Properties

Label 576.2.bl.a.419.2
Level $576$
Weight $2$
Character 576.419
Analytic conductor $4.599$
Analytic rank $0$
Dimension $1504$
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] = [576,2,Mod(11,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(48))
 
chi = DirichletCharacter(H, H._module([24, 15, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bl (of order \(48\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(1504\)
Relative dimension: \(94\) over \(\Q(\zeta_{48})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label 419.2
Character \(\chi\) \(=\) 576.419
Dual form 576.2.bl.a.11.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41165 - 0.0851593i) q^{2} +(-1.66601 + 0.473724i) q^{3} +(1.98550 + 0.240430i) q^{4} +(-1.72799 + 0.852148i) q^{5} +(2.39216 - 0.526855i) q^{6} +(0.749706 - 0.977036i) q^{7} +(-2.78234 - 0.508485i) q^{8} +(2.55117 - 1.57846i) q^{9} +O(q^{10})\) \(q+(-1.41165 - 0.0851593i) q^{2} +(-1.66601 + 0.473724i) q^{3} +(1.98550 + 0.240430i) q^{4} +(-1.72799 + 0.852148i) q^{5} +(2.39216 - 0.526855i) q^{6} +(0.749706 - 0.977036i) q^{7} +(-2.78234 - 0.508485i) q^{8} +(2.55117 - 1.57846i) q^{9} +(2.51187 - 1.05578i) q^{10} +(-1.03280 + 0.905738i) q^{11} +(-3.42175 + 0.540019i) q^{12} +(1.67090 - 0.109517i) q^{13} +(-1.14152 + 1.31539i) q^{14} +(2.47516 - 2.23827i) q^{15} +(3.88439 + 0.954745i) q^{16} +(2.19144 - 2.19144i) q^{17} +(-3.73577 + 2.01097i) q^{18} +(-0.262896 - 0.393452i) q^{19} +(-3.63579 + 1.27648i) q^{20} +(-0.786172 + 1.98290i) q^{21} +(1.53508 - 1.19063i) q^{22} +(-1.13581 - 1.48022i) q^{23} +(4.87629 - 0.470922i) q^{24} +(-0.784031 + 1.02177i) q^{25} +(-2.36805 + 0.0123061i) q^{26} +(-3.50252 + 3.83827i) q^{27} +(1.72345 - 1.75965i) q^{28} +(2.37989 + 7.01094i) q^{29} +(-3.68466 + 2.94887i) q^{30} +(0.773053 - 1.33897i) q^{31} +(-5.40208 - 1.67855i) q^{32} +(1.29158 - 1.99823i) q^{33} +(-3.28016 + 2.90692i) q^{34} +(-0.462902 + 2.32716i) q^{35} +(5.44485 - 2.52064i) q^{36} +(1.46296 + 0.977517i) q^{37} +(0.337611 + 0.577804i) q^{38} +(-2.73186 + 0.974002i) q^{39} +(5.24116 - 1.49231i) q^{40} +(-1.02065 + 0.783171i) q^{41} +(1.27866 - 2.73221i) q^{42} +(-6.95908 + 6.10295i) q^{43} +(-2.26838 + 1.55002i) q^{44} +(-3.06331 + 4.90152i) q^{45} +(1.47731 + 2.18627i) q^{46} +(-2.32556 + 8.67912i) q^{47} +(-6.92371 + 0.249514i) q^{48} +(1.41919 + 5.29650i) q^{49} +(1.19379 - 1.37561i) q^{50} +(-2.61282 + 4.68909i) q^{51} +(3.34390 + 0.184290i) q^{52} +(3.48275 - 0.692761i) q^{53} +(5.27119 - 5.12002i) q^{54} +(1.01283 - 2.44520i) q^{55} +(-2.58275 + 2.33724i) q^{56} +(0.624376 + 0.530955i) q^{57} +(-2.76252 - 10.0996i) q^{58} +(6.06064 + 12.2898i) q^{59} +(5.45256 - 3.84898i) q^{60} +(3.11847 + 9.18671i) q^{61} +(-1.20530 + 1.82432i) q^{62} +(0.370420 - 3.67597i) q^{63} +(7.48289 + 2.82956i) q^{64} +(-2.79397 + 1.61310i) q^{65} +(-1.99342 + 2.71080i) q^{66} +(-6.27596 - 5.50387i) q^{67} +(4.87798 - 3.82420i) q^{68} +(2.59348 + 1.92799i) q^{69} +(0.851634 - 3.24571i) q^{70} +(1.01633 - 0.420977i) q^{71} +(-7.90086 + 3.09458i) q^{72} +(8.19258 + 3.39348i) q^{73} +(-1.98194 - 1.50449i) q^{74} +(0.822166 - 2.07369i) q^{75} +(-0.427382 - 0.844406i) q^{76} +(0.110645 + 1.68812i) q^{77} +(3.93936 - 1.14230i) q^{78} +(-1.95474 + 7.29518i) q^{79} +(-7.52575 + 1.66029i) q^{80} +(4.01695 - 8.05383i) q^{81} +(1.50749 - 1.01864i) q^{82} +(-9.95929 - 4.91138i) q^{83} +(-2.03769 + 3.74803i) q^{84} +(-1.91934 + 5.65420i) q^{85} +(10.3435 - 8.02258i) q^{86} +(-7.28618 - 10.5529i) q^{87} +(3.33415 - 1.99491i) q^{88} +(3.53756 - 1.46530i) q^{89} +(4.74172 - 6.65835i) q^{90} +(1.14568 - 1.71464i) q^{91} +(-1.89926 - 3.21205i) q^{92} +(-0.653613 + 2.59695i) q^{93} +(4.02198 - 12.0538i) q^{94} +(0.789561 + 0.455853i) q^{95} +(9.79508 + 0.237392i) q^{96} +(-5.80249 + 3.35007i) q^{97} +(-1.55235 - 7.59765i) q^{98} +(-1.20517 + 3.94092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} - 16 q^{12} - 8 q^{13} - 24 q^{14} - 16 q^{15} - 8 q^{16} - 16 q^{18} - 32 q^{19} - 24 q^{20} - 16 q^{21} - 8 q^{22} - 24 q^{23} - 96 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} + 64 q^{30} - 16 q^{31} - 24 q^{32} - 8 q^{34} + 64 q^{36} - 32 q^{37} - 24 q^{38} - 16 q^{39} - 8 q^{40} - 24 q^{41} - 96 q^{42} - 8 q^{43} - 16 q^{45} - 32 q^{46} - 24 q^{47} - 16 q^{48} - 8 q^{49} - 24 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{54} - 32 q^{55} - 24 q^{56} - 16 q^{57} + 64 q^{58} - 24 q^{59} - 16 q^{60} - 8 q^{61} - 32 q^{64} - 48 q^{65} - 8 q^{67} - 24 q^{68} - 16 q^{69} - 8 q^{70} - 16 q^{72} - 32 q^{73} - 24 q^{74} - 16 q^{75} - 56 q^{76} - 24 q^{77} - 40 q^{78} - 8 q^{79} - 16 q^{81} - 32 q^{82} - 24 q^{83} - 128 q^{84} - 8 q^{85} - 24 q^{86} - 16 q^{87} - 8 q^{88} - 160 q^{90} - 32 q^{91} - 480 q^{92} + 8 q^{93} - 8 q^{94} - 48 q^{95} - 152 q^{96} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41165 0.0851593i −0.998185 0.0602167i
\(3\) −1.66601 + 0.473724i −0.961871 + 0.273505i
\(4\) 1.98550 + 0.240430i 0.992748 + 0.120215i
\(5\) −1.72799 + 0.852148i −0.772778 + 0.381092i −0.785528 0.618827i \(-0.787608\pi\)
0.0127492 + 0.999919i \(0.495942\pi\)
\(6\) 2.39216 0.526855i 0.976595 0.215088i
\(7\) 0.749706 0.977036i 0.283362 0.369285i −0.629887 0.776687i \(-0.716899\pi\)
0.913249 + 0.407402i \(0.133565\pi\)
\(8\) −2.78234 0.508485i −0.983707 0.179777i
\(9\) 2.55117 1.57846i 0.850390 0.526152i
\(10\) 2.51187 1.05578i 0.794324 0.333866i
\(11\) −1.03280 + 0.905738i −0.311400 + 0.273090i −0.800752 0.598996i \(-0.795567\pi\)
0.489352 + 0.872086i \(0.337233\pi\)
\(12\) −3.42175 + 0.540019i −0.987774 + 0.155890i
\(13\) 1.67090 0.109517i 0.463425 0.0303745i 0.168097 0.985770i \(-0.446238\pi\)
0.295328 + 0.955396i \(0.404571\pi\)
\(14\) −1.14152 + 1.31539i −0.305085 + 0.351552i
\(15\) 2.47516 2.23827i 0.639082 0.577920i
\(16\) 3.88439 + 0.954745i 0.971097 + 0.238686i
\(17\) 2.19144 2.19144i 0.531502 0.531502i −0.389517 0.921019i \(-0.627358\pi\)
0.921019 + 0.389517i \(0.127358\pi\)
\(18\) −3.73577 + 2.01097i −0.880530 + 0.473990i
\(19\) −0.262896 0.393452i −0.0603126 0.0902642i 0.800088 0.599883i \(-0.204786\pi\)
−0.860400 + 0.509619i \(0.829786\pi\)
\(20\) −3.63579 + 1.27648i −0.812987 + 0.285429i
\(21\) −0.786172 + 1.98290i −0.171557 + 0.432705i
\(22\) 1.53508 1.19063i 0.327279 0.253843i
\(23\) −1.13581 1.48022i −0.236833 0.308646i 0.659783 0.751456i \(-0.270648\pi\)
−0.896615 + 0.442810i \(0.853982\pi\)
\(24\) 4.87629 0.470922i 0.995369 0.0961266i
\(25\) −0.784031 + 1.02177i −0.156806 + 0.204354i
\(26\) −2.36805 + 0.0123061i −0.464413 + 0.00241343i
\(27\) −3.50252 + 3.83827i −0.674060 + 0.738676i
\(28\) 1.72345 1.75965i 0.325701 0.332543i
\(29\) 2.37989 + 7.01094i 0.441935 + 1.30190i 0.908675 + 0.417505i \(0.137095\pi\)
−0.466740 + 0.884395i \(0.654571\pi\)
\(30\) −3.68466 + 2.94887i −0.672723 + 0.538388i
\(31\) 0.773053 1.33897i 0.138844 0.240486i −0.788215 0.615400i \(-0.788995\pi\)
0.927059 + 0.374914i \(0.122328\pi\)
\(32\) −5.40208 1.67855i −0.954962 0.296729i
\(33\) 1.29158 1.99823i 0.224835 0.347847i
\(34\) −3.28016 + 2.90692i −0.562543 + 0.498532i
\(35\) −0.462902 + 2.32716i −0.0782447 + 0.393363i
\(36\) 5.44485 2.52064i 0.907475 0.420107i
\(37\) 1.46296 + 0.977517i 0.240509 + 0.160703i 0.669983 0.742376i \(-0.266301\pi\)
−0.429475 + 0.903079i \(0.641301\pi\)
\(38\) 0.337611 + 0.577804i 0.0547677 + 0.0937322i
\(39\) −2.73186 + 0.974002i −0.437447 + 0.155965i
\(40\) 5.24116 1.49231i 0.828699 0.235956i
\(41\) −1.02065 + 0.783171i −0.159398 + 0.122311i −0.685381 0.728185i \(-0.740364\pi\)
0.525983 + 0.850495i \(0.323698\pi\)
\(42\) 1.27866 2.73221i 0.197302 0.421589i
