Properties

Label 216.2.v.b.131.7
Level $216$
Weight $2$
Character 216.131
Analytic conductor $1.725$
Analytic rank $0$
Dimension $192$
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] = [216,2,Mod(11,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.v (of order \(18\), degree \(6\), 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: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 131.7
Character \(\chi\) \(=\) 216.131
Dual form 216.2.v.b.155.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.07669 - 0.916924i) q^{2} +(0.459797 + 1.66991i) q^{3} +(0.318502 + 1.97448i) q^{4} +(-0.221850 + 1.25817i) q^{5} +(1.03612 - 2.21956i) q^{6} +(-0.0241545 - 0.0287862i) q^{7} +(1.46752 - 2.41793i) q^{8} +(-2.57717 + 1.53564i) q^{9} +O(q^{10})\) \(q+(-1.07669 - 0.916924i) q^{2} +(0.459797 + 1.66991i) q^{3} +(0.318502 + 1.97448i) q^{4} +(-0.221850 + 1.25817i) q^{5} +(1.03612 - 2.21956i) q^{6} +(-0.0241545 - 0.0287862i) q^{7} +(1.46752 - 2.41793i) q^{8} +(-2.57717 + 1.53564i) q^{9} +(1.39251 - 1.15124i) q^{10} +(-3.96591 + 0.699297i) q^{11} +(-3.15074 + 1.43973i) q^{12} +(1.52273 + 4.18367i) q^{13} +(-0.000387960 + 0.0531414i) q^{14} +(-2.20304 + 0.208036i) q^{15} +(-3.79711 + 1.25775i) q^{16} +(-0.960657 - 0.554636i) q^{17} +(4.18287 + 0.709674i) q^{18} +(1.54631 + 2.67828i) q^{19} +(-2.55489 - 0.0373060i) q^{20} +(0.0369640 - 0.0535715i) q^{21} +(4.91124 + 2.88351i) q^{22} +(-1.78597 - 1.49861i) q^{23} +(4.71248 + 1.33886i) q^{24} +(3.16468 + 1.15185i) q^{25} +(2.19660 - 5.90072i) q^{26} +(-3.74934 - 3.59756i) q^{27} +(0.0491443 - 0.0568609i) q^{28} +(8.19341 + 2.98216i) q^{29} +(2.56273 + 1.79603i) q^{30} +(0.991533 - 1.18166i) q^{31} +(5.24156 + 2.12746i) q^{32} +(-2.99127 - 6.30116i) q^{33} +(0.525767 + 1.47802i) q^{34} +(0.0415766 - 0.0240043i) q^{35} +(-3.85291 - 4.59946i) q^{36} +(-0.0149964 - 0.00865816i) q^{37} +(0.790893 - 4.30151i) q^{38} +(-6.28618 + 4.46645i) q^{39} +(2.71661 + 2.38281i) q^{40} +(-0.470758 - 1.29340i) q^{41} +(-0.0889196 + 0.0237864i) q^{42} +(-0.0865581 - 0.490896i) q^{43} +(-2.64390 - 7.60786i) q^{44} +(-1.36035 - 3.58321i) q^{45} +(0.548820 + 3.25113i) q^{46} +(-7.19227 + 6.03503i) q^{47} +(-3.84623 - 5.76251i) q^{48} +(1.21529 - 6.89226i) q^{49} +(-2.35121 - 4.14195i) q^{50} +(0.484482 - 1.85923i) q^{51} +(-7.77556 + 4.33910i) q^{52} +14.3897 q^{53} +(0.738180 + 7.31130i) q^{54} -5.14494i q^{55} +(-0.105050 + 0.0161597i) q^{56} +(-3.76149 + 3.81365i) q^{57} +(-6.08731 - 10.7236i) q^{58} +(1.54236 + 0.271959i) q^{59} +(-1.11243 - 4.28358i) q^{60} +(-9.01061 - 10.7384i) q^{61} +(-2.15106 + 0.363119i) q^{62} +(0.106455 + 0.0370945i) q^{63} +(-3.69279 - 7.09671i) q^{64} +(-5.60159 + 0.987712i) q^{65} +(-2.55702 + 9.52714i) q^{66} +(7.92365 - 2.88397i) q^{67} +(0.789143 - 2.07345i) q^{68} +(1.68135 - 3.67146i) q^{69} +(-0.0667750 - 0.0122775i) q^{70} +(4.72079 - 8.17664i) q^{71} +(-0.0689819 + 8.48500i) q^{72} +(6.64650 + 11.5121i) q^{73} +(0.00820750 + 0.0230726i) q^{74} +(-0.468370 + 5.81434i) q^{75} +(-4.79570 + 3.90618i) q^{76} +(0.115924 + 0.0972722i) q^{77} +(10.8636 + 0.954985i) q^{78} +(3.05388 - 8.39047i) q^{79} +(-0.740079 - 5.05645i) q^{80} +(4.28364 - 7.91520i) q^{81} +(-0.679088 + 1.82423i) q^{82} +(-4.13336 + 11.3563i) q^{83} +(0.117549 + 0.0559220i) q^{84} +(0.910949 - 1.08563i) q^{85} +(-0.356918 + 0.607907i) q^{86} +(-1.21262 + 15.0534i) q^{87} +(-4.12919 + 10.6155i) q^{88} +(6.90026 - 3.98387i) q^{89} +(-1.82086 + 5.10533i) q^{90} +(0.0836510 - 0.144888i) q^{91} +(2.39013 - 4.00366i) q^{92} +(2.42917 + 1.11244i) q^{93} +(13.2775 + 0.0969323i) q^{94} +(-3.71279 + 1.35134i) q^{95} +(-1.14261 + 9.73111i) q^{96} +(-0.0961922 - 0.545533i) q^{97} +(-7.62817 + 6.30647i) q^{98} +(9.14697 - 7.89240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{11}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07669 0.916924i −0.761331 0.648363i
\(3\) 0.459797 + 1.66991i 0.265464 + 0.964121i
\(4\) 0.318502 + 1.97448i 0.159251 + 0.987238i
\(5\) −0.221850 + 1.25817i −0.0992142 + 0.562672i 0.894160 + 0.447748i \(0.147774\pi\)
−0.993374 + 0.114924i \(0.963337\pi\)
\(6\) 1.03612 2.21956i 0.422994 0.906132i
\(7\) −0.0241545 0.0287862i −0.00912953 0.0108801i 0.761460 0.648211i \(-0.224483\pi\)
−0.770590 + 0.637331i \(0.780038\pi\)
\(8\) 1.46752 2.41793i 0.518846 0.854868i
\(9\) −2.57717 + 1.53564i −0.859058 + 0.511879i
\(10\) 1.39251 1.15124i 0.440350 0.364053i
\(11\) −3.96591 + 0.699297i −1.19577 + 0.210846i −0.735868 0.677125i \(-0.763225\pi\)
−0.459899 + 0.887971i \(0.652114\pi\)
\(12\) −3.15074 + 1.43973i −0.909541 + 0.415614i
\(13\) 1.52273 + 4.18367i 0.422329 + 1.16034i 0.950370 + 0.311121i \(0.100705\pi\)
−0.528041 + 0.849219i \(0.677073\pi\)
\(14\) −0.000387960 0.0531414i −0.000103687 0.0142026i
\(15\) −2.20304 + 0.208036i −0.568821 + 0.0537146i
\(16\) −3.79711 + 1.25775i −0.949278 + 0.314438i
\(17\) −0.960657 0.554636i −0.232994 0.134519i 0.378959 0.925414i \(-0.376282\pi\)
−0.611952 + 0.790895i \(0.709616\pi\)
\(18\) 4.18287 + 0.709674i 0.985911 + 0.167272i
\(19\) 1.54631 + 2.67828i 0.354747 + 0.614439i 0.987075 0.160261i \(-0.0512337\pi\)
−0.632328 + 0.774701i \(0.717900\pi\)
\(20\) −2.55489 0.0373060i −0.571291 0.00834188i
\(21\) 0.0369640 0.0535715i 0.00806622 0.0116903i
\(22\) 4.91124 + 2.88351i 1.04708 + 0.614767i
\(23\) −1.78597 1.49861i −0.372400 0.312481i 0.437310 0.899311i \(-0.355931\pi\)
−0.809710 + 0.586830i \(0.800376\pi\)
\(24\) 4.71248 + 1.33886i 0.961931 + 0.273293i
\(25\) 3.16468 + 1.15185i 0.632936 + 0.230370i
\(26\) 2.19660 5.90072i 0.430789 1.15723i
\(27\) −3.74934 3.59756i −0.721562 0.692350i
\(28\) 0.0491443 0.0568609i 0.00928741 0.0107457i
\(29\) 8.19341 + 2.98216i 1.52148 + 0.553772i 0.961517 0.274747i \(-0.0885941\pi\)
0.559961 + 0.828519i \(0.310816\pi\)
\(30\) 2.56273 + 1.79603i 0.467888 + 0.327908i
\(31\) 0.991533 1.18166i 0.178085 0.212233i −0.669617 0.742707i \(-0.733542\pi\)
0.847701 + 0.530474i \(0.177986\pi\)
\(32\) 5.24156 + 2.12746i 0.926585 + 0.376085i
\(33\) −2.99127 6.30116i −0.520714 1.09689i
\(34\) 0.525767 + 1.47802i 0.0901683 + 0.253478i
\(35\) 0.0415766 0.0240043i 0.00702773 0.00405746i
\(36\) −3.85291 4.59946i −0.642152 0.766577i
\(37\) −0.0149964 0.00865816i −0.00246539 0.00142339i 0.498767 0.866736i \(-0.333786\pi\)
−0.501232 + 0.865313i \(0.667120\pi\)
\(38\) 0.790893 4.30151i 0.128300 0.697797i
\(39\) −6.28618 + 4.46645i −1.00660 + 0.715205i
\(40\) 2.71661 + 2.38281i 0.429533 + 0.376755i
\(41\) −0.470758 1.29340i −0.0735200 0.201995i 0.897489 0.441036i \(-0.145389\pi\)
−0.971009 + 0.239042i \(0.923167\pi\)
\(42\) −0.0889196 + 0.0237864i −0.0137206 + 0.00367032i
\(43\) −0.0865581 0.490896i −0.0132000 0.0748609i 0.977496 0.210953i \(-0.0676567\pi\)
−0.990696 + 0.136092i \(0.956546\pi\)
\(44\) −2.64390 7.60786i −0.398582 1.14693i
\(45\) −1.36035 3.58321i −0.202789 0.534153i
\(46\) 0.548820 + 3.25113i 0.0809191 + 0.479352i
\(47\) −7.19227 + 6.03503i −1.04910 + 0.880300i −0.992999 0.118125i \(-0.962312\pi\)
−0.0561017 + 0.998425i \(0.517867\pi\)
\(48\) −3.84623 5.76251i −0.555155 0.831747i
\(49\) 1.21529 6.89226i 0.173613 0.984609i
\(50\) −2.35121 4.14195i −0.332511 0.585760i
\(51\) 0.484482 1.85923i 0.0678411 0.260344i
\(52\) −7.77556 + 4.33910i −1.07828 + 0.601725i
\(53\) 14.3897 1.97657 0.988287 0.152609i \(-0.0487674\pi\)
0.988287 + 0.152609i \(0.0487674\pi\)
\(54\) 0.738180 + 7.31130i 0.100454 + 0.994942i
\(55\) 5.14494i 0.693743i
\(56\) −0.105050 + 0.0161597i −0.0140379 + 0.00215943i
\(57\) −3.76149 + 3.81365i −0.498221 + 0.505130i
\(58\) −6.08731 10.7236i −0.799303 1.40807i
\(59\) 1.54236 + 0.271959i 0.200798 + 0.0354060i 0.273142 0.961974i \(-0.411937\pi\)
−0.0723446 + 0.997380i \(0.523048\pi\)
\(60\) −1.11243 4.28358i −0.143615 0.553008i
\(61\) −9.01061 10.7384i −1.15369 1.37491i −0.914820 0.403862i \(-0.867667\pi\)
−0.238870 0.971052i \(-0.576777\pi\)
\(62\) −2.15106 + 0.363119i −0.273185 + 0.0461162i
\(63\) 0.106455 + 0.0370945i 0.0134121 + 0.00467347i
\(64\) −3.69279 7.09671i −0.461599 0.887089i
\(65\) −5.60159 + 0.987712i −0.694792 + 0.122511i
\(66\) −2.55702 + 9.52714i −0.314748 + 1.17271i
