1.11020i 0.170541 + 0.0706405i
\(248\) −14.9891 24.0077i −0.951808 1.52449i
\(249\) 17.4444 7.22572i 1.10550 0.457912i
\(250\) 8.63581 14.6079i 0.546177 0.923882i
\(251\) −0.380597 + 0.569604i −0.0240231 + 0.0359531i −0.843287 0.537464i \(-0.819382\pi\)
0.819264 + 0.573417i \(0.194382\pi\)
\(252\) −28.0060 22.4218i −1.76421 1.41244i
\(253\) 0.576245 + 0.114622i 0.0362282 + 0.00720625i
\(254\) −10.2813 + 29.2925i −0.645109 + 1.83797i
\(255\) 23.9354 1.49889
\(256\) −14.4682 + 6.83157i −0.904264 + 0.426973i
\(257\) 24.3404 1.51831 0.759156 0.650908i \(-0.225612\pi\)
0.759156 + 0.650908i \(0.225612\pi\)
\(258\) −5.52542 + 15.7424i −0.343997 + 0.980079i
\(259\) 1.51806 + 0.301960i 0.0943275 + 0.0187629i
\(260\) −1.47693 1.18244i −0.0915953 0.0733321i
\(261\) −18.1691 + 27.1919i −1.12464 + 1.68314i
\(262\) −5.17963 + 8.76157i −0.319998 + 0.541291i
\(263\) 9.60085 3.97680i 0.592014 0.245220i −0.0665030 0.997786i \(-0.521184\pi\)
0.658517 + 0.752566i \(0.271184\pi\)
\(264\) 5.75124 + 9.21165i 0.353964 + 0.566938i
\(265\) 6.31516 + 2.61583i 0.387937 + 0.160689i
\(266\) −12.3193 16.4021i −0.755344 1.00568i
\(267\) −2.30505 11.5883i −0.141067 0.709190i
\(268\) −7.90186 9.39411i −0.482683 0.573836i
\(269\) −17.3303 25.9367i −1.05665 1.58139i −0.785513 0.618845i \(-0.787601\pi\)
−0.271136 0.962541i \(-0.587399\pi\)
\(270\) 1.26319 + 22.8844i 0.0768754 + 1.39270i
\(271\) 11.8443 11.8443i 0.719491 0.719491i −0.249010 0.968501i \(-0.580105\pi\)
0.968501 + 0.249010i \(0.0801053\pi\)
\(272\) 10.2462 16.1691i 0.621269 0.980394i
\(273\) −3.55231 3.55231i −0.214996 0.214996i
\(274\) 10.4476 11.6684i 0.631162 0.704912i
\(275\) −2.40782 + 1.60885i −0.145197 + 0.0970176i
\(276\) 2.69607 0.853635i 0.162285 0.0513828i
\(277\) −25.5130 + 5.07485i −1.53293 + 0.304918i −0.888187 0.459483i \(-0.848035\pi\)
−0.644741 + 0.764401i \(0.723035\pi\)
\(278\) −5.39995 0.767617i −0.323867 0.0460386i
\(279\) −23.8959 + 57.6898i −1.43061 + 3.45380i
\(280\) 4.73489 + 12.5118i 0.282964 + 0.747722i
\(281\) −9.37710 22.6383i −0.559391 1.35049i −0.910249 0.414061i \(-0.864110\pi\)
0.350858 0.936429i \(-0.385890\pi\)
\(282\) 35.2759 9.06351i 2.10065 0.539724i
\(283\) −19.3155 12.9062i −1.14819 0.767195i −0.172210 0.985060i \(-0.555091\pi\)
−0.975979 + 0.217865i \(0.930091\pi\)
\(284\) 8.74024 + 2.53615i 0.518638 + 0.150493i
\(285\) −4.92372 + 24.7532i −0.291656 + 1.46625i
\(286\) 0.444699 + 0.925692i 0.0262956 + 0.0547373i
\(287\) 18.3369i 1.08239i
\(288\) 30.8134 + 17.2230i 1.81570 + 1.01487i
\(289\) 5.90150i 0.347147i
\(290\) 10.9922 5.28061i 0.645484 0.310088i
\(291\) −8.16852 + 41.0659i −0.478847 + 2.40733i
\(292\) 0.951041 + 1.72859i 0.0556555 + 0.101158i
\(293\) 23.5455 + 15.7326i 1.37554 + 0.919109i 0.999970 0.00768446i \(-0.00244606\pi\)
0.375573 + 0.926793i \(0.377446\pi\)
\(294\) 1.35121 + 5.25900i 0.0788040 + 0.306711i
\(295\) 1.17433 + 2.83507i 0.0683719 + 0.165064i
\(296\) −1.52223 0.0470838i −0.0884779 0.00273669i
\(297\) 4.76086 11.4937i 0.276253 0.666934i
\(298\) 4.42800 31.1496i 0.256507 1.80445i
\(299\) 0.262297 0.0521741i 0.0151690 0.00301731i
\(300\) −6.42129 + 12.3715i −0.370733 + 0.714268i
\(301\) 9.27596 6.19800i 0.534657 0.357247i
\(302\) −8.23377 7.37234i −0.473800 0.424230i
\(303\) −8.63761 8.63761i −0.496218 0.496218i
\(304\) 14.6138 + 13.9224i 0.838158 + 0.798507i
\(305\) −7.68088 + 7.68088i −0.439806 + 0.439806i
\(306\) −42.1684 + 2.32765i −2.41061 + 0.133063i
\(307\) −6.01712 9.00525i −0.343415 0.513957i 0.619054 0.785348i \(-0.287516\pi\)
−0.962469 + 0.271392i \(0.912516\pi\)
\(308\) 0.624184 7.23466i 0.0355662 0.412233i
\(309\) −4.68215 23.5388i −0.266358 1.33907i
\(310\) 18.6179 13.9835i 1.05742 0.794210i
\(311\) −6.91332 2.86359i −0.392018 0.162379i 0.177963 0.984037i \(-0.443049\pi\)
−0.569981 + 0.821658i \(0.693049\pi\)
\(312\) 4.02318 + 2.87200i 0.227768 + 0.162595i
\(313\) −20.9463 + 8.67625i −1.18396 + 0.490411i −0.885783 0.464101i \(-0.846378\pi\)
−0.298174 + 0.954511i \(0.596378\pi\)
\(314\) 25.5818 + 15.1233i 1.44366 + 0.853459i
\(315\) 16.3975 24.5406i 0.923894 1.38271i
\(316\) −0.428600 + 0.0474611i −0.0241106 + 0.00266989i
\(317\) −12.9479 2.57551i −0.727229 0.144655i −0.182427 0.983219i \(-0.558395\pi\)
−0.544802 + 0.838565i \(0.683395\pi\)
\(318\) −16.8512 5.91460i −0.944969 0.331674i
\(319\) −6.61944 −0.370617
\(320\) −6.62262 11.3757i −0.370216 0.635923i
\(321\) 16.7647 0.935712
\(322\) −1.78428 0.626265i −0.0994343 0.0349004i
\(323\) −23.6840 4.71104i −1.31781 0.262129i
\(324\) −2.46975 22.3033i −0.137209 1.23907i
\(325\) −0.732323 + 1.09600i −0.0406220 + 0.0607951i
\(326\) −24.9585 14.7548i −1.38232 0.817195i
\(327\) 12.2606 5.07850i 0.678012 0.280842i
\(328\) 2.97117 + 17.7963i 0.164056 + 0.982637i
\(329\) −22.5003 9.31994i −1.24048 0.513825i
\(330\) −7.14359 + 5.36540i −0.393242 + 0.295356i
\(331\) 0.994900 + 5.00170i 0.0546846 + 0.274918i 0.998447 0.0557056i \(-0.0177408\pi\)
−0.943763 + 0.330624i \(0.892741\pi\)
\(332\) 12.3771 + 1.06786i 0.679283 + 0.0586064i
\(333\) 1.86674 + 2.79377i 0.102297 + 0.153098i
\(334\) 20.5547 1.13459i 1.12470 0.0620822i
\(335\) 7.14106 7.14106i 0.390158 0.390158i
\(336\) −14.1537 31.9580i −0.772149 1.74345i
\(337\) −9.51763 9.51763i −0.518459 0.518459i 0.398646 0.917105i \(-0.369480\pi\)
−0.917105 + 0.398646i \(0.869480\pi\)
\(338\) −13.3485 11.9519i −0.726061 0.650099i
\(339\) 41.7952 27.9267i 2.27000 1.51677i
\(340\) 13.9775 + 7.25487i 0.758036 + 0.393451i
\(341\) −12.3961 + 2.46574i −0.671286 + 0.133527i
\(342\) 6.26723 44.0880i 0.338893 2.38401i