\(43\) −6.95908 + 6.10295i −1.06125 + 0.930691i −0.997733 0.0672903i \(-0.978565\pi\)
−0.0635157 + 0.997981i \(0.520231\pi\)
\(44\) −2.26838 + 1.55002i −0.341971 + 0.233675i
\(45\) −3.06331 + 4.90152i −0.456651 + 0.730676i
\(46\) 1.47731 + 2.18627i 0.217817 + 0.322348i
\(47\) −2.32556 + 8.67912i −0.339218 + 1.26598i 0.560005 + 0.828489i \(0.310799\pi\)
−0.899223 + 0.437490i \(0.855867\pi\)
\(48\) −6.92371 + 0.249514i −0.999351 + 0.0360143i
\(49\) 1.41919 + 5.29650i 0.202742 + 0.756643i
\(50\) 1.19379 1.37561i 0.168827 0.194541i
\(51\) −2.61282 + 4.68909i −0.365868 + 0.656604i
\(52\) 3.34390 + 0.184290i 0.463716 + 0.0255564i
\(53\) 3.48275 0.692761i 0.478392 0.0951581i 0.0499964 0.998749i \(-0.484079\pi\)
0.428395 + 0.903591i \(0.359079\pi\)
\(54\) 5.27119 5.12002i 0.717318 0.696746i
\(55\) 1.01283 2.44520i 0.136570 0.329710i
\(56\) −2.58275 + 2.33724i −0.345134 + 0.312326i
\(57\) 0.624376 + 0.530955i 0.0827006 + 0.0703267i
\(58\) −2.76252 10.0996i −0.362737 1.32615i
\(59\) 6.06064 + 12.2898i 0.789028 + 1.59999i 0.799962 + 0.600051i \(0.204853\pi\)
−0.0109331 + 0.999940i \(0.503480\pi\)
\(60\) 5.45256 3.84898i 0.703922 0.496902i
\(61\) 3.11847 + 9.18671i 0.399279 + 1.17624i 0.941794 + 0.336191i \(0.109139\pi\)
−0.542515 + 0.840046i \(0.682528\pi\)
\(62\) −1.20530 + 1.82432i −0.153074 + 0.231689i
\(63\) 0.370420 3.67597i 0.0466685 0.463128i
\(64\) 7.48289 + 2.82956i 0.935361 + 0.353695i
\(65\) −2.79397 + 1.61310i −0.346549 + 0.200080i
\(66\) −1.99342 + 2.71080i −0.245373 + 0.333677i
\(67\) −6.27596 5.50387i −0.766731 0.672405i 0.183825 0.982959i \(-0.441152\pi\)
−0.950556 + 0.310554i \(0.899485\pi\)
\(68\) 4.87798 3.82420i 0.591542 0.463753i
\(69\) 2.59348 + 1.92799i 0.312219 + 0.232103i
\(70\) 0.851634 3.24571i 0.101790 0.387937i
\(71\) 1.01633 0.420977i 0.120616 0.0499608i −0.321559 0.946889i \(-0.604207\pi\)
0.442175 + 0.896929i \(0.354207\pi\)
\(72\) −7.90086 + 3.09458i −0.931125 + 0.364699i
\(73\) 8.19258 + 3.39348i 0.958870 + 0.397177i 0.806557 0.591156i \(-0.201328\pi\)
0.152312 + 0.988332i \(0.451328\pi\)
\(74\) −1.98194 1.50449i −0.230395 0.174894i
\(75\) 0.822166 2.07369i 0.0949355 0.239449i
\(76\) −0.427382 0.844406i −0.0490241 0.0968600i
\(77\) 0.110645 + 1.68812i 0.0126092 + 0.192379i
\(78\) 3.93936 1.14230i 0.446045 0.129341i
\(79\) −1.95474 + 7.29518i −0.219925 + 0.820771i 0.764449 + 0.644684i \(0.223011\pi\)
−0.984374 + 0.176088i \(0.943656\pi\)
\(80\) −7.52575 + 1.66029i −0.841404 + 0.185626i
\(81\) 4.01695 8.05383i 0.446328 0.894870i
\(82\) 1.50749 1.01864i 0.166474 0.112490i
\(83\) −9.95929 4.91138i −1.09317 0.539094i −0.195925 0.980619i \(-0.562771\pi\)
−0.897249 + 0.441525i \(0.854438\pi\)
\(84\) −2.03769 + 3.74803i −0.222330 + 0.408944i
\(85\) −1.91934 + 5.65420i −0.208182 + 0.613284i
\(86\) 10.3435 8.02258i 1.11537 0.865097i
\(87\) −7.28618 10.5529i −0.781160 1.13139i
\(88\) 3.33415 1.99491i 0.355422 0.212658i
\(89\) 3.53756 1.46530i 0.374980 0.155322i −0.187230 0.982316i \(-0.559951\pi\)
0.562211 + 0.826994i \(0.309951\pi\)
\(90\) 4.74172 6.65835i 0.499821 0.701852i
\(91\) 1.14568 1.71464i 0.120100 0.179743i
\(92\) −1.89926 3.21205i −0.198011 0.334879i
\(93\) −0.653613 + 2.59695i −0.0677765 + 0.269291i
\(94\) 4.02198 12.0538i 0.414836 1.24326i
\(95\) 0.789561 + 0.455853i 0.0810072 + 0.0467695i
\(96\) 9.79508 + 0.237392i 0.999706 + 0.0242287i
\(97\) −5.80249 + 3.35007i −0.589154 + 0.340148i −0.764763 0.644312i \(-0.777144\pi\)
0.175609 + 0.984460i \(0.443811\pi\)
\(98\) −1.55235 7.59765i −0.156811 0.767478i
\(99\) −1.20517 + 3.94092i −0.121124 + 0.396077i
\(100\) −1.80235 + 1.84021i −0.180235 + 0.184021i
\(101\) 7.54370 + 0.494440i 0.750626 + 0.0491987i 0.435914 0.899988i \(-0.356425\pi\)
0.314713 + 0.949187i \(0.398092\pi\)
\(102\) 4.08770 6.39684i 0.404742 0.633381i
\(103\) 0.121885 0.925806i 0.0120097 0.0912224i −0.984390 0.175999i \(-0.943684\pi\)