\(67\) 7.92365 2.88397i 0.968028 0.352333i 0.190853 0.981619i \(-0.438875\pi\)
0.777174 + 0.629285i \(0.216652\pi\)
\(68\) 0.789143 2.07345i 0.0956977 0.251442i
\(69\) 1.68135 3.67146i 0.202411 0.441991i
\(70\) −0.0667750 0.0122775i −0.00798114 0.00146745i
\(71\) 4.72079 8.17664i 0.560254 0.970389i −0.437220 0.899355i \(-0.644037\pi\)
0.997474 0.0710340i \(-0.0226299\pi\)
\(72\) −0.0689819 + 8.48500i −0.00812960 + 0.999967i
\(73\) 6.64650 + 11.5121i 0.777914 + 1.34739i 0.933142 + 0.359507i \(0.117055\pi\)
−0.155229 + 0.987879i \(0.549611\pi\)
\(74\) 0.00820750 + 0.0230726i 0.000954103 + 0.00268214i
\(75\) −0.468370 + 5.81434i −0.0540827 + 0.671382i
\(76\) −4.79570 + 3.90618i −0.550104 + 0.448070i
\(77\) 0.115924 + 0.0972722i 0.0132108 + 0.0110852i
\(78\) 10.8636 + 0.954985i 1.23006 + 0.108131i
\(79\) 3.05388 8.39047i 0.343589 0.944002i −0.640756 0.767745i \(-0.721379\pi\)
0.984344 0.176257i \(-0.0563990\pi\)
\(80\) −0.740079 5.05645i −0.0827434 0.565329i
\(81\) 4.28364 7.91520i 0.475961 0.879467i
\(82\) −0.679088 + 1.82423i −0.0749927 + 0.201453i
\(83\) −4.13336 + 11.3563i −0.453696 + 1.24652i 0.476409 + 0.879224i \(0.341938\pi\)
−0.930105 + 0.367295i \(0.880284\pi\)
\(84\) 0.117549 + 0.0559220i 0.0128256 + 0.00610159i
\(85\) 0.910949 1.08563i 0.0988063 0.117753i
\(86\) −0.356918 + 0.607907i −0.0384874 + 0.0655523i
\(87\) −1.21262 + 15.0534i −0.130006 + 1.61389i
\(88\) −4.12919 + 10.6155i −0.440173 + 1.13162i
\(89\) 6.90026 3.98387i 0.731426 0.422289i −0.0875175 0.996163i \(-0.527893\pi\)
0.818944 + 0.573874i \(0.194560\pi\)
\(90\) −1.82086 + 5.10533i −0.191936 + 0.538149i
\(91\) 0.0836510 0.144888i 0.00876901 0.0151884i
\(92\) 2.39013 4.00366i 0.249188 0.417411i
\(93\) 2.42917 + 1.11244i 0.251893 + 0.115355i
\(94\) 13.2775 + 0.0969323i 1.36947 + 0.00999781i
\(95\) −3.71279 + 1.35134i −0.380924 + 0.138645i
\(96\) −1.14261 + 9.73111i −0.116617 + 0.993177i
\(97\) −0.0961922 0.545533i −0.00976684 0.0553905i 0.979535 0.201275i \(-0.0645084\pi\)
−0.989302 + 0.145884i \(0.953397\pi\)
\(98\) −7.62817 + 6.30647i −0.770561 + 0.637050i
\(99\) 9.14697 7.89240i 0.919305 0.793216i
\(100\) −1.26634 + 6.61546i −0.126634 + 0.661546i
\(101\) 0.735978 0.617559i 0.0732325 0.0614494i −0.605437 0.795894i \(-0.707001\pi\)
0.678669 + 0.734444i \(0.262557\pi\)
\(102\) −2.22640 + 1.55757i −0.220447 + 0.154222i
\(103\) −5.44272 0.959698i −0.536287 0.0945618i −0.101056 0.994881i \(-0.532222\pi\)
−0.435231 + 0.900319i \(0.643333\pi\)
\(104\) 12.3505 + 2.45774i 1.21106 + 0.241002i
\(105\) 0.0592017 + 0.0583920i 0.00577749 + 0.00569847i
\(106\) −15.4931 13.1942i −1.50483 1.28154i
\(107\) 13.8930i 1.34309i 0.740966 + 0.671543i \(0.234368\pi\)
−0.740966 + 0.671543i \(0.765632\pi\)
\(108\) 5.90911 8.54882i 0.568605 0.822611i
\(109\) 13.3583i 1.27949i 0.768586 + 0.639746i \(0.220961\pi\)
−0.768586 + 0.639746i \(0.779039\pi\)
\(110\) −4.71751 + 5.53948i −0.449797 + 0.528169i
\(111\) 0.00756303 0.0290235i 0.000717851 0.00275479i
\(112\) 0.127923 + 0.0789240i 0.0120876 + 0.00745762i
\(113\) 6.47027 + 1.14088i 0.608672 + 0.107325i 0.469484 0.882941i \(-0.344440\pi\)
0.139187 + 0.990266i \(0.455551\pi\)
\(114\) 7.54677 0.657103i 0.706819 0.0615434i
\(115\) 2.28172 1.91459i 0.212772 0.178537i
\(116\) −3.27858 + 17.1275i −0.304408 + 1.59025i
\(117\) −10.3489 8.44368i −0.956759 0.780618i
\(118\) −1.41127 1.70704i −0.129918 0.157145i
\(119\) 0.00723832 + 0.0410506i 0.000663536 + 0.00376310i
\(120\) −2.72998 + 5.63209i −0.249212 + 0.514137i
\(121\) 4.90280 1.78447i 0.445709 0.162225i
\(122\) −0.144725 + 19.8239i −0.0131028 + 1.79477i
\(123\) 1.94340 1.38082i 0.175230 0.124504i
\(124\) 2.64897 + 1.58140i 0.237885 + 0.142014i
\(125\) −5.34527 + 9.25827i −0.478095 + 0.828085i
\(126\) −0.0806061 0.137550i −0.00718096 0.0122540i
\(127\) 15.5376 8.97063i 1.37874 0.796015i 0.386730 0.922193i \(-0.373604\pi\)
0.992008 + 0.126178i \(0.0402711\pi\)
\(128\) −2.53117 + 11.0269i −0.223726 + 0.974652i
\(129\) 0.779950 0.370256i 0.0686708 0.0325993i
\(130\) 6.93681 + 4.07278i 0.608398 + 0.357206i
\(131\) 9.77701 11.6518i 0.854221 1.01802i −0.145368 0.989378i \(-0.546437\pi\)
0.999590 0.0286439i \(-0.00911889\pi\)
\(132\) 11.4888 7.91313i 0.999969 0.688750i
\(133\) 0.0397472 0.109205i 0.00344652 0.00946924i
\(134\) −11.1757 4.16025i −0.965430 0.359391i
\(135\) 5.35814 3.91921i 0.461155 0.337312i
\(136\) −2.75085 + 1.50887i −0.235884 + 0.129384i
\(137\) −3.50778 + 9.63755i −0.299690 + 0.823391i 0.694861 + 0.719144i \(0.255466\pi\)
−0.994551 + 0.104248i \(0.966757\pi\)
\(138\) −5.17673 + 2.41134i −0.440672 + 0.205267i
\(139\) −16.5421 13.8805i −1.40308 1.17733i −0.959712 0.280987i \(-0.909338\pi\)
−0.443370 0.896339i \(-0.646217\pi\)
\(140\) 0.0606381 + 0.0744466i 0.00512486 + 0.00629189i
\(141\) −13.3849 9.23553i −1.12721 0.777772i
\(142\) −12.5802 + 4.47507i −1.05570 + 0.375539i
\(143\) −8.96463 15.5272i −0.749660 1.29845i
\(144\) 7.85437 9.07242i 0.654531 0.756035i
\(145\) −5.56977 + 9.64713i −0.462544 + 0.801150i
\(146\) 3.39950 18.4892i 0.281345 1.53018i
\(147\) 12.0682 1.13962i 0.995370 0.0939942i
\(148\) 0.0123190 0.0323676i 0.00101261 0.00266060i
\(149\) −11.6387 + 4.23616i −0.953483 + 0.347039i −0.771476 0.636258i \(-0.780481\pi\)
−0.182007 + 0.983297i \(0.558259\pi\)
\(150\) 5.83559 5.83075i 0.476474 0.476079i
\(151\) 8.22863 1.45093i 0.669637 0.118075i 0.171514 0.985182i \(-0.445134\pi\)
0.498123 + 0.867107i \(0.334023\pi\)
\(152\) 8.74513 + 0.191559i 0.709323 + 0.0155375i
\(153\) 3.32750 0.0458274i 0.269012 0.00370493i
\(154\) −0.0356230 0.211025i −0.00287058 0.0170049i
\(155\) 1.26677 + 1.50967i 0.101749 + 0.121260i
\(156\) −10.8211 10.9893i −0.866379 0.879852i
\(157\) −7.33700 1.29371i −0.585556 0.103249i −0.126981 0.991905i \(-0.540529\pi\)
−0.458575 + 0.888656i \(0.651640\pi\)
\(158\) −10.9815 + 6.23372i −0.873641 + 0.495928i
\(159\) 6.61633 + 24.0294i 0.524709 + 1.90566i
\(160\) −3.83955 + 6.12281i −0.303543 + 0.484050i
\(161\) 0.0876093i 0.00690458i
\(162\) −11.8698 + 4.59440i −0.932577 + 0.360971i
\(163\) −8.72750 −0.683591 −0.341795 0.939774i \(-0.611035\pi\)
−0.341795 + 0.939774i \(0.611035\pi\)
\(164\) 2.40384 1.34145i 0.187709 0.104750i
\(165\) 8.59156 2.36563i 0.668852 0.184164i
\(166\) 14.8632 8.43721i 1.15361 0.654854i
\(167\) −1.28634 + 7.29522i −0.0995404 + 0.564521i 0.893721 + 0.448624i \(0.148086\pi\)
−0.993261 + 0.115898i \(0.963025\pi\)
\(168\) −0.0752868 0.167994i −0.00580851 0.0129610i
\(169\) −5.22578 + 4.38495i −0.401983 + 0.337304i
\(170\) −1.97624 + 0.333608i −0.151571 + 0.0255865i
\(171\) −8.09796 4.52783i −0.619266 0.346252i
\(172\) 0.941693 0.327258i 0.0718034 0.0249532i
\(173\) −1.10221 6.25096i −0.0837996 0.475251i −0.997609 0.0691084i \(-0.977985\pi\)
0.913810 0.406143i \(-0.133127\pi\)
\(174\) 15.1084 15.0959i 1.14537 1.14442i
\(175\) −0.0432838 0.118921i −0.00327195 0.00898961i
\(176\) 14.1795 7.64343i 1.06882 0.576146i
\(177\) 0.255025 + 2.70064i 0.0191688 + 0.202992i
\(178\) −11.0823 2.03764i −0.830654 0.152728i
\(179\) −10.8244 6.24945i −0.809051 0.467106i 0.0375750 0.999294i \(-0.488037\pi\)
−0.846626 + 0.532188i \(0.821370\pi\)
\(180\) 6.64169 3.82724i 0.495042 0.285266i
\(181\) −19.6860 + 11.3657i −1.46325 + 0.844807i −0.999160 0.0409826i \(-0.986951\pi\)
−0.464088 + 0.885789i \(0.653618\pi\)
\(182\) −0.222917 + 0.0792970i −0.0165237 + 0.00587788i
\(183\) 13.7891 19.9844i 1.01932 1.47729i
\(184\) −6.24447 + 2.11912i −0.460348 + 0.156224i
\(185\) 0.0142204 0.0169472i 0.00104550 0.00124598i
\(186\) −1.59543 3.42511i −0.116983 0.251142i
\(187\) 4.19773 + 1.52785i 0.306969 + 0.111727i
\(188\) −14.2068 12.2788i −1.03614 0.895523i
\(189\) −0.0129965 + 0.194826i −0.000945354 + 0.0141715i
\(190\) 5.23658 + 1.94937i 0.379901 + 0.141422i
\(191\) −3.53137 1.28531i −0.255521 0.0930020i 0.211084 0.977468i \(-0.432301\pi\)
−0.466605 + 0.884466i \(0.654523\pi\)
\(192\) 10.1529 9.42966i 0.732723 0.680527i
\(193\) −18.9554 15.9055i −1.36444 1.14490i −0.974583 0.224025i \(-0.928080\pi\)
−0.389857 0.920876i \(-0.627475\pi\)
\(194\) −0.396643 + 0.675568i −0.0284773 + 0.0485030i
\(195\) −4.22498 8.89999i −0.302557 0.637341i