\(343\) −6.31088 + 15.2358i −0.340755 + 0.822656i
\(344\) −7.99822 + 7.51829i −0.431235 + 0.405359i
\(345\) 0.890336 + 2.14946i 0.0479341 + 0.115723i
\(346\) 6.54425 + 25.4707i 0.351821 + 1.36931i
\(347\) 24.8873 + 16.6292i 1.33602 + 0.892701i 0.998812 0.0487284i \(-0.0155169\pi\)
0.337210 + 0.941430i \(0.390517\pi\)
\(348\) −27.9153 + 15.3585i −1.49642 + 0.823305i
\(349\) 2.77238 13.9377i 0.148402 0.746067i −0.832874 0.553462i \(-0.813306\pi\)
0.981276 0.192605i \(-0.0616936\pi\)
\(350\) 8.40128 4.03594i 0.449067 0.215730i
\(351\) 5.66280i 0.302258i
\(352\) 0.566468 + 7.12252i 0.0301928 + 0.379632i
\(353\) 22.9803i 1.22312i 0.791199 + 0.611558i \(0.209457\pi\)
−0.791199 + 0.611558i \(0.790543\pi\)
\(354\) −3.47174 7.22683i −0.184521 0.384102i
\(355\) −1.46066 + 7.34326i −0.0775240 + 0.389740i
\(356\) 2.16635 7.46584i 0.114817 0.395689i
\(357\) 34.7689 + 23.2318i 1.84016 + 1.22956i
\(358\) −14.7773 + 3.79676i −0.781003 + 0.200665i
\(359\) 2.63107 + 6.35196i 0.138862 + 0.335244i 0.977978 0.208710i \(-0.0669266\pi\)
−0.839115 + 0.543954i \(0.816927\pi\)
\(360\) −11.9377 + 26.4741i −0.629173 + 1.39531i
\(361\) 2.47302 5.97039i 0.130159 0.314231i
\(362\) 5.01000 + 0.712185i 0.263320 + 0.0374316i
\(363\) −28.0387 + 5.57725i −1.47165 + 0.292730i
\(364\) −0.997722 3.15115i −0.0522948 0.165165i
\(365\) −1.34958 + 0.901757i −0.0706400 + 0.0472001i
\(366\) 18.9313 21.1434i 0.989554 1.10518i
\(367\) −2.41091 2.41091i −0.125848 0.125848i 0.641377 0.767226i \(-0.278363\pi\)
−0.767226 + 0.641377i \(0.778363\pi\)
\(368\) 1.83316 + 0.318691i 0.0955600 + 0.0166129i
\(369\) 28.1476 28.1476i 1.46530 1.46530i
\(370\) −0.0690550 1.25102i −0.00359000 0.0650375i
\(371\) 6.63456 + 9.92931i 0.344449 + 0.515504i
\(372\) −46.5554 + 39.1601i −2.41378 + 2.03036i
\(373\) 2.78301 + 13.9911i 0.144099 + 0.724433i 0.983498 + 0.180918i \(0.0579068\pi\)
−0.839400 + 0.543515i \(0.817093\pi\)
\(374\) −5.13364 6.83502i −0.265454 0.353431i
\(375\) −33.6987 13.9585i −1.74019 0.720812i
\(376\) 23.3471 + 5.39940i 1.20404 + 0.278453i
\(377\) −2.78370 + 1.15305i −0.143368 + 0.0593849i
\(378\) −20.3768 + 34.4682i −1.04807 + 1.77285i
\(379\) 14.2902 21.3867i 0.734036 1.09856i −0.257187 0.966362i \(-0.582796\pi\)
0.991223 0.132201i \(-0.0422044\pi\)
\(380\) −10.3780 + 12.9627i −0.532382 + 0.664972i
\(381\) 65.4461 + 13.0180i 3.35290 + 0.666934i
\(382\) −0.338217 + 0.963608i −0.0173047 + 0.0493025i
\(383\) 21.5847 1.10293 0.551463 0.834199i \(-0.314070\pi\)
0.551463 + 0.834199i \(0.314070\pi\)
\(384\) 18.9147 + 28.7225i 0.965237 + 1.46574i
\(385\) 5.97401 0.304464
\(386\) −2.48597 + 7.08273i −0.126532 + 0.360502i
\(387\) 23.7529 + 4.72474i 1.20743 + 0.240172i
\(388\) −17.2173 + 21.5053i −0.874077 + 1.09177i
\(389\) 3.94394 5.90253i 0.199966 0.299270i −0.717911 0.696135i \(-0.754902\pi\)
0.917877 + 0.396864i \(0.129902\pi\)
\(390\) −2.06952 + 3.50068i −0.104794 + 0.177264i
\(391\) −2.05662 + 0.851878i −0.104007 + 0.0430813i
\(392\) −0.804954 + 3.48064i −0.0406563 + 0.175799i
\(393\) 20.2119 + 8.37206i 1.01956 + 0.422315i
\(394\) −12.6674 16.8656i −0.638173 0.849675i
\(395\) −0.0692105 0.347944i −0.00348236 0.0175070i
\(396\) 12.0635 10.1472i 0.606214 0.509918i
\(397\) −7.40790 11.0867i −0.371792 0.556426i 0.597647 0.801759i \(-0.296102\pi\)
−0.969439 + 0.245334i \(0.921102\pi\)
\(398\) 0.0374469 + 0.678400i 0.00187704 + 0.0340051i
\(399\) −31.1778 + 31.1778i −1.56084 + 1.56084i
\(400\) −7.49965 + 5.27824i −0.374983 + 0.263912i
\(401\) −8.50260 8.50260i −0.424600 0.424600i 0.462184 0.886784i \(-0.347066\pi\)
−0.886784 + 0.462184i \(0.847066\pi\)
\(402\) −17.6008 + 19.6574i −0.877846 + 0.980421i
\(403\) −4.78347 + 3.19622i −0.238282 + 0.159215i
\(404\) −2.42601 7.66217i −0.120698 0.381207i
\(405\) 18.1061 3.60154i 0.899702 0.178962i
\(406\) 21.0928 + 2.99840i 1.04682 + 0.148808i
\(407\) −0.260262 + 0.628329i −0.0129007 + 0.0311451i
\(408\) −37.5082 16.9132i −1.85693 0.837330i
\(409\) 10.8420 + 26.1750i 0.536104 + 1.29427i 0.927423 + 0.374014i \(0.122019\pi\)
−0.391320 + 0.920255i \(0.627981\pi\)
\(410\) −14.3766 + 3.69381i −0.710009 + 0.182424i
\(411\) −27.9914 18.7032i −1.38071 0.922563i
\(412\) 4.40043 15.1650i 0.216793 0.747128i
\(413\) −1.04590 + 5.25807i −0.0514651 + 0.258733i
\(414\) −1.77759 3.70025i −0.0873636 0.181857i
\(415\) 10.2204i 0.501699i
\(416\) 1.47890 + 2.89659i 0.0725089 + 0.142017i
\(417\) 11.7236i 0.574106i
\(418\) 8.12459 3.90302i 0.397387 0.190903i
\(419\) −4.06419 + 20.4320i −0.198549 + 0.998171i 0.745032 + 0.667028i \(0.232434\pi\)
−0.943581 + 0.331142i \(0.892566\pi\)
\(420\) 25.1934 13.8610i 1.22931 0.676348i
\(421\) −18.4939 12.3572i −0.901337 0.602254i 0.0162157 0.999869i \(-0.494838\pi\)
−0.917553 + 0.397614i \(0.869838\pi\)
\(422\) 5.16436 + 20.1001i 0.251397 + 0.978456i
\(423\) −20.2322 48.8449i −0.983723 2.37492i
\(424\) −8.04784 8.56158i −0.390838 0.415787i
\(425\) 4.19876 10.1367i 0.203670 0.491703i
\(426\) 2.75306 19.3669i 0.133386 0.938329i
\(427\) −18.6125 + 3.70225i −0.900720 + 0.179164i
\(428\) 9.79002 + 5.08141i 0.473219 + 0.245619i
\(429\) 1.83540 1.22637i 0.0886137 0.0592098i
\(430\) −6.72795 6.02405i −0.324450 0.290505i
\(431\) 9.16945 + 9.16945i 0.441677 + 0.441677i 0.892575 0.450898i \(-0.148896\pi\)
−0.450898 + 0.892575i \(0.648896\pi\)
\(432\) 14.1911 36.7538i 0.682769 1.76832i
\(433\) 9.06306 9.06306i 0.435543 0.435543i −0.454966 0.890509i \(-0.650349\pi\)
0.890509 + 0.454966i \(0.150349\pi\)
\(434\) 40.6171 2.24201i 1.94968 0.107620i
\(435\) −14.5627 21.7946i −0.698226 1.04497i