0.996400 + 0.0847768i \(0.0270177\pi\)
\(104\) −4.70471 0.544916i −0.461335 0.0534334i
\(105\) −0.331235 4.09636i −0.0323252 0.399764i
\(106\) −4.97540 + 0.681346i −0.483254 + 0.0661782i
\(107\) −14.5703 + 2.89822i −1.40857 + 0.280181i −0.840059 0.542496i \(-0.817479\pi\)
−0.568509 + 0.822677i \(0.692479\pi\)
\(108\) −7.87708 + 6.77877i −0.757972 + 0.652287i
\(109\) 1.16949 0.781430i 0.112017 0.0748474i −0.498300 0.867005i \(-0.666042\pi\)
0.610317 + 0.792157i \(0.291042\pi\)
\(110\) −1.63800 + 3.36550i −0.156177 + 0.320888i
\(111\) −2.90037 0.935514i −0.275291 0.0887951i
\(112\) 3.84497 3.07941i 0.363315 0.290977i
\(113\) −2.14511 + 0.574782i −0.201795 + 0.0540709i −0.358301 0.933606i \(-0.616644\pi\)
0.156505 + 0.987677i \(0.449977\pi\)
\(114\) −0.836182 0.802692i −0.0783157 0.0751790i
\(115\) 3.22403 + 1.58991i 0.300642 + 0.148260i
\(116\) 3.03963 + 14.4924i 0.282223 + 1.34558i
\(117\) 4.08989 2.91684i 0.378111 0.269662i
\(118\) −7.50890 17.8649i −0.691250 1.64460i
\(119\) −0.498180 3.78405i −0.0456680 0.346883i
\(120\) −8.02487 + 4.96907i −0.732567 + 0.453612i
\(121\) −1.18948 + 9.03501i −0.108135 + 0.821364i
\(122\) −3.61984 13.2340i −0.327725 1.19815i
\(123\) 1.32940 1.78828i 0.119868 0.161243i
\(124\) 1.85682 2.47265i 0.166748 0.222051i
\(125\) 2.36348 11.8820i 0.211396 1.06276i
\(126\) −0.835944 + 5.15762i −0.0744718 + 0.459477i
\(127\) 11.9551i 1.06084i −0.847734 0.530421i \(-0.822034\pi\)
0.847734 0.530421i \(-0.177966\pi\)
\(128\) −10.3222 4.63158i −0.912365 0.409378i
\(129\) 8.70277 13.4642i 0.766236 1.18546i
\(130\) 4.08147 2.03919i 0.357969 0.178849i
\(131\) 9.66608 11.0221i 0.844530 0.963001i −0.155161 0.987889i \(-0.549590\pi\)
0.999690 + 0.0248878i \(0.00792286\pi\)
\(132\) 3.04486 3.65694i 0.265021 0.318296i
\(133\) −0.581512 0.0381143i −0.0504235 0.00330493i
\(134\) 8.39074 + 8.30398i 0.724849 + 0.717354i
\(135\) 2.78153 9.61715i 0.239396 0.827712i
\(136\) −7.21165 + 4.98302i −0.618394 + 0.427291i
\(137\) 12.4251 1.63579i 1.06155 0.139755i 0.420527 0.907280i \(-0.361845\pi\)
0.641019 + 0.767525i \(0.278512\pi\)
\(138\) −3.49690 2.94250i −0.297676 0.250483i
\(139\) 0.309346 0.911305i 0.0262384 0.0772959i −0.933022 0.359820i \(-0.882838\pi\)
0.959260 + 0.282524i \(0.0911716\pi\)
\(140\) −1.47861 + 4.50928i −0.124965 + 0.381104i
\(141\) −0.237098 15.5612i −0.0199673 1.31049i
\(142\) −1.47055 + 0.507722i −0.123406 + 0.0426070i
\(143\) −1.62651 + 1.62651i −0.136015 + 0.136015i
\(144\) 11.4168 3.69562i 0.951397 0.307968i
\(145\) −10.0868 10.0868i −0.837662 0.837662i
\(146\) −11.2761 5.48807i −0.933213 0.454196i
\(147\) −4.87347 8.15171i −0.401957 0.672342i
\(148\) 2.66967 + 2.29260i 0.219446 + 0.188450i
\(149\) 0.888105 + 0.301471i 0.0727564 + 0.0246975i 0.357580 0.933882i \(-0.383602\pi\)
−0.284824 + 0.958580i \(0.591935\pi\)
\(150\) −1.33720 + 2.85730i −0.109182 + 0.233298i
\(151\) −1.26369 9.59866i −0.102837 0.781128i −0.962694 0.270592i \(-0.912781\pi\)
0.859857 0.510535i \(-0.170553\pi\)
\(152\) 0.531404 + 1.22840i 0.0431025 + 0.0996363i
\(153\) 2.13164 9.04983i 0.172333 0.731635i
\(154\) −0.0124329 2.39245i −0.00100187 0.192789i
\(155\) −0.194826 + 2.97247i −0.0156488 + 0.238755i
\(156\) −5.65827 + 1.27706i −0.453024 + 0.102246i
\(157\) 16.2627 + 14.2620i 1.29791 + 1.13823i 0.981884 + 0.189481i \(0.0606805\pi\)
0.316022 + 0.948752i \(0.397653\pi\)
\(158\) 3.38065 10.1318i 0.268950 0.806039i
\(159\) −5.47411 + 2.80401i −0.434125 + 0.222372i
\(160\) 10.7651 1.70285i 0.851055 0.134622i
\(161\) −2.29775 −0.181088
\(162\) −6.35637 + 11.0271i −0.499404 + 0.866369i
\(163\) −1.02062 0.203014i −0.0799412 0.0159013i 0.154958 0.987921i \(-0.450476\pi\)
−0.234899 + 0.972020i \(0.575476\pi\)
\(164\) −2.21479 + 1.30959i −0.172946 + 0.102262i
\(165\) −0.529042 + 4.55352i −0.0411858 + 0.354491i