\(196\) 13.9957 + 0.204362i 0.999692 + 0.0145973i
\(197\) 2.31882 + 4.01631i 0.165209 + 0.286150i 0.936729 0.350054i \(-0.113837\pi\)
−0.771521 + 0.636204i \(0.780504\pi\)
\(198\) −17.0851 + 0.110561i −1.21419 + 0.00785721i
\(199\) 12.8167 + 7.39975i 0.908555 + 0.524554i 0.879966 0.475037i \(-0.157565\pi\)
0.0285887 + 0.999591i \(0.490899\pi\)
\(200\) 7.42932 5.96163i 0.525332 0.421551i
\(201\) 8.45923 + 11.9057i 0.596668 + 0.839764i
\(202\) −1.35867 0.00991899i −0.0955957 0.000697898i
\(203\) −0.112062 0.307889i −0.00786524 0.0216096i
\(204\) 3.82531 + 0.364430i 0.267825 + 0.0255152i
\(205\) 1.73175 0.305355i 0.120951 0.0213269i
\(206\) 4.98012 + 6.02385i 0.346982 + 0.419701i
\(207\) 6.90407 + 1.11957i 0.479866 + 0.0778155i
\(208\) −11.0440 13.9706i −0.765763 0.968689i
\(209\) −8.00542 9.54049i −0.553746 0.659929i
\(210\) −0.0102006 0.117153i −0.000703910 0.00808434i
\(211\) −2.04564 + 11.6014i −0.140828 + 0.798673i 0.829795 + 0.558068i \(0.188457\pi\)
−0.970623 + 0.240606i \(0.922654\pi\)
\(212\) 4.58315 + 28.4121i 0.314772 + 1.95135i
\(213\) 15.8248 + 4.12367i 1.08430 + 0.282549i
\(214\) 12.7388 14.9584i 0.870807 1.02253i
\(215\) 0.636834 0.0434317
\(216\) −14.2009 + 3.78619i −0.966247 + 0.257617i
\(217\) −0.0579655 −0.00393496
\(218\) 12.2485 14.3827i 0.829575 0.974118i
\(219\) −16.1680 + 16.3922i −1.09253 + 1.10768i
\(220\) 10.1586 1.63868i 0.684890 0.110479i
\(221\) 0.857589 4.86363i 0.0576877 0.327163i
\(222\) −0.0347554 + 0.0243145i −0.00233263 + 0.00163188i
\(223\) 13.5037 + 16.0931i 0.904277 + 1.07768i 0.996636 + 0.0819499i \(0.0261148\pi\)
−0.0923592 + 0.995726i \(0.529441\pi\)
\(224\) −0.0653656 0.202272i −0.00436742 0.0135149i
\(225\) −9.92476 + 1.89128i −0.661650 + 0.126085i
\(226\) −5.92034 7.16111i −0.393815 0.476350i
\(227\) −2.94969 + 0.520110i −0.195778 + 0.0345209i −0.270677 0.962670i \(-0.587248\pi\)
0.0748993 + 0.997191i \(0.476136\pi\)
\(228\) −8.72800 6.21231i −0.578026 0.411421i
\(229\) 2.32907 + 6.39908i 0.153910 + 0.422863i 0.992552 0.121819i \(-0.0388727\pi\)
−0.838643 + 0.544682i \(0.816650\pi\)
\(230\) −4.21223 0.0307515i −0.277746 0.00202769i
\(231\) −0.109134 + 0.238308i −0.00718047 + 0.0156795i
\(232\) 19.2346 15.4347i 1.26281 1.01334i
\(233\) 9.35687 + 5.40219i 0.612989 + 0.353909i 0.774134 0.633021i \(-0.218185\pi\)
−0.161145 + 0.986931i \(0.551519\pi\)
\(234\) 3.40033 + 18.5804i 0.222287 + 1.21464i
\(235\) −5.99751 10.3880i −0.391234 0.677638i
\(236\) −0.0457323 + 3.13197i −0.00297692 + 0.203874i
\(237\) 15.4155 + 1.24178i 1.00134 + 0.0806624i
\(238\) 0.0298468 0.0508355i 0.00193468 0.00329518i
\(239\) 6.88390 + 5.77628i 0.445282 + 0.373636i 0.837682 0.546159i \(-0.183910\pi\)
−0.392399 + 0.919795i \(0.628355\pi\)
\(240\) 8.10352 3.56081i 0.523080 0.229849i
\(241\) 7.68472 + 2.79701i 0.495016 + 0.180171i 0.577451 0.816425i \(-0.304047\pi\)
−0.0824349 + 0.996596i \(0.526270\pi\)
\(242\) −6.91500 2.57418i −0.444513 0.165474i
\(243\) 15.1872 + 3.51390i 0.974262 + 0.225417i
\(244\) 18.3329 21.2114i 1.17364 1.35792i
\(245\) 8.40205 + 3.05809i 0.536787 + 0.195374i
\(246\) −3.35854 0.295237i −0.214132 0.0188236i
\(247\) −8.85042 + 10.5475i −0.563139 + 0.671123i
\(248\) −1.40209 4.13157i −0.0890328 0.262355i
\(249\) −20.8645 1.68073i −1.32223 0.106512i
\(250\) 14.2443 5.06704i 0.900888 0.320468i
\(251\) 16.1945 9.34989i 1.02219 0.590160i 0.107450 0.994210i \(-0.465731\pi\)
0.914737 + 0.404051i \(0.132398\pi\)
\(252\) −0.0393359 + 0.222008i −0.00247793 + 0.0139852i
\(253\) 8.13096 + 4.69441i 0.511189 + 0.295135i
\(254\) −24.9545 4.58823i −1.56578 0.287891i
\(255\) 2.23175 + 1.02203i 0.139757 + 0.0640021i
\(256\) 12.8361 9.55164i 0.802258 0.596978i
\(257\) −4.78002 13.1330i −0.298170 0.819214i −0.994806 0.101790i \(-0.967543\pi\)
0.696636 0.717424i \(-0.254679\pi\)
\(258\) −1.17926 0.316505i −0.0734174 0.0197048i
\(259\) 0.000112994 0 0.000640821i 7.02111e−6 0 3.98187e-5i
\(260\) −3.73433 10.7456i −0.231594 0.666415i
\(261\) −25.6953 + 4.89656i −1.59050 + 0.303089i
\(262\) −21.2106 + 3.58054i −1.31039 + 0.221206i
\(263\) −14.3635 + 12.0524i −0.885694 + 0.743186i −0.967342 0.253475i \(-0.918426\pi\)
0.0816475 + 0.996661i \(0.473982\pi\)
\(264\) −19.6255 2.01436i −1.20787 0.123976i
\(265\) −3.19235 + 18.1047i −0.196104 + 1.11216i
\(266\) −0.142928 + 0.0811338i −0.00876345 + 0.00497463i
\(267\) 9.82540 + 9.69102i 0.601305 + 0.593081i
\(268\) 8.21803 + 14.7265i 0.501996 + 0.899564i
\(269\) 1.60260 0.0977123 0.0488561 0.998806i \(-0.484442\pi\)
0.0488561 + 0.998806i \(0.484442\pi\)
\(270\) −9.36264 0.693252i −0.569792 0.0421900i
\(271\) 1.09029i 0.0662304i −0.999452 0.0331152i \(-0.989457\pi\)
0.999452 0.0331152i \(-0.0105428\pi\)
\(272\) 4.34532 + 0.897746i 0.263473 + 0.0544339i
\(273\) 0.280411 + 0.0730703i 0.0169713 + 0.00442242i
\(274\) 12.6137 7.16024i 0.762020 0.432566i
\(275\) −13.3563 2.35508i −0.805417 0.142017i
\(276\) 7.78472 + 2.15041i 0.468585 + 0.129440i
\(277\) −15.6324 18.6300i −0.939260 1.11937i −0.992678 0.120794i \(-0.961456\pi\)
0.0534180 0.998572i \(-0.482988\pi\)
\(278\) 5.08330 + 30.1127i 0.304876 + 1.80604i
\(279\) −0.740749 + 4.56799i −0.0443475 + 0.273478i
\(280\) 0.00297369 0.135756i 0.000177712 0.00811298i
\(281\) −1.76346 + 0.310946i −0.105199 + 0.0185495i −0.226000 0.974127i \(-0.572565\pi\)
0.120801 + 0.992677i \(0.461454\pi\)
\(282\) 5.94308 + 22.2167i 0.353905 + 1.32299i
\(283\) −3.16461 + 1.15182i −0.188117 + 0.0684688i −0.434361 0.900739i \(-0.643026\pi\)
0.246244 + 0.969208i \(0.420803\pi\)
\(284\) 17.6482 + 6.71680i 1.04723 + 0.398569i
\(285\) −3.96374 5.57866i −0.234792 0.330451i
\(286\) −4.58517 + 24.9378i −0.271127 + 1.47460i
\(287\) −0.0258610 + 0.0447926i −0.00152653 + 0.00264402i
\(288\) −16.7754 + 2.56629i −0.988500 + 0.151220i
\(289\) −7.88476 13.6568i −0.463809 0.803341i
\(290\) 14.8426 5.27987i 0.871586 0.310044i
\(291\) 0.866760 0.411466i 0.0508104 0.0241206i
\(292\) −20.6134 + 16.7900i −1.20631 + 0.982559i
\(293\) −19.4842 16.3492i −1.13828 0.955130i −0.138898 0.990307i \(-0.544356\pi\)
−0.999381 + 0.0351766i \(0.988801\pi\)
\(294\) −14.0386 9.83863i −0.818749 0.573800i
\(295\) −0.684343 + 1.88022i −0.0398440 + 0.109470i
\(296\) −0.0429423 + 0.0235542i −0.00249597 + 0.00136906i
\(297\) 17.3853 + 11.6457i 1.00880 + 0.675751i
\(298\) 16.4155 + 6.11083i 0.950924 + 0.353991i
\(299\) 3.55012 9.75388i 0.205309 0.564081i
\(300\) −11.6295 + 0.927096i −0.671427 + 0.0535259i
\(301\) −0.0120402 + 0.0143490i −0.000693988 + 0.000827062i
\(302\) −10.1900 5.98283i −0.586371 0.344273i
\(303\) 1.36967 + 0.945062i 0.0786852 + 0.0542924i
\(304\) −9.24010 8.22486i −0.529956 0.471728i
\(305\) 15.5098 8.95458i 0.888088 0.512738i
\(306\) −3.62469 3.00172i −0.207210 0.171597i
\(307\) −13.4800 + 23.3481i −0.769346 + 1.33255i 0.168572 + 0.985689i \(0.446084\pi\)
−0.937918 + 0.346857i \(0.887249\pi\)
\(308\) −0.155139 + 0.259872i −0.00883989 + 0.0148076i
\(309\) −0.899940 9.53009i −0.0511958 0.542148i
\(310\) 0.0203463 2.78697i 0.00115559 0.158289i
\(311\) 23.0984 8.40714i 1.30979 0.476725i 0.409618 0.912257i \(-0.365662\pi\)
0.900173 + 0.435532i \(0.143440\pi\)
\(312\) 1.57450 + 21.7542i 0.0891386 + 1.23159i
\(313\) 0.589807 + 3.34496i 0.0333379 + 0.189069i 0.996929 0.0783120i \(-0.0249530\pi\)
−0.963591 + 0.267381i \(0.913842\pi\)
\(314\) 6.71340 + 8.12039i 0.378859 + 0.458260i
\(315\) −0.0702883 + 0.125710i −0.00396030 + 0.00708294i
\(316\) 17.5395 + 3.35743i 0.986671 + 0.188870i
\(317\) 16.0239 13.4456i 0.899991 0.755182i −0.0701973 0.997533i \(-0.522363\pi\)
0.970189 + 0.242351i \(0.0779184\pi\)
\(318\) 14.9094 31.9388i 0.836079 1.79104i
\(319\) −34.5797 6.09734i −1.93609 0.341385i
\(320\) 9.74813 3.07176i 0.544937 0.171717i
\(321\) −23.2000 + 6.38795i −1.29490 + 0.356541i
\(322\) 0.0803310 0.0943276i 0.00447667 0.00525667i
\(323\) 3.43054i 0.190881i
\(324\) 16.9927 + 5.93694i 0.944040 + 0.329830i
\(325\) 14.9939i 0.831714i
\(326\) 9.39677 + 8.00245i 0.520439 + 0.443215i
\(327\) −22.3071 + 6.14210i −1.23359 + 0.339659i
\(328\) −3.81819 0.759821i −0.210824 0.0419541i
\(329\) 0.347451 + 0.0612650i 0.0191556 + 0.00337765i
\(330\) −11.4195 5.33077i −0.628623 0.293449i