\(436\) 8.69909 + 0.750530i 0.416611 + 0.0359439i
\(437\) −0.457921 2.30212i −0.0219053 0.110125i
\(438\) 3.39082 2.54678i 0.162020 0.121690i
\(439\) 37.3964 + 15.4901i 1.78483 + 0.739301i 0.991436 + 0.130594i \(0.0416884\pi\)
0.793395 + 0.608707i \(0.208312\pi\)
\(440\) −5.79789 + 0.967984i −0.276404 + 0.0461468i
\(441\) 7.28190 3.01626i 0.346757 0.143631i
\(442\) −3.34947 1.98013i −0.159318 0.0941850i
\(443\) −0.953921 + 1.42764i −0.0453222 + 0.0678294i −0.853439 0.521193i \(-0.825487\pi\)
0.808117 + 0.589023i \(0.200487\pi\)
\(444\) 0.360291 + 3.25363i 0.0170987 + 0.154411i
\(445\) 6.27255 + 1.24769i 0.297347 + 0.0591460i
\(446\) 27.4139 + 9.62198i 1.29808 + 0.455614i
\(447\) −67.6275 −3.19867
\(448\) 1.42123 22.9525i 0.0671470 1.08440i
\(449\) −24.6119 −1.16151 −0.580754 0.814079i \(-0.697242\pi\)
−0.580754 + 0.814079i \(0.697242\pi\)
\(450\) 19.0914 + 6.70089i 0.899978 + 0.315883i
\(451\) 7.90236 + 1.57188i 0.372108 + 0.0740168i
\(452\) 32.8717 3.64005i 1.54615 0.171214i
\(453\) −13.1979 + 19.7521i −0.620093 + 0.928034i
\(454\) −23.9131 14.1369i −1.12230 0.663476i
\(455\) 2.51227 1.04062i 0.117777 0.0487849i
\(456\) 25.2069 35.3105i 1.18042 1.65357i
\(457\) 0.962960 + 0.398871i 0.0450454 + 0.0186584i 0.405092 0.914276i \(-0.367239\pi\)
−0.360047 + 0.932934i \(0.617239\pi\)
\(458\) −24.6731 + 18.5315i −1.15290 + 0.865919i
\(459\) 9.19571 + 46.2300i 0.429219 + 2.15783i
\(460\) −0.131579 + 1.52508i −0.00613491 + 0.0711072i
\(461\) −7.72794 11.5657i −0.359926 0.538667i 0.606676 0.794949i \(-0.292502\pi\)
−0.966602 + 0.256282i \(0.917502\pi\)
\(462\) −15.5846 + 0.860250i −0.725059 + 0.0400224i
\(463\) 8.29596 8.29596i 0.385546 0.385546i −0.487549 0.873095i \(-0.662109\pi\)
0.873095 + 0.487549i \(0.162109\pi\)
\(464\) −20.9568 + 0.507716i −0.972896 + 0.0235701i
\(465\) −35.3897 35.3897i −1.64116 1.64116i
\(466\) 4.12300 + 3.69164i 0.190994 + 0.171012i
\(467\) −0.240041 + 0.160391i −0.0111078 + 0.00742199i −0.561112 0.827740i \(-0.689626\pi\)
0.550004 + 0.835162i \(0.314626\pi\)
\(468\) 3.30556 6.36861i 0.152800 0.294389i
\(469\) 17.3043 3.44205i 0.799040 0.158939i
\(470\) −2.77457 + 19.5182i −0.127981 + 0.900309i
\(471\) 24.4445 59.0143i 1.12634 2.71924i
\(472\) 0.163083 5.27253i 0.00750651 0.242688i
\(473\) 1.87590 + 4.52882i 0.0862539 + 0.208235i
\(474\) 0.230655 + 0.897726i 0.0105943 + 0.0412339i
\(475\) 9.61934 + 6.42743i 0.441365 + 0.294911i
\(476\) 13.2623 + 24.1052i 0.607876 + 1.10486i
\(477\) −5.05753 + 25.4259i −0.231568 + 1.16417i
\(478\) 8.79395 4.22458i 0.402226 0.193228i
\(479\) 27.3994i 1.25191i 0.779860 + 0.625954i \(0.215290\pi\)
−0.779860 + 0.625954i \(0.784710\pi\)
\(480\) −22.2047 + 17.5345i −1.01350 + 0.800338i
\(481\) 0.309569i 0.0141151i
\(482\) −1.47694 3.07443i −0.0672730 0.140036i
\(483\) −0.792964 + 3.98650i −0.0360811 + 0.181392i
\(484\) −18.0642 5.24167i −0.821099 0.238258i
\(485\) −18.8443 12.5913i −0.855675 0.571744i
\(486\) −6.24175 + 1.60371i −0.283132 + 0.0727456i
\(487\) −11.7477 28.3614i −0.532338 1.28518i −0.929971 0.367633i \(-0.880168\pi\)
0.397633 0.917544i \(-0.369832\pi\)
\(488\) 17.4639 6.60893i 0.790552 0.299172i
\(489\) −23.8489 + 57.5764i −1.07849 + 2.60369i
\(490\) −2.90982 0.413639i −0.131452 0.0186863i
\(491\) 1.43618 0.285675i 0.0648141 0.0128923i −0.162577 0.986696i \(-0.551981\pi\)
0.227391 + 0.973804i \(0.426981\pi\)
\(492\) 36.9727 11.7063i 1.66686 0.527763i
\(493\) 20.8531 13.9336i 0.939178 0.627539i
\(494\) 2.73680 3.05658i 0.123134 0.137522i
\(495\) 9.17024 + 9.17024i 0.412172 + 0.412172i
\(496\) −39.0564 + 8.75720i −1.75368 + 0.393210i
\(497\) −9.24919 + 9.24919i −0.414883 + 0.414883i
\(498\) −1.47172 26.6622i −0.0659495 1.19476i
\(499\) 8.33594 + 12.4756i 0.373168 + 0.558485i 0.969760 0.244059i \(-0.0784791\pi\)
−0.596592 + 0.802544i \(0.703479\pi\)
\(500\) −15.4481 18.3654i −0.690861 0.821328i
\(501\) −8.63244 43.3982i −0.385669 1.93889i
\(502\) 0.581825 + 0.774652i 0.0259681 + 0.0345744i
\(503\) −9.56425 3.96164i −0.426449 0.176641i 0.159128 0.987258i \(-0.449132\pi\)
−0.585577 + 0.810617i \(0.699132\pi\)
\(504\) −43.0367 + 26.8698i −1.91701 + 1.19687i
\(505\) 6.10871 2.53031i 0.271834 0.112597i
\(506\) 0.422844 0.715260i 0.0187977 0.0317972i
\(507\) −21.3963 + 32.0218i −0.950242 + 1.42214i
\(508\) 34.2726 + 27.4390i 1.52060 + 1.21741i
\(509\) −1.27790 0.254190i −0.0566419 0.0112668i 0.166688 0.986010i \(-0.446693\pi\)
−0.223330 + 0.974743i \(0.571693\pi\)
\(510\) 11.2104 31.9395i 0.496406 1.41430i
\(511\) −2.83566 −0.125442
\(512\) 2.33971 + 22.5061i 0.103402 + 0.994640i
\(513\) −49.7011 −2.19436
\(514\) 11.4001 32.4800i 0.502838 1.43263i
\(515\) 12.7412 + 2.53437i 0.561443 + 0.111678i
\(516\) 18.4188 + 14.7463i 0.810844 + 0.649169i
\(517\) 5.94524 8.89768i 0.261471 0.391320i
\(518\) 1.11394 1.88428i 0.0489436 0.0827904i
\(519\) 52.2233 21.6316i 2.29235 0.949522i
\(520\) −2.26960 + 1.41701i −0.0995284 + 0.0621400i
\(521\) −30.4733 12.6225i −1.33506 0.553001i −0.402967 0.915215i \(-0.632021\pi\)
−0.932095 + 0.362214i \(0.882021\pi\)
\(522\) 27.7753 + 36.9806i 1.21569 + 1.61860i
\(523\) 0.709853 + 3.56867i 0.0310397 + 0.156047i 0.993197 0.116448i \(-0.0371510\pi\)
−0.962157 + 0.272496i \(0.912151\pi\)
\(524\) 9.26554 + 11.0153i 0.404767 + 0.481206i
\(525\) −11.1302 16.6574i −0.485760 0.726991i
\(526\) −0.809988 14.6740i −0.0353172 0.639817i
\(527\) 33.8610 33.8610i 1.47501 1.47501i
\(528\) 14.9857 3.36010i 0.652170 0.146229i
\(529\) 16.1105 + 16.1105i 0.700455 + 0.700455i
\(530\) 6.44835 7.20183i 0.280099 0.312827i