\(166\) 13.6408 + 7.78126i 1.05873 + 0.603943i
\(167\) 18.5031 + 2.43598i 1.43181 + 0.188502i 0.806205 0.591636i \(-0.201518\pi\)
0.625608 + 0.780138i \(0.284851\pi\)
\(168\) 3.19568 5.11737i 0.246552 0.394814i
\(169\) −10.1089 + 1.33086i −0.777605 + 0.102374i
\(170\) 3.19094 7.81829i 0.244734 0.599635i
\(171\) −1.29174 0.588794i −0.0987819 0.0450262i
\(172\) −15.2845 + 10.4442i −1.16544 + 0.796363i
\(173\) −0.701684 + 1.42288i −0.0533481 + 0.108179i −0.921914 0.387394i \(-0.873375\pi\)
0.868566 + 0.495573i \(0.165042\pi\)
\(174\) 9.38684 + 15.5174i 0.711614 + 1.17637i
\(175\) 0.410512 + 1.53205i 0.0310318 + 0.115812i
\(176\) −4.87653 + 2.53218i −0.367582 + 0.190870i
\(177\) −15.9190 17.6038i −1.19655 1.32318i
\(178\) −5.11857 + 1.76724i −0.383653 + 0.132460i
\(179\) 7.60903 + 11.3877i 0.568726 + 0.851158i 0.998663 0.0517009i \(-0.0164642\pi\)
−0.429937 + 0.902859i \(0.641464\pi\)
\(180\) −7.26066 + 8.99545i −0.541177 + 0.670481i
\(181\) −1.99219 10.0154i −0.148078 0.744439i −0.981449 0.191725i \(-0.938592\pi\)
0.833371 0.552715i \(-0.186408\pi\)
\(182\) −1.76332 + 2.32290i −0.130706 + 0.172185i
\(183\) −9.54736 13.8278i −0.705761 1.02218i
\(184\) 2.40755 + 4.69601i 0.177487 + 0.346195i
\(185\) −3.36096 0.442479i −0.247103 0.0325317i
\(186\) 1.14382 3.61031i 0.0838693 0.264721i
\(187\) −0.278440 + 4.24818i −0.0203616 + 0.310658i
\(188\) −6.70411 + 16.6732i −0.488948 + 1.21602i
\(189\) 1.12427 + 6.29967i 0.0817787 + 0.458233i
\(190\) −1.07576 0.710742i −0.0780439 0.0515627i
\(191\) 7.85381 + 13.6032i 0.568282 + 0.984293i 0.996736 + 0.0807296i \(0.0257250\pi\)
−0.428454 + 0.903564i \(0.640942\pi\)
\(192\) −13.8070 1.16926i −0.996433 0.0843838i
\(193\) −2.04795 + 3.54716i −0.147415 + 0.255330i −0.930271 0.366872i \(-0.880429\pi\)
0.782856 + 0.622202i \(0.213762\pi\)
\(194\) 8.47636 4.23498i 0.608568 0.304054i
\(195\) 3.89062 4.01101i 0.278613 0.287234i
\(196\) 1.54437 + 10.8574i 0.110312 + 0.775528i
\(197\) −17.2745 11.5424i −1.23076 0.822364i −0.241764 0.970335i \(-0.577726\pi\)
−0.988992 + 0.147971i \(0.952726\pi\)
\(198\) 2.03688 5.46055i 0.144755 0.388065i
\(199\) 4.77676 + 11.5321i 0.338616 + 0.817490i 0.997849 + 0.0655521i \(0.0208809\pi\)
−0.659234 + 0.751938i \(0.729119\pi\)
\(200\) 2.70100 2.44425i 0.190989 0.172834i
\(201\) 13.0631 + 6.19642i 0.921401 + 0.437062i
\(202\) −10.6069 1.34039i −0.746302 0.0943096i
\(203\) 8.63417 + 2.93090i 0.606000 + 0.205709i
\(204\) −6.31514 + 8.68197i −0.442148 + 0.607860i
\(205\) 1.09629 2.22305i 0.0765680 0.155265i
\(206\) −0.250899 + 1.29653i −0.0174810 + 0.0903337i
\(207\) −5.23410 1.98346i −0.363795 0.137860i
\(208\) 6.59499 + 1.16988i 0.457280 + 0.0811166i
\(209\) 0.627883 + 0.168241i 0.0434316 + 0.0116375i
\(210\) 0.118744 + 5.81083i 0.00819409 + 0.400985i
\(211\) −3.32454 + 0.217902i −0.228871 + 0.0150010i −0.179407 0.983775i \(-0.557418\pi\)
−0.0494639 + 0.998776i \(0.515751\pi\)
\(212\) 7.08154 0.538119i 0.486362 0.0369581i
\(213\) −1.49379 + 1.18281i −0.102353 + 0.0810449i
\(214\) 20.8150 2.85046i 1.42288 0.194854i
\(215\) 6.82457 16.4760i 0.465432 1.12365i
\(216\) 11.6969 8.89842i 0.795875 0.605461i
\(217\) −0.728657 1.75913i −0.0494645 0.119418i
\(218\) −1.71746 + 1.00351i −0.116321 + 0.0679663i
\(219\) −15.2565 1.77254i −1.03094 0.119777i
\(220\) 2.59888 4.61141i 0.175216 0.310901i
\(221\) 3.42168 3.90168i 0.230167 0.262455i
\(222\) 4.01464 + 1.56761i 0.269445 + 0.105211i
\(223\) 9.45489 + 16.3763i 0.633146 + 1.09664i 0.986905 + 0.161305i \(0.0515701\pi\)
−0.353759 + 0.935337i \(0.615097\pi\)
\(224\) −5.68998 + 4.01960i −0.380178 + 0.268571i
\(225\) −0.387379 + 3.84427i −0.0258253 + 0.256284i
\(226\) 3.07709 0.628712i 0.204685 0.0418213i
\(227\) 11.3514 3.85328i 0.753419 0.255751i 0.0818006 0.996649i \(-0.473933\pi\)
0.671618 + 0.740898i \(0.265600\pi\)