\(331\) 21.5215 18.0587i 1.18293 0.992594i 0.182972 0.983118i \(-0.441428\pi\)
0.999955 0.00947543i \(-0.00301617\pi\)
\(332\) −23.7393 4.54421i −1.30286 0.249396i
\(333\) 0.0519440 0.000715390i 0.00284652 3.92032e-5i
\(334\) 8.07415 6.67518i 0.441798 0.365250i
\(335\) 1.87067 + 10.6091i 0.102206 + 0.579638i
\(336\) −0.0729771 + 0.249908i −0.00398122 + 0.0136336i
\(337\) 16.1167 5.86598i 0.877930 0.319540i 0.136556 0.990632i \(-0.456397\pi\)
0.741374 + 0.671092i \(0.234174\pi\)
\(338\) 9.64719 + 0.0704294i 0.524738 + 0.00383086i
\(339\) 1.06984 + 11.3293i 0.0581059 + 0.615324i
\(340\) 2.43368 + 1.45287i 0.131985 + 0.0787931i
\(341\) −3.10600 + 5.37975i −0.168199 + 0.291330i
\(342\) 4.56728 + 12.3003i 0.246970 + 0.665122i
\(343\) −0.455559 + 0.263017i −0.0245979 + 0.0142016i
\(344\) −1.31398 0.511106i −0.0708449 0.0275570i
\(345\) 4.24632 + 2.92994i 0.228614 + 0.157743i
\(346\) −4.54491 + 7.74096i −0.244336 + 0.416156i
\(347\) 3.20624 3.82105i 0.172120 0.205125i −0.673087 0.739563i \(-0.735032\pi\)
0.845208 + 0.534438i \(0.179477\pi\)
\(348\) −30.1088 + 2.40026i −1.61400 + 0.128668i
\(349\) −0.573161 + 1.57475i −0.0306806 + 0.0842943i −0.954087 0.299529i \(-0.903171\pi\)
0.923407 + 0.383823i \(0.125393\pi\)
\(350\) −0.0624387 + 0.167729i −0.00333749 + 0.00896549i
\(351\) 9.34174 21.1641i 0.498625 1.12966i
\(352\) −22.2753 4.77191i −1.18728 0.254344i
\(353\) 10.7094 29.4240i 0.570006 1.56608i −0.234489 0.972119i \(-0.575342\pi\)
0.804495 0.593960i \(-0.202436\pi\)
\(354\) 2.20170 3.14157i 0.117019 0.166973i
\(355\) 9.24032 + 7.75355i 0.490425 + 0.411516i
\(356\) 10.0638 + 12.3555i 0.533380 + 0.654842i
\(357\) −0.0652224 + 0.0309622i −0.00345194 + 0.00163870i
\(358\) 5.92417 + 16.6538i 0.313102 + 0.880181i
\(359\) −14.7790 25.5979i −0.780004 1.35101i −0.931938 0.362617i \(-0.881883\pi\)
0.151934 0.988391i \(-0.451450\pi\)
\(360\) −10.6603 1.96919i −0.561847 0.103785i
\(361\) 4.71788 8.17161i 0.248309 0.430085i
\(362\) 31.6171 + 5.81325i 1.66176 + 0.305538i
\(363\) 5.23419 + 7.36672i 0.274724 + 0.386652i
\(364\) 0.312721 + 0.119020i 0.0163910 + 0.00623833i
\(365\) −15.9587 + 5.80849i −0.835316 + 0.304030i
\(366\) −33.1707 + 8.87331i −1.73386 + 0.463815i
\(367\) −19.6688 + 3.46814i −1.02670 + 0.181035i −0.661541 0.749909i \(-0.730097\pi\)
−0.365162 + 0.930944i \(0.618986\pi\)
\(368\) 8.66640 + 3.44407i 0.451767 + 0.179535i
\(369\) 3.19941 + 2.61039i 0.166555 + 0.135892i
\(370\) −0.0308502 + 0.00520780i −0.00160383 + 0.000270740i
\(371\) −0.347575 0.414223i −0.0180452 0.0215054i
\(372\) −1.42279 + 5.15066i −0.0737684 + 0.267049i
\(373\) 29.7847 + 5.25185i 1.54219 + 0.271930i 0.879112 0.476616i \(-0.158137\pi\)
0.663082 + 0.748546i \(0.269248\pi\)
\(374\) −3.11872 5.49401i −0.161265 0.284089i
\(375\) −17.9182 4.66917i −0.925291 0.241115i
\(376\) 4.03752 + 26.2469i 0.208219 + 1.35358i
\(377\) 38.8195i 1.99931i
\(378\) 0.192634 0.197850i 0.00990802 0.0101763i
\(379\) −2.37587 −0.122040 −0.0610201 0.998137i \(-0.519435\pi\)
−0.0610201 + 0.998137i \(0.519435\pi\)
\(380\) −3.85073 6.90040i −0.197538 0.353983i
\(381\) 22.1242 + 21.8216i 1.13346 + 1.11796i
\(382\) 2.62364 + 4.62187i 0.134237 + 0.236476i
\(383\) 2.35543 13.3583i 0.120357 0.682578i −0.863601 0.504176i \(-0.831796\pi\)
0.983958 0.178402i \(-0.0570926\pi\)
\(384\) −19.5778 + 0.843334i −0.999074 + 0.0430362i
\(385\) −0.148103 + 0.124273i −0.00754803 + 0.00633355i
\(386\) 5.82490 + 34.5058i 0.296480 + 1.75630i
\(387\) 0.976912 + 1.13220i 0.0496592 + 0.0575530i
\(388\) 1.04650 0.363683i 0.0531282 0.0184632i
\(389\) 0.151459 + 0.858969i 0.00767929 + 0.0435514i 0.988407 0.151830i \(-0.0485166\pi\)
−0.980727 + 0.195381i \(0.937406\pi\)
\(390\) −3.61163 + 13.4565i −0.182882 + 0.681395i
\(391\) 0.884524 + 2.43021i 0.0447323 + 0.122901i
\(392\) −14.8816 13.0530i −0.751632 0.659276i
\(393\) 23.9528 + 10.9692i 1.20826 + 0.553325i
\(394\) 1.18601 6.45048i 0.0597504 0.324970i
\(395\) 9.87916 + 5.70374i 0.497074 + 0.286986i
\(396\) 18.4967 + 15.5467i 0.929494 + 0.781252i
\(397\) 14.0922 8.13615i 0.707269 0.408342i −0.102780 0.994704i \(-0.532774\pi\)
0.810049 + 0.586362i \(0.199440\pi\)
\(398\) −7.01459 19.7192i −0.351610 0.988433i
\(399\) 0.200637 + 0.0161622i 0.0100444 + 0.000809121i
\(400\) −13.4654 0.393322i −0.673270 0.0196661i
\(401\) −3.43727 + 4.09638i −0.171649 + 0.204563i −0.845010 0.534751i \(-0.820406\pi\)
0.673361 + 0.739314i \(0.264850\pi\)
\(402\) 1.80869 20.5752i 0.0902093 1.02620i
\(403\) 6.45352 + 2.34889i 0.321473 + 0.117007i
\(404\) 1.45377 + 1.25648i 0.0723276 + 0.0625121i
\(405\) 9.00836 + 7.14555i 0.447629 + 0.355065i
\(406\) −0.161655 + 0.434252i −0.00802279 + 0.0215516i
\(407\) 0.0655289 + 0.0238506i 0.00324815 + 0.00118223i
\(408\) −3.78450 3.89989i −0.187361 0.193073i
\(409\) −3.30579 2.77389i −0.163461 0.137160i 0.557388 0.830252i \(-0.311803\pi\)
−0.720849 + 0.693092i \(0.756248\pi\)
\(410\) −2.14454 1.25911i −0.105911 0.0621832i
\(411\) −17.7067 1.42635i −0.873406 0.0703566i
\(412\) 0.161382 11.0522i 0.00795071 0.544502i
\(413\) −0.0294261 0.0509675i −0.00144796 0.00250795i
\(414\) −6.40695 7.53593i −0.314884 0.370371i
\(415\) −13.3712 7.71988i −0.656368 0.378954i
\(416\) −0.919106 + 25.1685i −0.0450629 + 1.23399i
\(417\) 15.5731 34.0059i 0.762616 1.66528i
\(418\) −0.128580 + 17.6125i −0.00628905 + 0.861454i
\(419\) −7.20187 19.7870i −0.351834 0.966657i −0.981781 0.190018i \(-0.939145\pi\)
0.629946 0.776639i \(-0.283077\pi\)
\(420\) −0.0964377 + 0.135490i −0.00470568 + 0.00661125i
\(421\) 14.9273 2.63209i 0.727513 0.128280i 0.202388 0.979305i \(-0.435130\pi\)
0.525125 + 0.851025i \(0.324019\pi\)
\(422\) 12.8401 10.6154i 0.625047 0.516748i
\(423\) 9.26812 26.5980i 0.450631 1.29324i
\(424\) 21.1171 34.7932i 1.02554 1.68971i
\(425\) −2.40132 2.86178i −0.116481 0.138817i
\(426\) −13.2573 18.9501i −0.642317 0.918133i
\(427\) −0.0914717 + 0.518762i −0.00442662 + 0.0251046i
\(428\) −27.4314 + 4.42495i −1.32594 + 0.213888i
\(429\) 21.8071 22.1095i 1.05285 1.06745i
\(430\) −0.685670 0.583928i −0.0330660 0.0281595i
\(431\) 17.8689 0.860714 0.430357 0.902659i \(-0.358388\pi\)
0.430357 + 0.902659i \(0.358388\pi\)
\(432\) 18.7615 + 8.94458i 0.902664 + 0.430347i
\(433\) 6.59150 0.316767 0.158384 0.987378i \(-0.449372\pi\)
0.158384 + 0.987378i \(0.449372\pi\)
\(434\) 0.0624106 + 0.0531500i 0.00299581 + 0.00255128i
\(435\) −18.6708 4.86528i −0.895195 0.233272i
\(436\) −26.3756 + 4.25465i −1.26316 + 0.203761i
\(437\) 1.25203 7.10063i 0.0598928 0.339669i
\(438\) 32.4383 2.82443i 1.54996 0.134957i
\(439\) 24.6051 + 29.3233i 1.17434 + 1.39952i 0.898871 + 0.438213i \(0.144388\pi\)
0.275468 + 0.961310i \(0.411167\pi\)
\(440\) −12.4401 7.55028i −0.593059 0.359946i
\(441\) 7.45199 + 19.6288i 0.354857 + 0.934705i
\(442\) −5.38293 + 4.45025i −0.256040 + 0.211677i
\(443\) 25.9385 4.57366i 1.23237 0.217301i 0.480730 0.876869i \(-0.340372\pi\)
0.751645 + 0.659568i \(0.229261\pi\)
\(444\) 0.0597151 + 0.00568895i 0.00283395 + 0.000269986i
\(445\) 3.48157 + 9.56554i 0.165042 + 0.453450i
\(446\) 0.216892 29.7091i 0.0102701 1.40677i
\(447\) −12.4254 17.4878i −0.587703 0.827146i
\(448\) −0.115090 + 0.277718i −0.00543748 + 0.0131210i
\(449\) −25.4654 14.7025i −1.20179 0.693852i −0.240835 0.970566i \(-0.577421\pi\)
−0.960952 + 0.276714i \(0.910755\pi\)
\(450\) 12.4200 + 7.06393i 0.585484 + 0.332997i
\(451\) 2.77145 + 4.80029i 0.130503 + 0.226037i
\(452\) −0.191850 + 13.1388i −0.00902385 + 0.617996i
\(453\) 6.20642 + 13.0739i 0.291603 + 0.614266i
\(454\) 3.65279 + 2.14465i 0.171434 + 0.100653i
\(455\) 0.163736 + 0.137391i 0.00767606 + 0.00644098i
\(456\) 3.70110 + 14.6916i 0.173320 + 0.687998i
\(457\) −11.4536 4.16878i −0.535778 0.195007i 0.0599382 0.998202i \(-0.480910\pi\)
−0.595717 + 0.803195i \(0.703132\pi\)
\(458\) 3.35978 9.02537i 0.156992 0.421728i
\(459\) 1.60650 + 5.53554i 0.0749851 + 0.258377i
\(460\) 4.50705 + 3.89540i 0.210142 + 0.181624i
\(461\) 3.68812 + 1.34237i 0.171773 + 0.0625203i 0.426475 0.904499i \(-0.359755\pi\)
−0.254702 + 0.967020i \(0.581977\pi\)
\(462\) 0.336013 0.156516i 0.0156328 0.00728178i
\(463\) −3.95108 + 4.70872i −0.183622 + 0.218833i −0.850001 0.526781i \(-0.823399\pi\)