\(531\) −9.67673 + 6.46579i −0.419934 + 0.280591i
\(532\) −27.6569 + 8.75678i −1.19908 + 0.379655i
\(533\) 3.59702 0.715492i 0.155804 0.0309914i
\(534\) −16.5430 2.35164i −0.715887 0.101765i
\(535\) −3.47264 + 8.38370i −0.150135 + 0.362459i
\(536\) −16.2365 + 6.14444i −0.701309 + 0.265399i
\(537\) 12.5499 + 30.2982i 0.541570 + 1.30747i
\(538\) −42.7269 + 10.9779i −1.84209 + 0.473292i
\(539\) 1.32649 + 0.886330i 0.0571358 + 0.0381769i
\(540\) 31.1287 + 9.03257i 1.33956 + 0.388700i
\(541\) 0.728776 3.66380i 0.0313325 0.157519i −0.961952 0.273220i \(-0.911911\pi\)
0.993284 + 0.115701i \(0.0369113\pi\)
\(542\) −10.2577 21.3525i −0.440605 0.917170i
\(543\) 10.8770i 0.466776i
\(544\) −16.7771 21.2456i −0.719314 0.910898i
\(545\) 7.18326i 0.307697i
\(546\) −6.40399 + 3.07645i −0.274066 + 0.131660i
\(547\) 2.21811 11.1512i 0.0948394 0.476790i −0.903952 0.427635i \(-0.859347\pi\)
0.998791 0.0491555i \(-0.0156530\pi\)
\(548\) −10.6771 19.4063i −0.456102 0.828998i
\(549\) −34.2536 22.8875i −1.46191 0.976815i
\(550\) 1.01913 + 3.96653i 0.0434559 + 0.169134i
\(551\) 10.1200 + 24.4319i 0.431128 + 1.04083i
\(552\) 0.123644 3.99746i 0.00526266 0.170143i
\(553\) 0.237181 0.572605i 0.0100859 0.0243496i
\(554\) −5.17742 + 36.4215i −0.219968 + 1.54740i
\(555\) −2.64135 + 0.525397i −0.112119 + 0.0223019i
\(556\) −3.55344 + 6.84619i −0.150700 + 0.290343i
\(557\) −15.2399 + 10.1830i −0.645734 + 0.431466i −0.834841 0.550491i \(-0.814441\pi\)
0.189107 + 0.981956i \(0.439441\pi\)
\(558\) 65.7897 + 58.9066i 2.78510 + 2.49371i
\(559\) 1.57776 + 1.57776i 0.0667321 + 0.0667321i
\(560\) 18.9134 0.458211i 0.799239 0.0193630i
\(561\) −12.9923 + 12.9923i −0.548536 + 0.548536i
\(562\) −34.6006 + 1.90991i −1.45954 + 0.0805648i
\(563\) 2.21898 + 3.32093i 0.0935187 + 0.139961i 0.875279 0.483619i \(-0.160678\pi\)
−0.781760 + 0.623579i \(0.785678\pi\)
\(564\) 4.42750 51.3173i 0.186431 2.16085i
\(565\) 5.30813 + 26.6858i 0.223315 + 1.12268i
\(566\) −26.2688 + 19.7300i −1.10416 + 0.829312i
\(567\) 29.7969 + 12.3423i 1.25135 + 0.518327i
\(568\) 7.47785 10.4752i 0.313764 0.439529i
\(569\) 27.7449 11.4923i 1.16313 0.481783i 0.284213 0.958761i \(-0.408268\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(570\) 30.7247 + 18.1637i 1.28692 + 0.760794i
\(571\) 17.3752 26.0038i 0.727128 1.08822i −0.265152 0.964207i \(-0.585422\pi\)
0.992280 0.124017i \(-0.0395777\pi\)
\(572\) 1.44353 0.159849i 0.0603569 0.00668363i
\(573\) 2.15292 + 0.428243i 0.0899396 + 0.0178901i
\(574\) −24.4688 8.58831i −1.02131 0.358469i
\(575\) 1.06649 0.0444756
\(576\) 37.4142 33.0510i 1.55893 1.37712i
\(577\) −4.61192 −0.191997 −0.0959984 0.995381i \(-0.530604\pi\)
−0.0959984 + 0.995381i \(0.530604\pi\)
\(578\) 7.87499 + 2.76404i 0.327557 + 0.114969i
\(579\) 15.8244 + 3.14768i 0.657642 + 0.130813i
\(580\) −1.89814 17.1413i −0.0788161 0.711753i
\(581\) −9.91996 + 14.8463i −0.411549 + 0.615927i
\(582\) 50.9727 + 30.1338i 2.11289 + 1.24909i
\(583\) −4.84781 + 2.00803i −0.200776 + 0.0831640i
\(584\) 2.75207 0.459470i 0.113881 0.0190130i
\(585\) 5.45377 + 2.25903i 0.225486 + 0.0933992i
\(586\) 32.0215 24.0507i 1.32280 0.993524i
\(587\) −4.06182 20.4202i −0.167649 0.842831i −0.969459 0.245252i \(-0.921129\pi\)
0.801810 0.597579i \(-0.203871\pi\)
\(588\) 7.65049 + 0.660061i 0.315501 + 0.0272204i
\(589\) 28.0525 + 41.9835i 1.15588 + 1.72990i
\(590\) 4.33314 0.239185i 0.178393 0.00984707i
\(591\) −32.0588 + 32.0588i −1.31872 + 1.31872i
\(592\) −0.775785 + 2.00922i −0.0318846 + 0.0825785i
\(593\) −3.69463 3.69463i −0.151720 0.151720i 0.627166 0.778886i \(-0.284215\pi\)
−0.778886 + 0.627166i \(0.784215\pi\)
\(594\) −13.1075 11.7361i −0.537806 0.481540i
\(595\) −18.8199 + 12.5750i −0.771539 + 0.515526i
\(596\) −39.4923 20.4981i −1.61767 0.839633i
\(597\) 1.43234 0.284911i 0.0586218 0.0116606i
\(598\) 0.0532287 0.374447i 0.00217668 0.0153123i
\(599\) −4.44136 + 10.7224i −0.181469 + 0.438105i −0.988270 0.152719i \(-0.951197\pi\)
0.806801 + 0.590824i \(0.201197\pi\)
\(600\) 13.5011 + 14.3629i 0.551179 + 0.586364i
\(601\) −4.16840 10.0634i −0.170033 0.410495i 0.815776 0.578368i \(-0.196310\pi\)
−0.985809 + 0.167873i \(0.946310\pi\)
\(602\) −3.92613 15.2808i −0.160017 0.622799i
\(603\) 31.8462 + 21.2789i 1.29688 + 0.866546i
\(604\) −13.6941 + 7.53427i −0.557204 + 0.306565i
\(605\) 3.01888 15.1769i 0.122735 0.617030i
\(606\) −15.5716 + 7.48054i −0.632553 + 0.303876i
\(607\) 29.1457i 1.18299i −0.806310 0.591493i \(-0.798539\pi\)
0.806310 0.591493i \(-0.201461\pi\)
\(608\) 25.4227 12.9800i 1.03103 0.526407i
\(609\) 45.7937i 1.85565i
\(610\) 6.65197 + 13.8468i 0.269330 + 0.560642i
\(611\) 0.950281 4.77739i 0.0384443 0.193272i
\(612\) −16.6441 + 57.3599i −0.672796 + 2.31864i
\(613\) −5.29850 3.54035i −0.214005 0.142993i 0.443948 0.896052i \(-0.353577\pi\)
−0.657953 + 0.753059i \(0.728577\pi\)
\(614\) −14.8348 + 3.81155i −0.598686 + 0.153822i
\(615\) 12.2096 + 29.4767i 0.492340 + 1.18862i
\(616\) −9.36163 4.22136i −0.377191 0.170083i
\(617\) 3.88763 9.38556i 0.156510 0.377849i −0.826102 0.563521i \(-0.809446\pi\)
0.982612 + 0.185673i \(0.0594464\pi\)
\(618\) −33.6032 4.77678i −1.35172 0.192150i
\(619\) −3.09719 + 0.616070i −0.124487 + 0.0247620i −0.256940 0.966427i \(-0.582714\pi\)
0.132454 + 0.991189i \(0.457714\pi\)
\(620\) −9.93975 31.3931i −0.399190 1.26078i
\(621\) −3.80951 + 2.54544i −0.152871 + 0.102145i
\(622\) −7.05913 + 7.88397i −0.283045 + 0.316118i
\(623\) 7.90057 + 7.90057i 0.316530 + 0.316530i
\(624\) 5.71671 4.02341i 0.228852 0.161065i
\(625\) 5.85477 5.85477i 0.234191 0.234191i