\(228\) 1.11204 + 1.20433i 0.0736465 + 0.0797585i
\(229\) −13.7569 + 6.78417i −0.909084 + 0.448311i −0.835821 0.549002i \(-0.815008\pi\)
−0.0732631 + 0.997313i \(0.523341\pi\)
\(230\) −4.41579 2.51895i −0.291169 0.166095i
\(231\) −0.984037 2.76000i −0.0647449 0.181595i
\(232\) −3.05672 20.7170i −0.200684 1.36014i
\(233\) −1.17227 0.485572i −0.0767982 0.0318109i 0.343954 0.938987i \(-0.388234\pi\)
−0.420752 + 0.907176i \(0.638234\pi\)
\(234\) −6.02188 + 3.76926i −0.393663 + 0.246404i
\(235\) −3.37736 16.9791i −0.220314 1.10760i
\(236\) 9.07855 + 25.8584i 0.590964 + 1.68324i
\(237\) −0.199291 13.0798i −0.0129454 0.849626i
\(238\) 0.381007 + 5.38417i 0.0246970 + 0.349004i
\(239\) −4.17371 + 1.11834i −0.269975 + 0.0723395i −0.391267 0.920277i \(-0.627963\pi\)
0.121292 + 0.992617i \(0.461296\pi\)
\(240\) 11.7514 6.33118i 0.758552 0.408676i
\(241\) −25.2008 6.75254i −1.62333 0.434970i −0.671351 0.741139i \(-0.734286\pi\)
−0.951977 + 0.306170i \(0.900953\pi\)
\(242\) 2.44854 12.6529i 0.157398 0.813362i
\(243\) −2.87698 + 15.3207i −0.184558 + 0.982822i
\(244\) 3.98295 + 18.9899i 0.254982 + 1.21571i
\(245\) −6.96575 7.94291i −0.445025 0.507454i
\(246\) −2.02894 + 2.41120i −0.129360 + 0.153733i
\(247\) −0.482364 0.628629i −0.0306921 0.0399987i
\(248\) −2.83175 + 3.33238i −0.179816 + 0.211607i
\(249\) 18.9189 + 3.46445i 1.19894 + 0.219550i
\(250\) −4.34826 + 16.5719i −0.275008 + 1.04810i
\(251\) −13.5514 + 20.2811i −0.855357 + 1.28013i 0.103035 + 0.994678i \(0.467145\pi\)
−0.958392 + 0.285454i \(0.907855\pi\)
\(252\) 1.61928 7.20955i 0.102005 0.454159i
\(253\) 2.51375 + 0.500016i 0.158038 + 0.0314357i
\(254\) −1.01809 + 16.8764i −0.0638804 + 1.05892i
\(255\) 0.519111 10.3292i 0.0325080 0.646839i
\(256\) 14.1769 + 7.41719i 0.886058 + 0.463575i
\(257\) −11.5845 6.68832i −0.722622 0.417206i 0.0930947 0.995657i \(-0.470324\pi\)
−0.815717 + 0.578451i \(0.803657\pi\)
\(258\) −13.4318 + 18.2656i −0.836230 + 1.13717i
\(259\) 2.05186 0.696512i 0.127496 0.0432792i
\(260\) −5.93525 + 2.53105i −0.368089 + 0.156969i
\(261\) 17.1380 + 14.1296i 1.06081 + 0.874597i
\(262\) −14.5837 + 14.7361i −0.900986 + 0.910399i
\(263\) 25.0384 + 19.2126i 1.54393 + 1.18470i 0.912362 + 0.409385i \(0.134257\pi\)
0.631572 + 0.775317i \(0.282410\pi\)
\(264\) −4.60968 + 4.90301i −0.283706 + 0.301759i
\(265\) −5.42780 + 4.16489i −0.333427 + 0.255847i
\(266\) 0.817644 + 0.103325i 0.0501330 + 0.00633527i
\(267\) −5.19945 + 4.11703i −0.318201 + 0.251958i
\(268\) −11.1376 12.4368i −0.680337 0.759701i
\(269\) 7.93176 5.29983i 0.483608 0.323136i −0.289754 0.957101i \(-0.593574\pi\)
0.773362 + 0.633965i \(0.218574\pi\)
\(270\) −4.74552 + 13.3391i −0.288803 + 0.811794i
\(271\) 16.7254 + 16.7254i 1.01599 + 1.01599i 0.999870 + 0.0161232i \(0.00513241\pi\)
0.0161232 + 0.999870i \(0.494868\pi\)
\(272\) 10.6047 6.42013i 0.643002 0.389278i
\(273\) −1.09646 + 3.39934i −0.0663605 + 0.205737i
\(274\) −17.6791 + 1.25105i −1.06804 + 0.0755787i
\(275\) −0.115711 1.76541i −0.00697762 0.106458i
\(276\) 4.68580 + 4.45157i 0.282052 + 0.267953i
\(277\) 5.16415 + 5.88858i 0.310284 + 0.353811i 0.885873 0.463929i \(-0.153561\pi\)
−0.575589 + 0.817739i \(0.695227\pi\)
\(278\) −0.514294 + 1.26010i −0.0308453 + 0.0755756i
\(279\) −0.141311 4.63617i −0.00846008 0.277560i
\(280\) 2.47128 6.23960i 0.147687 0.372887i
\(281\) −5.28881 4.05825i −0.315504 0.242095i 0.438853 0.898559i \(-0.355385\pi\)
−0.754357 + 0.656464i \(0.772051\pi\)
\(282\) −0.990478 + 21.9871i −0.0589821 + 1.30931i
\(283\) −1.48687 3.01506i −0.0883850 0.179227i 0.848192 0.529689i \(-0.177691\pi\)
−0.936577 + 0.350462i \(0.886025\pi\)
\(284\) 2.11913 0.591493i 0.125747 0.0350986i
\(285\) −1.53136 0.385421i −0.0907102 0.0228304i
\(286\) 2.43457 2.15754i 0.143959 0.127578i
\(287\) 1.58436i 0.0935217i