0.666379 + 0.745613i \(0.267843\pi\)
\(464\) −34.8621 1.01832i −1.61843 0.0472741i
\(465\) −1.93856 + 2.80952i −0.0898984 + 0.130288i
\(466\) −5.12101 14.3960i −0.237226 0.666882i
\(467\) −17.5858 + 10.1531i −0.813772 + 0.469832i −0.848264 0.529573i \(-0.822352\pi\)
0.0344919 + 0.999405i \(0.489019\pi\)
\(468\) 13.3757 23.1230i 0.618291 1.06886i
\(469\) −0.274410 0.158431i −0.0126711 0.00731565i
\(470\) −3.06756 + 16.6838i −0.141496 + 0.769569i
\(471\) −1.21315 12.8469i −0.0558992 0.591956i
\(472\) 2.92101 3.33021i 0.134450 0.153285i
\(473\) 0.686563 + 1.88632i 0.0315682 + 0.0867330i
\(474\) −15.4590 15.4718i −0.710055 0.710644i
\(475\) 1.80859 + 10.2570i 0.0829837 + 0.470624i
\(476\) −0.0787479 + 0.0273666i −0.00360941 + 0.00125435i
\(477\) −37.0847 + 22.0973i −1.69799 + 1.01177i
\(478\) −2.11539 12.5312i −0.0967556 0.573166i
\(479\) 0.0276350 0.0231885i 0.00126268 0.00105951i −0.642156 0.766574i \(-0.721960\pi\)
0.643419 + 0.765514i \(0.277515\pi\)
\(480\) −11.9899 3.59644i −0.547263 0.164154i
\(481\) 0.0133874 0.0759239i 0.000610414 0.00346183i
\(482\) −5.70938 10.0578i −0.260055 0.458120i
\(483\) −0.146299 + 0.0402825i −0.00665685 + 0.00183292i
\(484\) 5.08495 + 9.11210i 0.231134 + 0.414186i
\(485\) 0.707715 0.0321357
\(486\) −13.1299 17.7089i −0.595585 0.803292i
\(487\) 27.8804i 1.26338i −0.775220 0.631692i \(-0.782361\pi\)
0.775220 0.631692i \(-0.217639\pi\)
\(488\) −39.1880 + 6.02822i −1.77396 + 0.272885i
\(489\) −4.01288 14.5741i −0.181469 0.659064i
\(490\) −6.24232 10.9966i −0.281999 0.496777i
\(491\) 4.20879 + 0.742123i 0.189940 + 0.0334916i 0.267809 0.963472i \(-0.413700\pi\)
−0.0778688 + 0.996964i \(0.524812\pi\)
\(492\) 3.34538 + 3.39740i 0.150821 + 0.153167i
\(493\) −6.21704 7.40918i −0.280002 0.333693i
\(494\) 19.2004 3.24120i 0.863867 0.145829i
\(495\) 7.90075 + 13.2594i 0.355112 + 0.595965i
\(496\) −2.27873 + 5.73401i −0.102318 + 0.257465i
\(497\) −0.349402 + 0.0616090i −0.0156728 + 0.00276354i
\(498\) 20.9234 + 20.9408i 0.937600 + 0.938378i
\(499\) −16.1486 + 5.87762i −0.722912 + 0.263119i −0.677162 0.735834i \(-0.736790\pi\)
−0.0457508 + 0.998953i \(0.514568\pi\)
\(500\) −19.9827 7.60532i −0.893654 0.340120i
\(501\) −12.7738 + 1.20625i −0.570691 + 0.0538912i
\(502\) −26.0095 4.78221i −1.16086 0.213441i
\(503\) −13.1215 + 22.7271i −0.585059 + 1.01335i 0.409809 + 0.912171i \(0.365595\pi\)
−0.994868 + 0.101180i \(0.967738\pi\)
\(504\) 0.245917 0.202965i 0.0109540 0.00904078i
\(505\) 0.613719 + 1.06299i 0.0273101 + 0.0473025i
\(506\) −4.45007 12.5099i −0.197830 0.556132i
\(507\) −9.72526 6.71038i −0.431914 0.298018i
\(508\) 22.6611 + 27.8214i 1.00542 + 1.23438i
\(509\) −16.9060 14.1858i −0.749347 0.628777i 0.185983 0.982553i \(-0.440453\pi\)
−0.935330 + 0.353776i \(0.884897\pi\)
\(510\) −1.46576 3.14675i −0.0649051 0.139340i
\(511\) 0.170846 0.469395i 0.00755777 0.0207648i
\(512\) −22.5786 1.48563i −0.997842 0.0656562i
\(513\) 3.83763 15.6047i 0.169436 0.688965i
\(514\) −6.89538 + 18.5230i −0.304142 + 0.817016i
\(515\) 2.41493 6.63497i 0.106415 0.292372i
\(516\) 0.979478 + 1.42207i 0.0431191 + 0.0626030i
\(517\) 24.3036 28.9639i 1.06887 1.27383i
\(518\) 0.000465925 0 0.000793570i 2.04716e−5 0 3.48675e-5i
\(519\) 9.93172 4.71476i 0.435954 0.206955i
\(520\) −5.83221 + 14.9938i −0.255759 + 0.657520i
\(521\) 22.9164 13.2308i 1.00399 0.579652i 0.0945615 0.995519i \(-0.469855\pi\)
0.909426 + 0.415867i \(0.136522\pi\)
\(522\) 32.1556 + 18.2886i 1.40741 + 0.800470i
\(523\) 17.4375 30.2027i 0.762490 1.32067i −0.179074 0.983836i \(-0.557310\pi\)
0.941564 0.336835i \(-0.109357\pi\)
\(524\) 26.1202 + 15.5934i 1.14107 + 0.681199i
\(525\) 0.178686 0.126960i 0.00779849 0.00554097i
\(526\) 26.5162 + 0.193582i 1.15616 + 0.00844057i
\(527\) −1.60792 + 0.585234i −0.0700419 + 0.0254932i
\(528\) 19.2835 + 20.1639i 0.839206 + 0.877523i
\(529\) −3.05004 17.2976i −0.132611 0.752072i
\(530\) 20.0378 16.5659i 0.870385 0.719578i
\(531\) −4.39255 + 1.66761i −0.190620 + 0.0723682i
\(532\) 0.228281 + 0.0436980i 0.00989726 + 0.00189455i
\(533\) 4.69430 3.93899i 0.203333 0.170617i
\(534\) −1.69295 19.4433i −0.0732610 0.841395i
\(535\) −17.4798 3.08216i −0.755716 0.133253i
\(536\) 4.65484 23.3911i 0.201058 1.01034i
\(537\) 5.45899 20.9492i 0.235573 0.904023i
\(538\) −1.72550 1.46946i −0.0743914 0.0633530i
\(539\) 28.1839i 1.21397i
\(540\) 9.44496 + 9.33124i 0.406446 + 0.401553i
\(541\) 23.3686i 1.00469i −0.864666 0.502347i \(-0.832470\pi\)
0.864666 0.502347i \(-0.167530\pi\)
\(542\) −0.999712 + 1.17390i −0.0429413 + 0.0504233i
\(543\) −28.0312 27.6478i −1.20294 1.18648i
\(544\) −3.85537 4.95091i −0.165298 0.212269i
\(545\) −16.8070 2.96353i −0.719935 0.126944i
\(546\) −0.234915 0.335790i −0.0100534 0.0143705i
\(547\) 2.47846 2.07967i 0.105971 0.0889204i −0.588263 0.808670i \(-0.700188\pi\)
0.694234 + 0.719750i \(0.255743\pi\)
\(548\) −20.1464 3.85645i −0.860609 0.164739i
\(549\) 39.7122 + 13.8378i 1.69488 + 0.590581i
\(550\) 12.2211 + 14.7824i 0.521111 + 0.630324i
\(551\) 4.68246 + 26.5556i 0.199480 + 1.13130i
\(552\) −6.40993 9.45331i −0.272825 0.402360i
\(553\) −0.315294 + 0.114758i −0.0134077 + 0.00488000i
\(554\) −0.251082 + 34.3923i −0.0106674 + 1.46119i
\(555\) 0.0348388 + 0.0159545i 0.00147882 + 0.000677229i
\(556\) 22.1379 37.0829i 0.938858 1.57267i
\(557\) −14.4176 + 24.9721i −0.610894 + 1.05810i 0.380196 + 0.924906i \(0.375857\pi\)
−0.991090 + 0.133194i \(0.957477\pi\)
\(558\) 4.98605 4.23907i 0.211076 0.179454i
\(559\) 1.92194 1.10963i 0.0812894 0.0469324i
\(560\) −0.127680 + 0.143440i −0.00539545 + 0.00606145i
\(561\) −0.621261 + 7.71232i −0.0262296 + 0.325614i
\(562\) 2.18381 + 1.28217i 0.0921183 + 0.0540850i
\(563\) −11.4121 + 13.6005i −0.480964 + 0.573191i −0.950895 0.309512i \(-0.899834\pi\)
0.469931 + 0.882703i \(0.344279\pi\)
\(564\) 13.9722 29.3697i 0.588336 1.23669i
\(565\) −2.87086 + 7.88761i −0.120778 + 0.331834i
\(566\) 4.46342 + 1.66155i 0.187612 + 0.0698403i
\(567\) −0.331317 + 0.0678777i −0.0139140 + 0.00285059i
\(568\) −12.8427 23.4139i −0.538869 0.982425i
\(569\) −8.74755 + 24.0337i −0.366716 + 1.00754i 0.609886 + 0.792490i \(0.291215\pi\)
−0.976602 + 0.215055i \(0.931007\pi\)
\(570\) −0.847499 + 9.64091i −0.0354978 + 0.403813i
\(571\) 12.8608 + 10.7915i 0.538209 + 0.451611i 0.870925 0.491416i \(-0.163520\pi\)
−0.332716 + 0.943027i \(0.607965\pi\)
\(572\) 27.8028 22.6459i 1.16249 0.946873i
\(573\) 0.522639 6.48804i 0.0218336 0.271042i
\(574\) 0.0689156 0.0245150i 0.00287648 0.00102323i
\(575\) −3.92586 6.79978i −0.163720 0.283571i
\(576\) 20.4149 + 12.6187i 0.850622 + 0.525778i
\(577\) −4.28264 + 7.41775i −0.178289 + 0.308805i −0.941294 0.337587i \(-0.890389\pi\)
0.763006 + 0.646392i \(0.223723\pi\)
\(578\) −4.03284 + 21.9338i −0.167744 + 0.912326i
\(579\) 17.8450 38.9670i 0.741613 1.61941i
\(580\) −20.8220 7.92475i −0.864587 0.329057i
\(581\) 0.426744 0.155322i 0.0177043 0.00644385i
\(582\) −1.31051 0.351733i −0.0543224 0.0145798i
\(583\) −57.0681 + 10.0627i −2.36352 + 0.416752i
\(584\) 37.5892 + 0.823379i 1.55545 + 0.0340717i
\(585\) 12.9195 11.1475i 0.534156 0.460893i
\(586\) 5.98740 + 35.4685i 0.247337 + 1.46519i
\(587\) 21.1215 + 25.1716i 0.871778 + 1.03894i 0.998892 + 0.0470560i \(0.0149839\pi\)
−0.127115 + 0.991888i \(0.540572\pi\)
\(588\) 6.09391 + 23.4654i 0.251309 + 0.967699i
\(589\) 4.69804 + 0.828391i 0.193579 + 0.0341333i
\(590\) 2.46084 1.39691i 0.101311 0.0575099i
\(591\) −5.64067 + 5.71889i −0.232026 + 0.235244i
\(592\) 0.0678327 + 0.0140143i 0.00278791 + 0.000575984i
\(593\) 12.9354i 0.531195i 0.964084 + 0.265597i \(0.0855692\pi\)
−0.964084 + 0.265597i \(0.914431\pi\)
\(594\) −8.04032 28.4797i −0.329898 1.16854i
\(595\) −0.0532545 −0.00218322
\(596\) −12.0712 21.6312i −0.494454 0.886048i
\(597\) −6.46379 + 24.8051i −0.264545 + 1.01521i
\(598\) −12.7659 + 7.24667i −0.522037 + 0.296338i
\(599\) −3.81637 + 21.6437i −0.155932 + 0.884337i 0.801996 + 0.597330i \(0.203772\pi\)
−0.957928 + 0.287007i \(0.907340\pi\)
\(600\) 13.3713 + 9.66513i 0.545882 + 0.394577i
\(601\) −12.7487 + 10.6974i −0.520030 + 0.436357i −0.864642 0.502388i \(-0.832455\pi\)