\(626\) 1.76716 + 32.0145i 0.0706301 + 1.27956i
\(627\) −10.7636 16.1089i −0.429856 0.643326i
\(628\) 32.1622 27.0533i 1.28341 1.07954i
\(629\) −0.502703 2.52726i −0.0200441 0.100768i
\(630\) −25.0671 33.3748i −0.998698 1.32968i
\(631\) −29.9605 12.4100i −1.19271 0.494036i −0.304073 0.952649i \(-0.598347\pi\)
−0.888636 + 0.458613i \(0.848347\pi\)
\(632\) −0.137408 + 0.594155i −0.00546579 + 0.0236342i
\(633\) 41.2117 17.0705i 1.63802 0.678490i
\(634\) −9.50110 + 16.0715i −0.377337 + 0.638282i
\(635\) −20.0666 + 30.0318i −0.796319 + 1.19178i
\(636\) −15.7849 + 19.7162i −0.625914 + 0.781797i
\(637\) 0.712223 + 0.141670i 0.0282193 + 0.00561317i
\(638\) −3.10029 + 8.83301i −0.122742 + 0.349702i
\(639\) −28.3954 −1.12331
\(640\) −18.2816 + 3.50930i −0.722644 + 0.138717i
\(641\) 27.6811 1.09334 0.546668 0.837349i \(-0.315896\pi\)
0.546668 + 0.837349i \(0.315896\pi\)
\(642\) 7.85193 22.3708i 0.309891 0.882907i
\(643\) 42.4514 + 8.44410i 1.67412 + 0.333003i 0.938733 0.344646i \(-0.112001\pi\)
0.735386 + 0.677649i \(0.237001\pi\)
\(644\) −1.67138 + 2.08764i −0.0658617 + 0.0822645i
\(645\) −10.7842 + 16.1397i −0.424629 + 0.635502i
\(646\) −17.3791 + 29.3976i −0.683772 + 1.15663i
\(647\) −35.3075 + 14.6248i −1.38808 + 0.574962i −0.946630 0.322324i \(-0.895536\pi\)
−0.441451 + 0.897285i \(0.645536\pi\)
\(648\) −30.9183 7.15036i −1.21459 0.280893i
\(649\) −2.17633 0.901466i −0.0854285 0.0353856i
\(650\) 1.11951 + 1.49054i 0.0439109 + 0.0584638i
\(651\) −17.0581 85.7570i −0.668560 3.36108i
\(652\) −31.3785 + 26.3941i −1.22888 + 1.03367i
\(653\) 13.3150 + 19.9272i 0.521055 + 0.779813i 0.994908 0.100791i \(-0.0321372\pi\)
−0.473853 + 0.880604i \(0.657137\pi\)
\(654\) −1.03438 18.7392i −0.0404475 0.732759i
\(655\) −8.37343 + 8.37343i −0.327177 + 0.327177i
\(656\) 25.1391 + 4.37037i 0.981516 + 0.170634i
\(657\) −4.35281 4.35281i −0.169819 0.169819i
\(658\) −22.9749 + 25.6594i −0.895654 + 1.00031i
\(659\) 17.2984 11.5584i 0.673852 0.450253i −0.170988 0.985273i \(-0.554696\pi\)
0.844839 + 0.535020i \(0.179696\pi\)
\(660\) 3.81383 + 12.0454i 0.148453 + 0.468866i
\(661\) 14.9381 2.97137i 0.581025 0.115573i 0.104177 0.994559i \(-0.466779\pi\)
0.476848 + 0.878986i \(0.341779\pi\)
\(662\) 7.14027 + 1.01501i 0.277514 + 0.0394494i
\(663\) −3.20057 + 7.72685i −0.124300 + 0.300086i
\(664\) 7.22194 16.0160i 0.280266 0.621540i
\(665\) −9.13327 22.0497i −0.354173 0.855049i
\(666\) 4.60233 1.18249i 0.178337 0.0458204i
\(667\) 2.02696 + 1.35437i 0.0784842 + 0.0524415i
\(668\) 8.11303 27.9597i 0.313902 1.08179i
\(669\) 12.1832 61.2489i 0.471028 2.36802i
\(670\) −6.18446 12.8737i −0.238927 0.497353i
\(671\) 8.33848i 0.321903i
\(672\) −49.2740 + 3.91886i −1.90079 + 0.151173i
\(673\) 33.8371i 1.30432i −0.758080 0.652162i \(-0.773862\pi\)
0.758080 0.652162i \(-0.226138\pi\)
\(674\) −17.1581 + 8.24268i −0.660905 + 0.317496i
\(675\) 4.40558 22.1483i 0.169571 0.852490i
\(676\) −22.2006 + 12.2144i −0.853870 + 0.469786i
\(677\) 28.0419 + 18.7370i 1.07774 + 0.720121i 0.961970 0.273155i \(-0.0880672\pi\)
0.115768 + 0.993276i \(0.463067\pi\)
\(678\) −17.6902 68.8515i −0.679387 2.64423i
\(679\) −15.1522 36.5807i −0.581489 1.40384i
\(680\) 16.2275 15.2537i 0.622295 0.584954i
\(681\) −22.8501 + 55.1649i −0.875616 + 2.11392i
\(682\) −2.51557 + 17.6963i −0.0963263 + 0.677625i
\(683\) 14.0115 2.78707i 0.536137 0.106644i 0.0804066 0.996762i \(-0.474378\pi\)
0.455730 + 0.890118i \(0.349378\pi\)
\(684\) −55.8959 29.0122i −2.13723 1.10931i
\(685\) 15.1513 10.1238i 0.578901 0.386809i
\(686\) 17.3750 + 15.5571i 0.663379 + 0.593975i
\(687\) 46.8998 + 46.8998i 1.78934 + 1.78934i
\(688\) 6.28637 + 14.1942i 0.239666 + 0.541147i
\(689\) −1.68889 + 1.68889i −0.0643415 + 0.0643415i
\(690\) 3.28525 0.181342i 0.125067 0.00690358i
\(691\) 10.9236 + 16.3483i 0.415552 + 0.621918i 0.978909 0.204296i \(-0.0654904\pi\)
−0.563357 + 0.826214i \(0.690490\pi\)
\(692\) 37.0533 + 3.19685i 1.40856 + 0.121526i
\(693\) 4.42013 + 22.2215i 0.167907 + 0.844125i
\(694\) 33.8463 25.4213i 1.28479 0.964979i
\(695\) −5.86275 2.42843i −0.222387 0.0921156i
\(696\) 7.42006 + 44.4436i 0.281257 + 1.68463i
\(697\) −28.2035 + 11.6823i −1.06828 + 0.442497i
\(698\) −17.3000 10.2274i −0.654816 0.387111i
\(699\) 6.60877 9.89072i 0.249967 0.374101i
\(700\) −1.45074 13.1010i −0.0548328 0.495171i
\(701\) 11.0341 + 2.19482i 0.416753 + 0.0828974i 0.399013 0.916945i \(-0.369353\pi\)
0.0177402 + 0.999843i \(0.494353\pi\)
\(702\) −7.55647 2.65224i −0.285201 0.100102i
\(703\) 2.71702 0.102474
\(704\) 9.76964 + 2.58002i 0.368207 + 0.0972383i
\(705\) 42.3751 1.59594
\(706\) 30.6650 + 10.7631i 1.15409 + 0.405075i
\(707\) 11.3295 + 2.25358i 0.426091 + 0.0847548i
\(708\) −11.2695 + 1.24793i −0.423536 + 0.0469003i
\(709\) −23.4418 + 35.0831i −0.880374 + 1.31757i 0.0671017 + 0.997746i \(0.478625\pi\)
−0.947476 + 0.319827i \(0.896375\pi\)
\(710\) 9.11476 + 5.38842i 0.342071 + 0.202224i
\(711\) 1.24304 0.514884i 0.0466176 0.0193097i
\(712\) −8.94781 6.38751i −0.335333 0.239382i
\(713\) 4.30035 + 1.78127i 0.161050 + 0.0667089i
\(714\) 47.2851 35.5148i 1.76960 1.32911i
\(715\) 0.233101 + 1.17188i 0.00871749 + 0.0438258i
\(716\) −1.85470 + 21.4971i −0.0693135 + 0.803385i
\(717\) −11.6504 17.4360i −0.435091 0.651160i
\(718\) 9.70838 0.535892i 0.362314 0.0199993i
\(719\) −9.10621 + 9.10621i −0.339604 + 0.339604i −0.856218 0.516614i \(-0.827192\pi\)
0.516614 + 0.856218i \(0.327192\pi\)
\(720\) 29.7359 + 28.3292i 1.10819 + 1.05577i
\(721\) 16.0481 + 16.0481i 0.597663 + 0.597663i
\(722\) −6.80865 6.09631i −0.253392 0.226881i