\(288\) −16.4312 + 4.24467i −0.968215 + 0.250120i
\(289\) 7.39519i 0.435011i
\(290\) 13.3800 + 15.0980i 0.785700 + 0.886583i
\(291\) 8.08000 8.33003i 0.473658 0.488315i
\(292\) 15.4504 + 8.70748i 0.904169 + 0.509567i
\(293\) 9.23351 + 18.7237i 0.539427 + 1.09385i 0.980526 + 0.196392i \(0.0629224\pi\)
−0.441098 + 0.897459i \(0.645411\pi\)
\(294\) 6.18542 + 11.9224i 0.360741 + 0.695326i
\(295\) −20.9454 16.0720i −1.21949 0.935746i
\(296\) −3.57340 3.46368i −0.207700 0.201322i
\(297\) 0.140920 7.13652i 0.00817701 0.414103i
\(298\) −1.22802 0.501201i −0.0711371 0.0290338i
\(299\) −2.05994 2.34891i −0.119129 0.135841i
\(300\) 2.13098 3.91963i 0.123032 0.226300i
\(301\) 0.745536 + 11.3747i 0.0429720 + 0.655626i
\(302\) 0.966466 + 13.6575i 0.0556138 + 0.785903i
\(303\) −12.8021 + 2.74989i −0.735462 + 0.157977i
\(304\) −0.645545 1.77932i −0.0370246 0.102051i
\(305\) −13.2171 13.2171i −0.756809 0.756809i
\(306\) −3.77981 + 12.5936i −0.216077 + 0.719930i
\(307\) 12.1223 8.09988i 0.691857 0.462284i −0.159276 0.987234i \(-0.550916\pi\)
0.851133 + 0.524950i \(0.175916\pi\)
\(308\) −0.186188 + 3.37835i −0.0106091 + 0.192499i
\(309\) 0.235516 + 1.60014i 0.0133980 + 0.0910289i
\(310\) 0.528159 4.17949i 0.0299974 0.237379i
\(311\) 25.9868 19.9403i 1.47357 1.13071i 0.511038 0.859558i \(-0.329261\pi\)
0.962536 0.271155i \(-0.0874056\pi\)
\(312\) 8.09624 1.32090i 0.458359 0.0747813i
\(313\) −8.09855 6.21424i −0.457757 0.351249i 0.353999 0.935246i \(-0.384822\pi\)
−0.811756 + 0.583996i \(0.801488\pi\)
\(314\) −21.7427 21.5179i −1.22701 1.21432i
\(315\) 2.49239 + 6.66767i 0.140430 + 0.375680i
\(316\) −5.63510 + 14.0146i −0.316999 + 0.788381i
\(317\) 12.2263 4.15026i 0.686695 0.233102i 0.0437824 0.999041i \(-0.486059\pi\)
0.642913 + 0.765940i \(0.277726\pi\)
\(318\) 7.96629 3.49210i 0.446728 0.195827i
\(319\) −8.80802 5.08531i −0.493155 0.284723i
\(320\) −15.3415 + 1.48708i −0.857617 + 0.0831304i
\(321\) 22.9013 11.7308i 1.27823 0.654748i
\(322\) 3.24361 + 0.195675i 0.180759 + 0.0109045i
\(323\) −1.43835 0.286105i −0.0800318 0.0159193i
\(324\) 9.91201 15.0250i 0.550667 0.834725i
\(325\) −1.19814 + 1.79314i −0.0664608 + 0.0994655i
\(326\) 1.42347 + 0.373500i 0.0788386 + 0.0206862i
\(327\) −1.57820 + 1.85589i −0.0872748 + 0.102631i
\(328\) 3.23803 1.66007i 0.178790 0.0916619i
\(329\) 6.73632 + 8.77895i 0.371386 + 0.483999i
\(330\) 1.13459 6.38292i 0.0624574 0.351368i
\(331\) −16.2857 18.5703i −0.895145 1.02072i −0.999657 0.0261932i \(-0.991661\pi\)
0.104512 0.994524i \(-0.466672\pi\)
\(332\) −18.5933 12.1460i −1.02044 0.666600i
\(333\) 5.27523 + 0.184598i 0.289081 + 0.0101159i
\(334\) −25.9124 5.01445i −1.41786 0.274379i
\(335\) 15.5349 + 4.16256i 0.848761 + 0.227425i
\(336\) −4.94696 + 6.95178i −0.269879 + 0.379250i
\(337\) −29.9972 + 8.03773i −1.63405 + 0.437843i −0.955086 0.296327i \(-0.904238\pi\)
−0.678965 + 0.734170i \(0.737571\pi\)
\(338\) 14.3835 1.01784i 0.782358 0.0553630i
\(339\) 3.30149 1.97378i 0.179312 0.107201i
\(340\) −5.17029 + 10.7649i −0.280398 + 0.583810i
\(341\) 0.414347 + 2.08306i 0.0224382 + 0.112804i
\(342\) 1.77334 + 0.941173i 0.0958914 + 0.0508928i
\(343\) 14.2033 + 5.88321i 0.766908 + 0.317664i
\(344\) 22.4658 13.4419i 1.21128 0.724739i
\(345\) −6.12443 1.12151i −0.329728 0.0603802i
\(346\) 1.11170 1.94884i 0.0597655 0.104770i
\(347\) −18.5589 + 9.15224i −0.996294 + 0.491318i −0.865939 0.500150i \(-0.833278\pi\)
−0.130355 + 0.991467i \(0.541612\pi\)
\(348\) −11.9294 22.7045i −0.639485 1.21709i
\(349\) 28.2673 9.59547i 1.51312 0.513634i 0.563249 0.826287i \(-0.309551\pi\)
0.949867 + 0.312654i \(0.101218\pi\)
\(350\) −0.449030 2.19768i −0.0240017 0.117471i
\(351\) −5.43202 + 6.79697i −0.289940 + 0.362795i
\(352\) 7.09958 3.15926i 0.378409 0.168389i
\(353\) 3.92924 + 6.80564i 0.209132 + 0.362228i 0.951441 0.307830i \(-0.0996027\pi\)