0.344612 + 0.938745i \(0.388010\pi\)
\(602\) 0.0261205 0.00440938i 0.00106459 0.000179713i
\(603\) −15.9919 + 19.6003i −0.651240 + 0.798187i
\(604\) 5.48567 + 15.7851i 0.223209 + 0.642287i
\(605\) 1.15749 + 6.56445i 0.0470587 + 0.266883i
\(606\) −0.608149 2.27341i −0.0247044 0.0923511i
\(607\) 5.65521 + 15.5376i 0.229538 + 0.630650i 0.999976 0.00686394i \(-0.00218488\pi\)
−0.770438 + 0.637514i \(0.779963\pi\)
\(608\) 2.40712 + 17.3281i 0.0976214 + 0.702745i
\(609\) 0.462620 0.328700i 0.0187463 0.0133196i
\(610\) −24.9098 4.58003i −1.00857 0.185440i
\(611\) −36.2004 20.9003i −1.46451 0.845537i
\(612\) 1.15030 + 6.55547i 0.0464982 + 0.264989i
\(613\) 8.59588 4.96283i 0.347184 0.200447i −0.316260 0.948672i \(-0.602427\pi\)
0.663444 + 0.748226i \(0.269094\pi\)
\(614\) 35.9222 12.7784i 1.44970 0.515694i
\(615\) 1.30617 + 2.75147i 0.0526698 + 0.110950i
\(616\) 0.405319 0.137549i 0.0163308 0.00554200i
\(617\) −16.0619 + 19.1418i −0.646626 + 0.770619i −0.985401 0.170248i \(-0.945543\pi\)
0.338775 + 0.940867i \(0.389987\pi\)
\(618\) −7.76941 + 11.0861i −0.312532 + 0.445948i
\(619\) −21.8055 7.93656i −0.876437 0.318997i −0.135666 0.990755i \(-0.543317\pi\)
−0.740771 + 0.671757i \(0.765540\pi\)
\(620\) −2.57734 + 2.98203i −0.103509 + 0.119761i
\(621\) 1.30489 + 12.0439i 0.0523636 + 0.483306i
\(622\) −32.5784 12.1276i −1.30628 0.486274i
\(623\) −0.281352 0.102404i −0.0112721 0.00410273i
\(624\) 18.2517 24.8661i 0.730651 0.995440i
\(625\) 2.43670 + 2.04464i 0.0974682 + 0.0817855i
\(626\) 2.43204 4.14228i 0.0972038 0.165559i
\(627\) 12.2508 17.7550i 0.489252 0.709066i
\(628\) 0.217549 14.8988i 0.00868115 0.594526i
\(629\) 0.00960425 + 0.0166350i 0.000382946 + 0.000663283i
\(630\) 0.190945 0.0709008i 0.00760742 0.00282476i
\(631\) −8.21645 4.74377i −0.327092 0.188847i 0.327457 0.944866i \(-0.393808\pi\)
−0.654549 + 0.756019i \(0.727142\pi\)
\(632\) −15.8060 19.6972i −0.628728 0.783514i
\(633\) −20.3138 + 1.91826i −0.807402 + 0.0762441i
\(634\) −29.5813 0.215959i −1.17482 0.00857682i
\(635\) 7.83959 + 21.5391i 0.311105 + 0.854753i
\(636\) −45.3382 + 20.7172i −1.79778 + 0.821491i
\(637\) 30.6855 5.41068i 1.21580 0.214379i
\(638\) 31.6407 + 38.2719i 1.25267 + 1.51520i
\(639\) 0.390060 + 28.3220i 0.0154305 + 1.12040i
\(640\) −13.3122 5.63097i −0.526213 0.222584i
\(641\) 7.44194 + 8.86896i 0.293939 + 0.350303i 0.892721 0.450609i \(-0.148793\pi\)
−0.598783 + 0.800912i \(0.704349\pi\)
\(642\) 30.8363 + 14.3948i 1.21701 + 0.568117i
\(643\) −5.63647 + 31.9660i −0.222281 + 1.26062i 0.645535 + 0.763731i \(0.276635\pi\)
−0.867816 + 0.496886i \(0.834477\pi\)
\(644\) −0.172982 + 0.0279038i −0.00681646 + 0.00109956i
\(645\) 0.292815 + 1.06345i 0.0115296 + 0.0418734i
\(646\) −3.14555 + 3.69362i −0.123760 + 0.145323i
\(647\) 40.5576 1.59448 0.797242 0.603660i \(-0.206292\pi\)
0.797242 + 0.603660i \(0.206292\pi\)
\(648\) −12.8521 21.9732i −0.504878 0.863191i
\(649\) −6.30702 −0.247572
\(650\) 13.7483 16.1437i 0.539252 0.633210i
\(651\) −0.0266524 0.0967970i −0.00104459 0.00379377i
\(652\) −2.77973 17.2322i −0.108863 0.674867i
\(653\) 1.89217 10.7310i 0.0740463 0.419937i −0.925141 0.379624i \(-0.876053\pi\)
0.999187 0.0403132i \(-0.0128356\pi\)
\(654\) 29.6496 + 13.8408i 1.15939 + 0.541218i
\(655\) 12.4909 + 14.8861i 0.488061 + 0.581649i
\(656\) 3.41429 + 4.31908i 0.133306 + 0.168632i
\(657\) −34.8075 19.4620i −1.35797 0.759285i
\(658\) −0.317920 0.384549i −0.0123938 0.0149913i
\(659\) −15.6898 + 2.76653i −0.611187 + 0.107769i −0.470670 0.882309i \(-0.655988\pi\)
−0.140517 + 0.990078i \(0.544877\pi\)
\(660\) 7.40731 + 16.2104i 0.288329 + 0.630988i
\(661\) −3.94900 10.8498i −0.153598 0.422008i 0.838897 0.544290i \(-0.183201\pi\)
−0.992495 + 0.122282i \(0.960979\pi\)
\(662\) −39.7303 0.290051i −1.54416 0.0112732i
\(663\) 8.51612 0.804189i 0.330739 0.0312321i
\(664\) 21.3930 + 26.6598i 0.830211 + 1.03460i
\(665\) 0.128580 + 0.0742359i 0.00498613 + 0.00287874i
\(666\) −0.0565833 0.0468585i −0.00219256 0.00181573i
\(667\) −10.1641 17.6047i −0.393555 0.681658i
\(668\) −14.8140 0.216310i −0.573169 0.00836930i
\(669\) −20.6650 + 29.9496i −0.798956 + 1.15792i
\(670\) 7.71363 13.1380i 0.298003 0.507563i
\(671\) 43.2446 + 36.2865i 1.66944 + 1.40083i
\(672\) 0.307720 0.202158i 0.0118706 0.00779843i
\(673\) 11.8463 + 4.31169i 0.456640 + 0.166203i 0.560091 0.828431i \(-0.310766\pi\)
−0.103451 + 0.994635i \(0.532988\pi\)
\(674\) −22.7312 8.46192i −0.875574 0.325941i
\(675\) −7.72164 15.7038i −0.297206 0.604440i
\(676\) −10.3224 8.92157i −0.397016 0.343137i
\(677\) −35.2718 12.8379i −1.35560 0.493399i −0.440912 0.897551i \(-0.645345\pi\)
−0.914692 + 0.404151i \(0.867567\pi\)
\(678\) 9.23623 13.1791i 0.354715 0.506139i
\(679\) −0.0133803 + 0.0159461i −0.000513490 + 0.000611954i
\(680\) −1.28814 3.79579i −0.0493979 0.145562i
\(681\) −2.22479 4.68656i −0.0852543 0.179589i
\(682\) 8.27700 2.94433i 0.316943 0.112744i
\(683\) 24.5827 14.1928i 0.940631 0.543073i 0.0504727 0.998725i \(-0.483927\pi\)
0.890158 + 0.455652i \(0.150594\pi\)
\(684\) 6.36087 17.4314i 0.243214 0.666504i
\(685\) −11.3475 6.55148i −0.433566 0.250319i
\(686\) 0.731660 + 0.134526i 0.0279349 + 0.00513623i
\(687\) −9.61496 + 6.83161i −0.366833 + 0.260642i
\(688\) 0.946095 + 1.75512i 0.0360696 + 0.0669132i
\(689\) 21.9116 + 60.2016i 0.834765 + 2.29350i
\(690\) −1.88542 7.04817i −0.0717767 0.268319i
\(691\) 5.71664 + 32.4207i 0.217471 + 1.23334i 0.876566 + 0.481281i \(0.159828\pi\)
−0.659095 + 0.752060i \(0.729060\pi\)
\(692\) 11.9913 4.16724i 0.455841 0.158415i
\(693\) −0.448132 0.0726695i −0.0170231 0.00276049i
\(694\) −6.95573 + 1.17419i −0.264036 + 0.0445717i
\(695\) 21.1339 17.7334i 0.801654 0.672667i
\(696\) 34.6186 + 25.0231i 1.31221 + 0.948500i
\(697\) −0.265127 + 1.50361i −0.0100424 + 0.0569533i
\(698\) 2.06104 1.16996i 0.0780114 0.0442837i
\(699\) −4.71889 + 18.1090i −0.178485 + 0.684946i
\(700\) 0.221021 0.123340i 0.00835382 0.00466180i
\(701\) −2.58326 −0.0975684 −0.0487842 0.998809i \(-0.515535\pi\)
−0.0487842 + 0.998809i \(0.515535\pi\)
\(702\) −29.4640 + 14.2214i −1.11205 + 0.536753i
\(703\) 0.0535526i 0.00201978i
\(704\) 19.6080 + 25.5626i 0.739003 + 0.963425i
\(705\) 14.5893 14.7916i 0.549466 0.557085i
\(706\) −38.5102 + 21.8606i −1.44935 + 0.822734i
\(707\) −0.0355543 0.00626918i −0.00133716 0.000235777i
\(708\) −5.25112 + 1.36370i −0.197349 + 0.0512510i
\(709\) −25.7394 30.6751i −0.966665 1.15203i −0.988340 0.152261i \(-0.951345\pi\)
0.0216755 0.999765i \(-0.493100\pi\)
\(710\) −2.83951 16.8208i −0.106565 0.631273i
\(711\) 5.01433 + 26.3134i 0.188052 + 0.986828i
\(712\) 0.493528 22.5308i 0.0184958 0.844376i
\(713\) −3.54170 + 0.624497i −0.132638 + 0.0233876i
\(714\) 0.0986140 + 0.0264674i 0.00369054 + 0.000990517i
\(715\) 21.5247 7.83435i 0.804978 0.292988i
\(716\) 8.89181 23.3629i 0.332302 0.873113i
\(717\) −6.48064 + 14.1514i −0.242024 + 0.528493i
\(718\) −7.55904 + 41.1121i −0.282101 + 1.53429i
\(719\) −1.78773 + 3.09644i −0.0666710 + 0.115478i −0.897434 0.441149i \(-0.854571\pi\)
0.830763 + 0.556626i \(0.187904\pi\)
\(720\) 9.67219 + 11.8949i 0.360461 + 0.443296i
\(721\) 0.103840 + 0.179856i 0.00386720 + 0.00669818i
\(722\) −12.5724 + 4.47231i −0.467897 + 0.166442i
\(723\) −1.13733 + 14.1188i −0.0422978 + 0.525084i
\(724\) −28.7114 35.2495i −1.06705 1.31004i
\(725\) 22.4945 + 18.8751i 0.835426 + 0.701005i
\(726\) 1.11914 12.7310i 0.0415351 0.472492i
\(727\) 11.0625 30.3940i 0.410285 1.12725i −0.546755 0.837293i \(-0.684137\pi\)
0.957040 0.289956i \(-0.0936408\pi\)
\(728\) −0.227570 0.414888i −0.00843429 0.0153768i
\(729\) 1.11517 + 26.9770i 0.0413026 + 0.999147i
\(730\) 22.5084 + 8.37899i 0.833074 + 0.310120i
\(731\) −0.189115 + 0.519591i −0.00699469 + 0.0192177i
\(732\) 43.8505 + 20.8612i 1.62076 + 0.771052i
\(733\) 19.2878 22.9862i 0.712409 0.849016i −0.281460 0.959573i \(-0.590819\pi\)
0.993870 + 0.110556i \(0.0352633\pi\)
\(734\) 24.3571 + 14.3007i 0.899038 + 0.527848i
\(735\) −1.24349 + 15.4367i −0.0458670 + 0.569392i
\(736\) −6.17304 11.6546i −0.227541 0.429595i
\(737\) −29.4077 + 16.9785i −1.08325 + 0.625413i
\(738\) −1.05123 5.74419i −0.0386962 0.211447i