\(723\) −6.09576 + 4.07305i −0.226704 + 0.151479i
\(724\) 3.29684 6.35181i 0.122526 0.236063i
\(725\) −11.7847 + 2.34411i −0.437671 + 0.0870582i
\(726\) −5.68997 + 40.0272i −0.211175 + 1.48555i
\(727\) 8.28934 20.0122i 0.307435 0.742213i −0.692352 0.721560i \(-0.743426\pi\)
0.999787 0.0206529i \(-0.00657449\pi\)
\(728\) −4.67221 0.144515i −0.173163 0.00535607i
\(729\) −7.57994 18.2996i −0.280739 0.677763i
\(730\) 0.571219 + 2.22323i 0.0211418 + 0.0822854i
\(731\) −15.4426 10.3184i −0.571165 0.381640i
\(732\) −19.3471 35.1648i −0.715090 1.29973i
\(733\) −1.86746 + 9.38837i −0.0689763 + 0.346767i −0.999826 0.0186340i \(-0.994068\pi\)
0.930850 + 0.365401i \(0.119068\pi\)
\(734\) −4.34630 + 2.08795i −0.160425 + 0.0770676i
\(735\) 6.31738i 0.233020i
\(736\) 1.28384 2.29691i 0.0473232 0.0846653i
\(737\) 7.75244i 0.285565i
\(738\) −24.3770 50.7435i −0.897329 1.86789i
\(739\) −3.72209 + 18.7122i −0.136919 + 0.688340i 0.849956 + 0.526854i \(0.176629\pi\)
−0.986875 + 0.161486i \(0.948371\pi\)
\(740\) −1.70171 0.493784i −0.0625562 0.0181519i
\(741\) −7.33247 4.89940i −0.269365 0.179984i
\(742\) 16.3571 4.20267i 0.600488 0.154285i
\(743\) −2.74886 6.63633i −0.100846 0.243463i 0.865402 0.501079i \(-0.167063\pi\)
−0.966248 + 0.257615i \(0.917063\pi\)
\(744\) 30.4507 + 80.4648i 1.11638 + 2.94998i
\(745\) 14.0084 33.8193i 0.513228 1.23904i
\(746\) 19.9733 + 2.83926i 0.731274 + 0.103953i
\(747\) −38.0168 + 7.56200i −1.39096 + 0.276679i
\(748\) −11.5251 + 3.64909i −0.421399 + 0.133424i
\(749\) −13.1817 + 8.80771i −0.481648 + 0.321827i
\(750\) −34.4094 + 38.4301i −1.25645 + 1.40327i
\(751\) −1.88191 1.88191i −0.0686719 0.0686719i 0.671937 0.740609i \(-0.265463\pi\)
−0.740609 + 0.671937i \(0.765463\pi\)
\(752\) 18.1399 28.6257i 0.661494 1.04387i
\(753\) 1.47249 1.47249i 0.0536606 0.0536606i
\(754\) 0.234850 + 4.25462i 0.00855275 + 0.154944i
\(755\) −7.14383 10.6915i −0.259991 0.389104i
\(756\) 36.4508 + 43.3345i 1.32570 + 1.57606i
\(757\) 7.70412 + 38.7312i 0.280011 + 1.40771i 0.823034 + 0.567992i \(0.192280\pi\)
−0.543023 + 0.839718i \(0.682720\pi\)
\(758\) −21.8456 29.0856i −0.793468 1.05644i
\(759\) −1.65002 0.683463i −0.0598921 0.0248081i
\(760\) 12.4368 + 19.9197i 0.451130 + 0.722565i
\(761\) −7.53878 + 3.12266i −0.273280 + 0.113196i −0.515115 0.857121i \(-0.672251\pi\)
0.241835 + 0.970317i \(0.422251\pi\)
\(762\) 48.0238 81.2344i 1.73972 2.94281i
\(763\) −6.97211 + 10.4345i −0.252407 + 0.377754i
\(764\) 1.12744 + 0.902636i 0.0407892 + 0.0326562i
\(765\) −48.1919 9.58596i −1.74238 0.346581i
\(766\) 10.1095 28.8027i 0.365270 1.04068i
\(767\) −1.07225 −0.0387167
\(768\) 47.1864 11.7873i 1.70269 0.425338i
\(769\) 3.77877 0.136266 0.0681330 0.997676i \(-0.478296\pi\)
0.0681330 + 0.997676i \(0.478296\pi\)
\(770\) 2.79800 7.97175i 0.100833 0.287282i
\(771\) −72.5677 14.4346i −2.61346 0.519850i
\(772\) 8.28690 + 6.63457i 0.298252 + 0.238783i
\(773\) −2.84091 + 4.25173i −0.102181 + 0.152924i −0.879037 0.476754i \(-0.841813\pi\)
0.776856 + 0.629678i \(0.216813\pi\)
\(774\) 17.4297 29.4831i 0.626497 1.05975i
\(775\) −21.1957 + 8.77956i −0.761373 + 0.315371i
\(776\) 20.6328 + 33.0472i 0.740675 + 1.18632i
\(777\) −4.34681 1.80051i −0.155941 0.0645929i
\(778\) −6.02917 8.02734i −0.216156 0.287794i
\(779\) −6.27971 31.5702i −0.224994 1.13112i
\(780\) 3.70204 + 4.40116i 0.132554 + 0.157587i
\(781\) −3.19312 4.77884i −0.114259 0.171000i
\(782\) 0.173509 + 3.14335i 0.00620467 + 0.112406i
\(783\) 36.5002 36.5002i 1.30441 1.30441i
\(784\) 4.26758 + 2.70434i 0.152413 + 0.0965835i
\(785\) 24.4485 + 24.4485i 0.872605 + 0.872605i
\(786\) 20.6382 23.0498i 0.736142 0.822158i
\(787\) −25.7884 + 17.2312i −0.919257 + 0.614228i −0.922596 0.385767i \(-0.873937\pi\)
0.00333965 + 0.999994i \(0.498937\pi\)
\(788\) −28.4384 + 9.00422i −1.01308 + 0.320762i
\(789\) −30.9820 + 6.16271i −1.10299 + 0.219398i
\(790\) −0.496714 0.0706093i −0.0176723 0.00251217i
\(791\) −18.1907 + 43.9162i −0.646786 + 1.56148i
\(792\) −7.89043 20.8502i −0.280374 0.740879i
\(793\) −1.45249 3.50662i −0.0515793 0.124524i
\(794\) −18.2637 + 4.69254i −0.648156 + 0.166532i
\(795\) −17.2765 11.5438i −0.612736 0.409417i
\(796\) 0.922799 + 0.267768i 0.0327077 + 0.00949077i
\(797\) 0.860359 4.32532i 0.0304755 0.153211i −0.962551 0.271100i \(-0.912613\pi\)
0.993027 + 0.117889i \(0.0376127\pi\)
\(798\) 27.0013 + 56.2064i 0.955837 + 1.98968i
\(799\) 40.5448i 1.43437i
\(800\) 3.53076 + 12.4797i 0.124831 + 0.441224i
\(801\) 24.2551i 0.857013i
\(802\) −15.3282 + 7.36362i −0.541258 + 0.260018i
\(803\) 0.243079 1.22204i 0.00857807 0.0431249i
\(804\) 17.9874 + 32.6933i 0.634365 + 1.15300i
\(805\) −1.82932 1.22231i −0.0644751 0.0430809i
\(806\) 2.02465 + 7.88008i 0.0713151 + 0.277564i
\(807\) 36.2868 + 87.6041i 1.27736 + 3.08381i
\(808\) −11.3607 0.351394i −0.399668 0.0123620i
\(809\) −4.29079 + 10.3589i −0.150856 + 0.364199i −0.981184 0.193077i \(-0.938153\pi\)
0.830327 + 0.557276i \(0.188153\pi\)
\(810\) 3.67433 25.8478i 0.129103 0.908198i
\(811\) 3.92167 0.780069i 0.137709 0.0273919i −0.125755 0.992061i \(-0.540135\pi\)
0.263463 + 0.964669i \(0.415135\pi\)
\(812\) 13.8802 26.7420i 0.487098 0.938461i
\(813\) −42.3363 + 28.2882i −1.48480 + 0.992110i
\(814\) 0.716548 + 0.641581i 0.0251150 + 0.0224874i
\(815\) −23.8528 23.8528i −0.835528 0.835528i
\(816\) −40.1365 + 42.1296i −1.40506 + 1.47483i
\(817\) 13.8476 13.8476i 0.484467 0.484467i
\(818\) 40.0060 2.20828i 1.39878 0.0772109i
\(819\) 5.72960 + 8.57495i 0.200208 + 0.299633i
\(820\) −1.80441 + 20.9142i −0.0630129 + 0.730356i