\(739\) 6.60975 11.4484i 0.243143 0.421137i −0.718465 0.695564i \(-0.755155\pi\)
0.961608 + 0.274427i \(0.0884881\pi\)
\(740\) 0.0379911 + 0.0226801i 0.00139658 + 0.000833738i
\(741\) −21.6828 9.92966i −0.796537 0.364775i
\(742\) −0.00558261 + 0.764688i −0.000204944 + 0.0280726i
\(743\) 24.1121 8.77610i 0.884588 0.321964i 0.140528 0.990077i \(-0.455120\pi\)
0.744060 + 0.668113i \(0.232898\pi\)
\(744\) 6.25466 4.24104i 0.229307 0.155484i
\(745\) −2.74776 15.5833i −0.100670 0.570929i
\(746\) −27.2532 32.9649i −0.997811 1.20693i
\(747\) −6.78678 35.6146i −0.248315 1.30307i
\(748\) −1.67971 + 8.77495i −0.0614165 + 0.320844i
\(749\) 0.399926 0.335578i 0.0146130 0.0122617i
\(750\) 15.0110 + 21.4568i 0.548123 + 0.783492i
\(751\) 24.9654 + 4.40207i 0.911000 + 0.160634i 0.609458 0.792819i \(-0.291387\pi\)
0.301543 + 0.953453i \(0.402498\pi\)
\(752\) 19.7193 31.9618i 0.719089 1.16553i
\(753\) 23.0596 + 22.7442i 0.840339 + 0.828845i
\(754\) 35.5945 41.7964i 1.29628 1.52213i
\(755\) 10.6749i 0.388500i
\(756\) −0.388819 + 0.0363914i −0.0141412 + 0.00132354i
\(757\) 7.76347i 0.282168i 0.989998 + 0.141084i \(0.0450588\pi\)
−0.989998 + 0.141084i \(0.954941\pi\)
\(758\) 2.55806 + 2.17849i 0.0929130 + 0.0791263i
\(759\) −4.10064 + 15.7364i −0.148844 + 0.571196i
\(760\) −2.18112 + 10.9604i −0.0791175 + 0.397575i
\(761\) −9.22102 1.62592i −0.334262 0.0589394i 0.00399834 0.999992i \(-0.498727\pi\)
−0.338260 + 0.941053i \(0.609838\pi\)
\(762\) −3.81207 43.7813i −0.138097 1.58603i
\(763\) 0.384534 0.322662i 0.0139211 0.0116812i
\(764\) 1.41307 7.38198i 0.0511231 0.267071i
\(765\) −0.680546 + 4.19673i −0.0246052 + 0.151733i
\(766\) −14.7846 + 12.2229i −0.534190 + 0.441633i
\(767\) 1.21081 + 6.86682i 0.0437197 + 0.247947i
\(768\) 21.8524 + 17.0433i 0.788529 + 0.614997i
\(769\) −25.0021 + 9.10003i −0.901600 + 0.328156i −0.750894 0.660423i \(-0.770377\pi\)
−0.150706 + 0.988579i \(0.548155\pi\)
\(770\) 0.273409 + 0.00199603i 0.00985299 + 7.19319e-5i
\(771\) 19.7330 14.0207i 0.710668 0.504943i
\(772\) 25.3676 42.4929i 0.913001 1.52935i
\(773\) −8.90177 + 15.4183i −0.320174 + 0.554558i −0.980524 0.196400i \(-0.937075\pi\)
0.660349 + 0.750959i \(0.270408\pi\)
\(774\) −0.0136851 2.11478i −0.000491900 0.0760141i
\(775\) 4.49899 2.59749i 0.161608 0.0933047i
\(776\) −1.46023 0.567993i −0.0524190 0.0203898i
\(777\) −0.00101816 0.000483337i −3.65262e−5 1.73396e-5i
\(778\) 0.624535 1.06372i 0.0223906 0.0381361i
\(779\) 2.73614 3.26081i 0.0980325 0.116831i
\(780\) 16.2271 11.1768i 0.581025 0.400193i
\(781\) −13.0043 + 35.7290i −0.465331 + 1.27849i
\(782\) 1.27596 3.42761i 0.0456283 0.122571i
\(783\) −19.9914 40.6574i −0.714435 1.45298i
\(784\) 4.05415 + 27.6992i 0.144791 + 0.989258i
\(785\) 3.25542 8.94420i 0.116191 0.319232i
\(786\) −15.7317 33.7733i −0.561132 1.20465i
\(787\) 16.8309 + 14.1228i 0.599957 + 0.503424i 0.891432 0.453155i \(-0.149701\pi\)
−0.291475 + 0.956579i \(0.594146\pi\)
\(788\) −7.19156 + 5.85765i −0.256189 + 0.208670i
\(789\) −26.7308 18.4441i −0.951641 0.656627i
\(790\) −5.40686 15.1996i −0.192367 0.540776i
\(791\) −0.123444 0.213812i −0.00438917 0.00760227i
\(792\) −5.65996 33.6990i −0.201118 1.19744i
\(793\) 31.2053 54.0491i 1.10813 1.91934i
\(794\) −22.6331 4.16142i −0.803220 0.147683i
\(795\) −31.7010 + 2.99357i −1.12432 + 0.106171i
\(796\) −10.5285 + 27.6632i −0.373171 + 0.980496i
\(797\) 14.4147 5.24652i 0.510595 0.185841i −0.0738582 0.997269i \(-0.523531\pi\)
0.584453 + 0.811427i \(0.301309\pi\)
\(798\) −0.201204 0.201370i −0.00712253 0.00712844i
\(799\) 10.2565 1.80851i 0.362851 0.0639803i
\(800\) 14.1373 + 12.7702i 0.499831 + 0.451495i
\(801\) −11.6654 + 20.8634i −0.412177 + 0.737172i
\(802\) 7.45692 1.25880i 0.263313 0.0444496i
\(803\) −34.4098 41.0079i −1.21429 1.44714i
\(804\) −20.8132 + 20.4945i −0.734027 + 0.722787i
\(805\) −0.110228 0.0194361i −0.00388501 0.000685032i
\(806\) −4.79466 8.44641i −0.168885 0.297512i
\(807\) 0.736871 + 2.67619i 0.0259391 + 0.0942064i
\(808\) −0.413155 2.68582i −0.0145347 0.0944869i
\(809\) 38.3503i 1.34832i −0.738584 0.674162i \(-0.764505\pi\)
0.738584 0.674162i \(-0.235495\pi\)
\(810\) −3.14725 15.9535i −0.110583 0.560548i
\(811\) 2.84191 0.0997928 0.0498964 0.998754i \(-0.484111\pi\)
0.0498964 + 0.998754i \(0.484111\pi\)
\(812\) 0.572227 0.319328i 0.0200812 0.0112062i
\(813\) 1.82068 0.501312i 0.0638541 0.0175818i
\(814\) −0.0486848 0.0857645i −0.00170640 0.00300604i
\(815\) 1.93619 10.9807i 0.0678219 0.384637i
\(816\) 0.498812 + 7.66905i 0.0174619 + 0.268470i
\(817\) 1.18091 0.990901i 0.0413148 0.0346673i
\(818\) 1.01585 + 6.01776i 0.0355185 + 0.210406i
\(819\) 0.00691176 + 0.501858i 0.000241516 + 0.0175364i
\(820\) 1.15448 + 3.32205i 0.0403163 + 0.116011i
\(821\) −6.41903 36.4041i −0.224026 1.27051i −0.864539 0.502565i \(-0.832390\pi\)
0.640514 0.767947i \(-0.278721\pi\)
\(822\) 17.7567 + 17.7714i 0.619335 + 0.619849i
\(823\) −17.0571 46.8639i −0.594572 1.63357i −0.761918 0.647674i \(-0.775742\pi\)
0.167346 0.985898i \(-0.446480\pi\)
\(824\) −10.3078 + 11.7517i −0.359088 + 0.409391i
\(825\) −2.20844 23.3867i −0.0768879 0.814219i
\(826\) −0.0150507 + 0.0818575i −0.000523680 + 0.00284819i
\(827\) −25.4053 14.6677i −0.883428 0.510047i −0.0116409 0.999932i \(-0.503705\pi\)
−0.871787 + 0.489885i \(0.837039\pi\)
\(828\) −0.0116007 + 13.9885i −0.000403153 + 0.486134i
\(829\) −35.7709 + 20.6523i −1.24237 + 0.717285i −0.969577 0.244786i \(-0.921282\pi\)
−0.272797 + 0.962072i \(0.587949\pi\)
\(830\) 7.31806 + 20.5723i 0.254014 + 0.714074i
\(831\) 23.9226 34.6706i 0.829864 1.20271i
\(832\) 24.0672 26.2558i 0.834378 0.910255i
\(833\) −4.99017 + 5.94706i −0.172899 + 0.206053i
\(834\) −47.9481 + 22.3344i −1.66031 + 0.773376i
\(835\) −8.89328 3.23689i −0.307765 0.112017i
\(836\) 16.2877 18.8452i 0.563323 0.651774i
\(837\) −7.96870 + 0.863366i −0.275439 + 0.0298423i
\(838\) −10.3890 + 27.9079i −0.358882 + 0.964063i
\(839\) −19.7178 7.17669i −0.680734 0.247767i −0.0215712 0.999767i \(-0.506867\pi\)
−0.659163 + 0.752001i \(0.729089\pi\)
\(840\) 0.228067 0.0574545i 0.00786907 0.00198237i
\(841\) 36.0233 + 30.2272i 1.24218 + 1.04232i
\(842\) −18.4855 10.8533i −0.637051 0.374029i
\(843\) −1.33008 2.80184i −0.0458106 0.0965006i
\(844\) −23.5582 0.343993i −0.810908 0.0118407i
\(845\) −4.35769 7.54774i −0.149909 0.259650i
\(846\) −34.3672 + 20.1396i −1.18157 + 0.692412i
\(847\) −0.169793 0.0980298i −0.00583414 0.00336834i
\(848\) −54.6392 + 18.0986i −1.87632 + 0.621509i
\(849\) −3.37852 4.75500i −0.115950 0.163191i
\(850\) −0.0385690 + 5.28306i −0.00132291 + 0.181207i
\(851\) 0.0138079 + 0.0379369i 0.000473329 + 0.00130046i
\(852\) −3.10185 + 32.5591i −0.106268 + 1.11546i
\(853\) 23.5698 4.15599i 0.807015 0.142299i 0.245105 0.969497i \(-0.421178\pi\)
0.561910 + 0.827198i \(0.310067\pi\)
\(854\) 0.574151 0.474670i 0.0196470 0.0162429i
\(855\) 7.49332 9.18413i 0.256266 0.314091i
\(856\) 33.5923 + 20.3882i 1.14816 + 0.696854i
\(857\) 11.8477 + 14.1196i 0.404710 + 0.482315i 0.929450 0.368948i \(-0.120282\pi\)
−0.524740 + 0.851263i \(0.675837\pi\)
\(858\) −43.7520 + 3.80953i −1.49367 + 0.130055i
\(859\) 4.54416 25.7712i 0.155045 0.879303i −0.803700 0.595035i \(-0.797138\pi\)
0.958745 0.284268i \(-0.0917506\pi\)
\(860\) 0.202833 + 1.25741i 0.00691656 + 0.0428775i
\(861\) −0.0866903 0.0225900i −0.00295440 0.000769864i
\(862\) −19.2392 16.3844i −0.655288 0.558055i
\(863\) −16.7507 −0.570199 −0.285100 0.958498i \(-0.592027\pi\)
−0.285100 + 0.958498i \(0.592027\pi\)
\(864\) −11.9987 26.8334i −0.408206 0.912890i
\(865\) 8.10931 0.275725
\(866\) −7.09697 6.04390i −0.241165 0.205380i
\(867\) 19.1802 19.4462i 0.651393 0.660426i
\(868\) −0.0184622 0.114452i −0.000626647 0.00388474i
\(869\) −6.24399 + 35.4114i −0.211813 + 1.20125i
\(870\) 15.6415 + 22.3580i 0.530295 + 0.758008i
\(871\) 24.1312 + 28.7584i 0.817653 + 0.974441i
\(872\) 32.2994 + 19.6035i 1.09380 + 0.663859i
\(873\) 1.08564 + 1.25822i 0.0367435 + 0.0425842i
\(874\) −7.85878 + 6.49713i −0.265827 + 0.219769i
\(875\) 0.395622 0.0697589i 0.0133745 0.00235828i
\(876\) −37.5156 26.7024i −1.26754 0.902192i
\(877\) −11.8079 32.4419i −0.398724 1.09549i −0.962907 0.269835i \(-0.913031\pi\)