\(821\) −7.39036 37.1538i −0.257925 1.29668i −0.864895 0.501953i \(-0.832615\pi\)
0.606970 0.794725i \(-0.292385\pi\)
\(822\) −38.0678 + 28.5919i −1.32777 + 0.997258i
\(823\) 13.1154 + 5.43259i 0.457175 + 0.189368i 0.599373 0.800470i \(-0.295417\pi\)
−0.142197 + 0.989838i \(0.545417\pi\)
\(824\) −18.1753 12.9747i −0.633167 0.451995i
\(825\) 8.13270 3.36867i 0.283144 0.117282i
\(826\) 6.52654 + 3.85833i 0.227087 + 0.134248i
\(827\) 13.3036 19.9102i 0.462611 0.692347i −0.524674 0.851303i \(-0.675813\pi\)
0.987286 + 0.158956i \(0.0508129\pi\)
\(828\) −5.77019 + 0.638962i −0.200528 + 0.0222055i
\(829\) 12.2166 + 2.43003i 0.424299 + 0.0843983i 0.402621 0.915367i \(-0.368099\pi\)
0.0216779 + 0.999765i \(0.493099\pi\)
\(830\) 13.6381 + 4.78685i 0.473387 + 0.166154i
\(831\) 79.0731 2.74302
\(832\) 4.55788 0.616795i 0.158016 0.0213835i
\(833\) −6.04450 −0.209430
\(834\) 15.6440 + 5.49088i 0.541707 + 0.190134i
\(835\) 23.4908 + 4.67260i 0.812932 + 0.161702i
\(836\) −1.40296 12.6695i −0.0485224 0.438185i
\(837\) 54.7570 81.9497i 1.89268 2.83259i
\(838\) 25.3611 + 14.9929i 0.876085 + 0.517920i
\(839\) −26.8826 + 11.1351i −0.928089 + 0.384427i −0.794953 0.606671i \(-0.792505\pi\)
−0.133136 + 0.991098i \(0.542505\pi\)
\(840\) −6.69657 40.1102i −0.231054 1.38393i
\(841\) 1.41778 + 0.587262i 0.0488888 + 0.0202504i
\(842\) −25.1514 + 18.8907i −0.866774 + 0.651016i
\(843\) 14.5314 + 73.0540i 0.500486 + 2.51612i
\(844\) 29.2404 + 2.52277i 1.00650 + 0.0868374i
\(845\) −11.5815 17.3329i −0.398415 0.596270i
\(846\) −74.6548 + 4.12086i −2.56669 + 0.141678i
\(847\) 19.1161 19.1161i 0.656836 0.656836i
\(848\) −15.1939 + 6.72915i −0.521761 + 0.231080i
\(849\) 49.9329 + 49.9329i 1.71369 + 1.71369i
\(850\) −11.5599 10.3505i −0.396503 0.355019i
\(851\) 0.208255 0.139152i 0.00713889 0.00477006i
\(852\) −24.5539 12.7444i −0.841201 0.436617i
\(853\) 29.6923 5.90616i 1.01664 0.202223i 0.341479 0.939889i \(-0.389072\pi\)
0.675165 + 0.737666i \(0.264072\pi\)
\(854\) −3.77708 + 26.5705i −0.129249 + 0.909225i
\(855\) 19.8270 47.8665i 0.678068 1.63700i
\(856\) 11.3659 10.6839i 0.388480 0.365169i
\(857\) −0.425175 1.02646i −0.0145237 0.0350633i 0.916451 0.400146i \(-0.131041\pi\)
−0.930975 + 0.365083i \(0.881041\pi\)
\(858\) −0.776847 3.02355i −0.0265211 0.103222i
\(859\) −40.2028 26.8627i −1.37170 0.916543i −0.371773 0.928324i \(-0.621250\pi\)
−0.999931 + 0.0117809i \(0.996250\pi\)
\(860\) −11.1896 + 6.15637i −0.381564 + 0.209930i
\(861\) −10.8743 + 54.6690i −0.370596 + 1.86311i
\(862\) 16.5304 7.94114i 0.563027 0.270476i
\(863\) 54.0259i 1.83906i −0.393018 0.919531i \(-0.628569\pi\)
0.393018 0.919531i \(-0.371431\pi\)
\(864\) −42.3978 36.1507i −1.44240 1.22987i
\(865\) 30.5967i 1.04032i
\(866\) −7.84900 16.3386i −0.266720 0.555208i
\(867\) 3.49977 17.5945i 0.118858 0.597542i
\(868\) 16.0317 55.2497i 0.544153 1.87530i
\(869\) 0.226435 + 0.151299i 0.00768127 + 0.00513246i
\(870\) −35.9034 + 9.22473i −1.21724 + 0.312748i
\(871\) 1.35040 + 3.26016i 0.0457567 + 0.110466i
\(872\) 5.07584 11.2566i 0.171890 0.381196i
\(873\) 32.8932 79.4113i 1.11327 2.68766i
\(874\) −3.28644 0.467176i −0.111165 0.0158025i
\(875\) 33.8299 6.72919i 1.14366 0.227488i
\(876\) −1.81030 5.71754i −0.0611643 0.193178i
\(877\) 25.7807 17.2261i 0.870552 0.581684i −0.0380835 0.999275i \(-0.512125\pi\)
0.908635 + 0.417590i \(0.137125\pi\)
\(878\) 38.1851 42.6469i 1.28868 1.43926i
\(879\) −60.8679 60.8679i −2.05302 2.05302i
\(880\) −1.42383 + 8.19010i −0.0479974 + 0.276088i
\(881\) 24.7406 24.7406i 0.833533 0.833533i −0.154465 0.987998i \(-0.549365\pi\)
0.987998 + 0.154465i \(0.0493655\pi\)
\(882\) −0.614347 11.1297i −0.0206861 0.374757i
\(883\) −17.5606 26.2813i −0.590962 0.884436i 0.408639 0.912696i \(-0.366003\pi\)
−0.999601 + 0.0282597i \(0.991003\pi\)
\(884\) −4.21106 + 3.54213i −0.141633 + 0.119135i
\(885\) −1.81981 9.14880i −0.0611722 0.307534i
\(886\) 1.45827 + 1.94157i 0.0489917 + 0.0652284i
\(887\) −15.7202 6.51152i −0.527833 0.218635i 0.102821 0.994700i \(-0.467213\pi\)
−0.630654 + 0.776064i \(0.717213\pi\)
\(888\) 4.51041 + 1.04310i 0.151359 + 0.0350043i
\(889\) −58.2981 + 24.1479i −1.95525 + 0.809893i
\(890\) 4.60274 7.78575i 0.154284 0.260979i
\(891\) −7.87321 + 11.7831i −0.263763 + 0.394749i
\(892\) 25.6792 32.0746i 0.859805 1.07394i
\(893\) −41.9301 8.34041i −1.40314 0.279101i
\(894\) −31.6742 + 90.2425i −1.05934 + 3.01816i
\(895\) −17.7512 −0.593357
\(896\) −29.9623 12.6466i −1.00097 0.422493i
\(897\) −0.812945 −0.0271434
\(898\) −11.5273 + 32.8423i −0.384671 + 1.09596i
\(899\) −51.4340 10.2309i −1.71542 0.341218i
\(900\) 17.8834 22.3372i 0.596114 0.744575i
\(901\) 11.0452 16.5303i 0.367968 0.550704i
\(902\) 5.79869 9.80874i 0.193075 0.326595i
\(903\) −31.3306 + 12.9776i −1.04262 + 0.431867i
\(904\) 10.5386 45.5690i 0.350507 1.51560i
\(905\) 5.43938 + 2.25306i 0.180811 + 0.0748944i
\(906\) 20.1759 + 26.8625i 0.670299 + 0.892447i
\(907\) 7.39593 + 37.1818i 0.245578 + 1.23460i 0.884943 + 0.465699i \(0.154197\pi\)
−0.639365 + 0.768903i \(0.720803\pi\)
\(908\) −30.0643 + 25.2886i −0.997720 + 0.839233i
\(909\) 13.9318 + 20.8504i 0.462088 + 0.691564i
\(910\) −0.211951 3.83978i −0.00702612 0.127287i
\(911\) −30.6254 + 30.6254i −1.01467 + 1.01467i −0.0147749 + 0.999891i \(0.504703\pi\)
−0.999891 + 0.0147749i \(0.995297\pi\)
\(912\) −35.3126 50.1743i −1.16932 1.66144i
\(913\) −5.54770 5.54770i −0.183602 0.183602i
\(914\) 0.983270 1.09816i 0.0325237 0.0363240i
\(915\) 27.4545 18.3445i 0.907618 0.606451i
\(916\) 13.1725 + 41.6034i 0.435233 + 1.37461i