0.564183 0.825650i \(-0.309191\pi\)
\(878\) 0.395198 54.1330i 0.0133373 1.82690i
\(879\) 18.3428 40.0541i 0.618688 1.35099i
\(880\) 6.47105 + 19.5359i 0.218139 + 0.658555i
\(881\) −26.4274 15.2579i −0.890362 0.514050i −0.0163008 0.999867i \(-0.505189\pi\)
−0.874061 + 0.485817i \(0.838522\pi\)
\(882\) 9.97466 27.9669i 0.335864 0.941696i
\(883\) 16.0187 + 27.7452i 0.539073 + 0.933701i 0.998954 + 0.0457210i \(0.0145585\pi\)
−0.459882 + 0.887980i \(0.652108\pi\)
\(884\) 9.87626 + 0.144211i 0.332175 + 0.00485035i
\(885\) −3.45444 0.278270i −0.116120 0.00935395i
\(886\) −32.1213 18.8592i −1.07914 0.633588i
\(887\) −0.309940 0.260070i −0.0104068 0.00873231i 0.637569 0.770393i \(-0.279940\pi\)
−0.647976 + 0.761661i \(0.724384\pi\)
\(888\) −0.0590781 0.0608794i −0.00198253 0.00204298i
\(889\) −0.633532 0.230587i −0.0212480 0.00773363i
\(890\) 5.02231 13.4914i 0.168348 0.452233i
\(891\) −11.4535 + 34.3865i −0.383706 + 1.15199i
\(892\) −27.4745 + 31.7885i −0.919915 + 1.06436i
\(893\) −27.2849 9.93091i −0.913056 0.332325i
\(894\) −2.65672 + 30.2221i −0.0888539 + 1.01078i
\(895\) 10.2643 12.2325i 0.343097 0.408887i
\(896\) 0.378562 0.193487i 0.0126469 0.00646394i
\(897\) 17.9204 + 1.44356i 0.598345 + 0.0481992i
\(898\) 13.9372 + 39.1798i 0.465091 + 1.30745i
\(899\) 11.6479 6.72494i 0.388481 0.224289i
\(900\) −6.89535 18.9938i −0.229845 0.633127i
\(901\) −13.8235 7.98102i −0.460529 0.265886i
\(902\) 1.41752 7.70961i 0.0471983 0.256702i
\(903\) −0.0294975 0.0135084i −0.000981617 0.000449533i
\(904\) 12.2538 13.9704i 0.407555 0.464649i
\(905\) −9.93269 27.2898i −0.330174 0.907145i
\(906\) 5.30542 19.7673i 0.176261 0.656724i
\(907\) −6.48461 36.7760i −0.215318 1.22113i −0.880354 0.474317i \(-0.842695\pi\)
0.665036 0.746811i \(-0.268416\pi\)
\(908\) −1.96643 5.65844i −0.0652582 0.187782i
\(909\) −0.948397 + 2.72175i −0.0314563 + 0.0902748i
\(910\) −0.0503152 0.298060i −0.00166793 0.00988059i
\(911\) 12.5899 10.5642i 0.417122 0.350007i −0.409945 0.912110i \(-0.634452\pi\)
0.827067 + 0.562103i \(0.190008\pi\)
\(912\) 9.48617 19.2119i 0.314119 0.636169i
\(913\) 8.45110 47.9286i 0.279691 1.58620i
\(914\) 8.50950 + 14.9906i 0.281469 + 0.495844i
\(915\) 22.0847 + 21.7826i 0.730097 + 0.720111i
\(916\) −11.8930 + 6.63682i −0.392956 + 0.219287i
\(917\) −0.571569 −0.0188749
\(918\) 3.34597 7.43307i 0.110433 0.245328i
\(919\) 37.7169i 1.24417i 0.782951 + 0.622084i \(0.213714\pi\)
−0.782951 + 0.622084i \(0.786286\pi\)
\(920\) −1.28089 8.32675i −0.0422296 0.274525i
\(921\) −45.1872 11.7750i −1.48897 0.387999i
\(922\) −2.74010 4.82703i −0.0902404 0.158970i
\(923\) 41.3968 + 7.29938i 1.36259 + 0.240262i
\(924\) −0.505294 0.139580i −0.0166229 0.00459185i
\(925\) −0.0374859 0.0446739i −0.00123253 0.00146887i
\(926\) 8.57160 1.44697i 0.281680 0.0475502i
\(927\) 15.5006 5.88472i 0.509105 0.193280i
\(928\) 36.6018 + 33.0623i 1.20151 + 1.08532i
\(929\) 35.1367 6.19555i 1.15280 0.203270i 0.435601 0.900140i \(-0.356536\pi\)
0.717197 + 0.696870i \(0.245425\pi\)
\(930\) 4.66333 1.24746i 0.152917 0.0409059i
\(931\) 20.3386 7.40265i 0.666571 0.242612i
\(932\) −7.68631 + 20.1955i −0.251774 + 0.661527i
\(933\) 24.6597 + 34.7066i 0.807323 + 1.13624i
\(934\) 28.2440 + 5.19306i 0.924172 + 0.169922i
\(935\) −2.85357 + 4.94252i −0.0933216 + 0.161638i
\(936\) −35.6035 + 12.6318i −1.16374 + 0.412882i
\(937\) 17.8075 + 30.8434i 0.581744 + 1.00761i 0.995273 + 0.0971193i \(0.0309628\pi\)
−0.413529 + 0.910491i \(0.635704\pi\)
\(938\) 0.150184 + 0.422193i 0.00490369 + 0.0137851i
\(939\) −5.31458 + 2.52293i −0.173435 + 0.0823326i
\(940\) 18.6006 15.1505i 0.606685 0.494156i
\(941\) 2.81572 + 2.36267i 0.0917898 + 0.0770208i 0.687528 0.726158i \(-0.258696\pi\)
−0.595738 + 0.803179i \(0.703140\pi\)
\(942\) −10.4735 + 14.9445i −0.341244 + 0.486918i
\(943\) −1.09753 + 3.01545i −0.0357406 + 0.0981965i
\(944\) −6.19856 + 0.907241i −0.201746 + 0.0295282i
\(945\) −0.242242 0.0595740i −0.00788013 0.00193794i
\(946\) 0.990396 2.66050i 0.0322006 0.0865002i
\(947\) −1.54304 + 4.23946i −0.0501420 + 0.137764i −0.962236 0.272218i \(-0.912243\pi\)
0.912094 + 0.409982i \(0.134465\pi\)
\(948\) 2.45800 + 30.8330i 0.0798320 + 1.00141i
\(949\) −38.0418 + 45.3365i −1.23489 + 1.47169i
\(950\) 7.45762 12.7019i 0.241957 0.412105i
\(951\) 29.8207 + 20.5761i 0.967002 + 0.667227i
\(952\) 0.109880 + 0.0427406i 0.00356122 + 0.00138523i
\(953\) 11.2227 6.47942i 0.363538 0.209889i −0.307093 0.951679i \(-0.599356\pi\)
0.670632 + 0.741790i \(0.266023\pi\)
\(954\) 60.1901 + 10.2120i 1.94873 + 0.330625i
\(955\) 2.40058 4.15793i 0.0776809 0.134547i
\(956\) −9.21258 + 15.4319i −0.297956 + 0.499102i
\(957\) −5.71767 60.5484i −0.184826 1.95725i
\(958\) −0.0510163 0.000372445i −0.00164826 1.20332e-5i
\(959\) 0.362157 0.131814i 0.0116946 0.00425650i
\(960\) 9.61172 + 14.8661i 0.310217 + 0.479801i
\(961\) 4.96990 + 28.1857i 0.160319 + 0.909217i
\(962\) −0.0840304 + 0.0694709i −0.00270925 + 0.00223983i
\(963\) −21.3346 35.8046i −0.687497 1.15379i
\(964\) −3.07503 + 16.0641i −0.0990399 + 0.517391i
\(965\) 24.2171 20.3205i 0.779575 0.654141i
\(966\) 0.194454 + 0.0907737i 0.00625646 + 0.00292059i
\(967\) 53.8023 + 9.48680i 1.73017 + 0.305075i 0.948065 0.318076i \(-0.103037\pi\)
0.782101 + 0.623151i \(0.214148\pi\)
\(968\) 2.88021 14.4734i 0.0925733 0.465192i
\(969\) 5.72869 1.57735i 0.184032 0.0506719i
\(970\) −0.761986 0.648921i −0.0244659 0.0208356i
\(971\) 42.8083i 1.37378i −0.726760 0.686892i \(-0.758975\pi\)
0.726760 0.686892i \(-0.241025\pi\)
\(972\) −2.10093 + 31.1060i −0.0673875 + 0.997727i
\(973\) 0.811458i 0.0260142i
\(974\) −25.5642 + 30.0185i −0.819131 + 0.961853i
\(975\) −25.0385 + 6.89417i −0.801872 + 0.220790i
\(976\) 47.7205 + 29.4419i 1.52750 + 0.942412i
\(977\) 33.9041 + 5.97821i 1.08469 + 0.191260i 0.687287 0.726386i \(-0.258801\pi\)
0.397400 + 0.917645i \(0.369912\pi\)
\(978\) −9.04273 + 19.3712i −0.289155 + 0.619424i
\(979\) −24.5799 + 20.6250i −0.785577 + 0.659177i
\(980\) −3.36206 + 17.5636i −0.107397 + 0.561050i
\(981\) −20.5135 34.4266i −0.654945 1.09916i
\(982\) −3.85107 4.65817i −0.122893 0.148648i
\(983\) −7.45500 42.2794i −0.237778 1.34850i −0.836684 0.547685i \(-0.815509\pi\)
0.598907 0.800819i \(-0.295602\pi\)
\(984\) −0.486763 6.72538i −0.0155174 0.214397i
\(985\) −5.56764 + 2.02646i −0.177400 + 0.0645682i
\(986\) −0.0998557 + 13.6779i −0.00318005 + 0.435593i
\(987\) 0.0574501 + 0.608380i 0.00182866 + 0.0193649i
\(988\) −23.6447 14.1155i −0.752239 0.449075i
\(989\) −0.581069 + 1.00644i −0.0184769 + 0.0320030i
\(990\) 3.65123 21.5206i 0.116044 0.683969i
\(991\) −34.3889 + 19.8544i −1.09240 + 0.630697i −0.934214 0.356713i \(-0.883897\pi\)
−0.158185 + 0.987410i \(0.550564\pi\)
\(992\) 7.71112 4.08431i 0.244828 0.129677i
\(993\) 40.0518 + 27.6355i 1.27100 + 0.876987i
\(994\) 0.432687 + 0.254042i 0.0137240 + 0.00805771i
\(995\) −12.1536 + 14.4840i −0.385293 + 0.459175i
\(996\) −3.32684 41.7318i −0.105415 1.32232i
\(997\) −3.81126 + 10.4713i −0.120704 + 0.331631i −0.985299 0.170838i \(-0.945353\pi\)
0.864595 + 0.502469i \(0.167575\pi\)
\(998\) 22.7763 + 8.47872i 0.720972 + 0.268389i
\(999\) 0.0250784 + 0.0864127i 0.000793444 + 0.00273398i
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 216.2.v.b.131.7 192
3.2 odd 2 648.2.v.b.179.26 192
4.3 odd 2 864.2.bh.b.239.13 192
8.3 odd 2 inner 216.2.v.b.131.32 yes 192
8.5 even 2 864.2.bh.b.239.14 192
24.11 even 2 648.2.v.b.179.1 192
27.7 even 9 648.2.v.b.467.1 192
27.20 odd 18 inner 216.2.v.b.155.32 yes 192
108.47 even 18 864.2.bh.b.47.14 192
216.101 odd 18 864.2.bh.b.47.13 192
216.115 odd 18 648.2.v.b.467.26 192
216.155 even 18 inner 216.2.v.b.155.7 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.v.b.131.7 192 1.1 even 1 trivial
216.2.v.b.131.32 yes 192 8.3 odd 2 inner
216.2.v.b.155.7 yes 192 216.155 even 18 inner
216.2.v.b.155.32 yes 192 27.20 odd 18 inner
648.2.v.b.179.1 192 24.11 even 2
648.2.v.b.179.26 192 3.2 odd 2
648.2.v.b.467.1 192 27.7 even 9
648.2.v.b.467.26 192 216.115 odd 18
864.2.bh.b.47.13 192 216.101 odd 18
864.2.bh.b.47.14 192 108.47 even 18
864.2.bh.b.239.13 192 4.3 odd 2
864.2.bh.b.239.14 192 8.5 even 2