\(917\) −20.2907 + 4.03606i −0.670057 + 0.133283i
\(918\) 65.9964 + 9.38157i 2.17821 + 0.309638i
\(919\) 3.89489 9.40310i 0.128481 0.310180i −0.846529 0.532343i \(-0.821312\pi\)
0.975010 + 0.222163i \(0.0713117\pi\)
\(920\) 1.97345 + 0.889869i 0.0650626 + 0.0293381i
\(921\) 12.5988 + 30.4163i 0.415146 + 1.00225i
\(922\) −19.0528 + 4.89527i −0.627469 + 0.161217i
\(923\) −2.17524 1.45345i −0.0715990 0.0478409i
\(924\) −6.15130 + 21.1990i −0.202363 + 0.697397i
\(925\) −0.240840 + 1.21079i −0.00791878 + 0.0398104i
\(926\) −7.18465 14.9557i −0.236102 0.491474i
\(927\) 49.2684i 1.61819i
\(928\) −9.13789 + 28.2027i −0.299966 + 0.925799i
\(929\) 0.932872i 0.0306066i 0.999883 + 0.0153033i \(0.00487137\pi\)
−0.999883 + 0.0153033i \(0.995129\pi\)
\(930\) −63.7994 + 30.6490i −2.09206 + 1.00502i
\(931\) 1.24341 6.25102i 0.0407510 0.204869i
\(932\) 6.85721 3.77273i 0.224615 0.123580i
\(933\) 18.9129 + 12.6372i 0.619182 + 0.413724i
\(934\) 0.101600 + 0.395433i 0.00332444 + 0.0129390i
\(935\) −3.80598 9.18845i −0.124469 0.300494i
\(936\) −6.95011 7.39378i −0.227171 0.241673i
\(937\) 9.77432 23.5973i 0.319313 0.770890i −0.679978 0.733233i \(-0.738010\pi\)
0.999291 0.0376573i \(-0.0119895\pi\)
\(938\) 3.51162 24.7031i 0.114658 0.806586i
\(939\) 67.5940 13.4453i 2.20585 0.438770i
\(940\) 24.7457 + 12.8440i 0.807117 + 0.418925i
\(941\) 14.0830 9.40994i 0.459092 0.306755i −0.304433 0.952534i \(-0.598467\pi\)
0.763525 + 0.645778i \(0.223467\pi\)
\(942\) −67.3001 60.2590i −2.19276 1.96334i
\(943\) −2.09819 2.09819i −0.0683266 0.0683266i
\(944\) −6.95931 2.68707i −0.226506 0.0874568i
\(945\) −32.9413 + 32.9413i −1.07158 + 1.07158i
\(946\) 6.92188 0.382080i 0.225050 0.0124225i
\(947\) 13.0115 + 19.4731i 0.422818 + 0.632791i 0.980327 0.197379i \(-0.0632430\pi\)
−0.557510 + 0.830171i \(0.688243\pi\)
\(948\) 1.30596 + 0.112674i 0.0424156 + 0.00365949i
\(949\) −0.110645 0.556252i −0.00359170 0.0180567i
\(950\) 13.0821 9.82572i 0.424441 0.318789i
\(951\) 37.0752 + 15.3571i 1.20225 + 0.497987i
\(952\) 38.3776 6.40731i 1.24383 0.207662i
\(953\) 44.5204 18.4410i 1.44216 0.597361i 0.481838 0.876261i \(-0.339970\pi\)
0.960320 + 0.278899i \(0.0899695\pi\)
\(954\) 31.5597 + 18.6573i 1.02178 + 0.604054i
\(955\) −0.660114 + 0.987930i −0.0213608 + 0.0319687i
\(956\) −1.51855 13.7133i −0.0491133 0.443521i
\(957\) 19.7350 + 3.92553i 0.637941 + 0.126894i
\(958\) 36.5618 + 12.8328i 1.18126 + 0.414610i
\(959\) 31.8352 1.02801
\(960\) 12.9983 + 37.8426i 0.419518 + 1.22137i
\(961\) −69.1305 −2.23002
\(962\) 0.413090 + 0.144990i 0.0133186 + 0.00467468i
\(963\) −33.7542 6.71413i −1.08771 0.216360i
\(964\) −4.79428 + 0.530895i −0.154413 + 0.0170990i
\(965\) −4.85198 + 7.26150i −0.156191 + 0.233756i
\(966\) 4.94821 + 2.92526i 0.159206 + 0.0941188i
\(967\) 25.4255 10.5316i 0.817629 0.338673i 0.0656353 0.997844i \(-0.479093\pi\)
0.751993 + 0.659171i \(0.229093\pi\)
\(968\) −15.4551 + 21.6499i −0.496745 + 0.695855i
\(969\) 67.8169 + 28.0907i 2.17859 + 0.902402i
\(970\) −25.6279 + 19.2486i −0.822863 + 0.618035i
\(971\) 3.37327 + 16.9586i 0.108254 + 0.544227i 0.996408 + 0.0846822i \(0.0269875\pi\)
−0.888154 + 0.459545i \(0.848012\pi\)
\(972\) −0.783406 + 9.08014i −0.0251278 + 0.291246i
\(973\) −6.15926 9.21798i −0.197457 0.295515i
\(974\) −43.3477 + 2.39275i −1.38895 + 0.0766685i
\(975\) 2.83328 2.83328i 0.0907377 0.0907377i
\(976\) −0.639568 26.3992i −0.0204721 0.845019i
\(977\) −26.1853 26.1853i −0.837743 0.837743i 0.150818 0.988562i \(-0.451809\pi\)
−0.988562 + 0.150818i \(0.951809\pi\)
\(978\) 65.6603 + 58.7907i 2.09958 + 1.87992i
\(979\) −4.08204 + 2.72753i −0.130463 + 0.0871723i
\(980\) −1.91481 + 3.68915i −0.0611664 + 0.117845i
\(981\) −26.7195 + 5.31485i −0.853089 + 0.169690i
\(982\) 0.291449 2.05025i 0.00930050 0.0654261i
\(983\) −0.628339 + 1.51695i −0.0200409 + 0.0483831i −0.933583 0.358361i \(-0.883336\pi\)
0.913542 + 0.406744i \(0.133336\pi\)
\(984\) 1.69560 54.8193i 0.0540538 1.74758i
\(985\) −9.39134 22.6727i −0.299233 0.722412i
\(986\) −8.82627 34.3525i −0.281086 1.09401i
\(987\) 61.5547 + 41.1295i 1.95931 + 1.30917i
\(988\) −2.79691 5.08358i −0.0889815 0.161730i
\(989\) 0.352195 1.77060i 0.0111991 0.0563019i
\(990\) 16.5318 7.94182i 0.525415 0.252408i
\(991\) 0.482249i 0.0153191i −0.999971 0.00765957i \(-0.997562\pi\)
0.999971 0.00765957i \(-0.00243814\pi\)
\(992\) −6.60687 + 56.2186i −0.209768 + 1.78494i
\(993\) 15.5019i 0.491938i
\(994\) 8.01019 + 16.6741i 0.254068 + 0.528871i
\(995\) −0.154218 + 0.775305i −0.00488903 + 0.0245788i
\(996\) −36.2675 10.5237i −1.14918 0.333456i
\(997\) −5.71075 3.81580i −0.180861 0.120848i 0.461844 0.886961i \(-0.347188\pi\)
−0.642705 + 0.766114i \(0.722188\pi\)
\(998\) 20.5518 5.28041i 0.650555 0.167149i
\(999\) −2.02955 4.89978i −0.0642123 0.155022i
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 64.2.i.a.29.6 56
3.2 odd 2 576.2.bd.a.541.2 56
4.3 odd 2 256.2.i.a.209.7 56
8.3 odd 2 512.2.i.a.161.1 56
8.5 even 2 512.2.i.b.161.7 56
64.11 odd 16 256.2.i.a.49.7 56
64.21 even 16 512.2.i.b.353.7 56
64.43 odd 16 512.2.i.a.353.1 56
64.53 even 16 inner 64.2.i.a.53.6 yes 56
192.53 odd 16 576.2.bd.a.181.2 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
64.2.i.a.29.6 56 1.1 even 1 trivial
64.2.i.a.53.6 yes 56 64.53 even 16 inner
256.2.i.a.49.7 56 64.11 odd 16
256.2.i.a.209.7 56 4.3 odd 2
512.2.i.a.161.1 56 8.3 odd 2
512.2.i.a.353.1 56 64.43 odd 16
512.2.i.b.161.7 56 8.5 even 2
512.2.i.b.353.7 56 64.21 even 16
576.2.bd.a.181.2 56 192.53 odd 16
576.2.bd.a.541.2 56 3.2 odd 2