−0.742309 + 0.670058i \(0.766269\pi\)
\(354\) 20.9729 + 26.2060i 1.11470 + 1.39283i
\(355\) −1.39747 + 1.59351i −0.0741698 + 0.0845745i
\(356\) 7.37611 2.05882i 0.390933 0.109117i
\(357\) 2.62257 + 6.06826i 0.138801 + 0.321166i
\(358\) −9.77150 16.7234i −0.516440 0.883860i
\(359\) −4.36281 10.5328i −0.230260 0.555898i 0.765947 0.642903i \(-0.222270\pi\)
−0.996208 + 0.0870053i \(0.972270\pi\)
\(360\) 11.0155 12.0801i 0.580569 0.636676i
\(361\) 7.18529 17.3468i 0.378173 0.912991i
\(362\) 1.95936 + 14.3079i 0.102982 + 0.752005i
\(363\) −2.29841 15.6159i −0.120635 0.819622i
\(364\) 2.68700 3.12895i 0.140837 0.164001i
\(365\) −17.0484 + 1.11741i −0.892355 + 0.0584880i
\(366\) 12.2999 + 20.3331i 0.642928 + 1.06283i
\(367\) −8.16061 2.18663i −0.425981 0.114141i 0.0394582 0.999221i \(-0.487437\pi\)
−0.465439 + 0.885080i \(0.654103\pi\)
\(368\) −2.99870 6.83414i −0.156318 0.356254i
\(369\) −1.36765 + 3.60905i −0.0711969 + 0.187880i
\(370\) 4.70681 + 0.910841i 0.244695 + 0.0473524i
\(371\) 1.93418 3.92214i 0.100418 0.203627i
\(372\) −1.92213 + 4.99908i −0.0996577 + 0.259190i
\(373\) −11.0251 3.74253i −0.570860 0.193781i 0.0210594 0.999778i \(-0.493296\pi\)
−0.591919 + 0.805998i \(0.701629\pi\)
\(374\) 0.754831 5.97322i 0.0390314 0.308868i
\(375\) 1.69122 + 20.9152i 0.0873340 + 1.08005i
\(376\) 10.8837 22.9658i 0.561285 1.18437i
\(377\) 4.74439 + 11.4540i 0.244348 + 0.589909i
\(378\) −1.05060 8.98865i −0.0540370 0.462326i
\(379\) −19.5353 13.0531i −1.00346 0.670493i −0.0587101 0.998275i \(-0.518699\pi\)
−0.944753 + 0.327782i \(0.893699\pi\)
\(380\) 1.45807 + 1.09493i 0.0747974 + 0.0561686i
\(381\) 5.66341 + 19.9173i 0.290145 + 1.02039i
\(382\) −9.92837 19.8717i −0.507980 1.01673i
\(383\) 10.8460 18.7859i 0.554206 0.959912i −0.443759 0.896146i \(-0.646355\pi\)
0.997965 0.0637663i \(-0.0203112\pi\)
\(384\) 19.3910 + 2.82637i 0.989544 + 0.144233i
\(385\) −1.62972 2.82275i −0.0830581 0.143861i
\(386\) 3.19306 4.83293i 0.162522 0.245990i
\(387\) −8.12056 + 26.5543i −0.412791 + 1.34983i
\(388\) −12.3263 + 5.25646i −0.625772 + 0.266856i
\(389\) 1.06012 16.1743i 0.0537502 0.820070i −0.882847 0.469661i \(-0.844376\pi\)
0.936597 0.350409i \(-0.113957\pi\)
\(390\) −5.83375 + 5.33081i −0.295403 + 0.269936i
\(391\) −5.73286 0.754745i −0.289923 0.0381691i
\(392\) −1.25549 15.4583i −0.0634119 0.780764i
\(393\) −10.8824 + 22.9419i −0.548943 + 1.15727i
\(394\) 23.4025 + 17.7649i 1.17900 + 0.894984i
\(395\) −2.83881 14.2717i −0.142836 0.718086i
\(396\) −3.34038 + 7.53491i −0.167860 + 0.378644i
\(397\) −6.95794 10.4133i −0.349209 0.522628i 0.614735 0.788734i \(-0.289263\pi\)
−0.963944 + 0.266106i \(0.914263\pi\)
\(398\) −5.76103 16.6861i −0.288775 0.836397i
\(399\) 0.986860 0.211978i 0.0494048 0.0106121i
\(400\) −4.02101 + 3.22040i −0.201050 + 0.161020i
\(401\) −3.16286 11.8040i −0.157946 0.589461i −0.998835 0.0482542i \(-0.984634\pi\)
0.840889 0.541207i \(-0.182032\pi\)
\(402\) −17.9128 9.85961i −0.893411 0.491753i
\(403\) 1.14506 2.32195i 0.0570394 0.115664i
\(404\) 14.8591 + 2.79544i 0.739268 + 0.139078i
\(405\) −0.0781755 + 17.3399i −0.00388457 + 0.861628i
\(406\) −11.9388 4.87268i −0.592513 0.241827i
\(407\) −2.39631 + 0.315480i −0.118781 + 0.0156378i
\(408\) 9.65410 11.7181i 0.477949 0.580132i
\(409\) 15.5365 + 2.04542i 0.768233 + 0.101140i 0.504448 0.863442i \(-0.331696\pi\)
0.263784 + 0.964582i \(0.415029\pi\)
\(410\) −1.73688 + 3.04480i −0.0857786 + 0.150372i
\(411\) −19.9254 + 8.61130i −0.982846 + 0.424764i
\(412\) 0.464593 1.80888i 0.0228889 0.0891171i
\(413\) 16.5512 + 3.29225i 0.814434 + 0.162001i
\(414\) 7.21980 + 3.24568i 0.354834 + 0.159516i
\(415\) 21.3947 1.05023
\(416\) −9.21018 2.21308i −0.451566 0.108505i
\(417\) −0.0836667 + 1.66479i −0.00409718 + 0.0815250i
\(418\) −0.872022 0.290967i −0.0426520 0.0142316i
\(419\) −14.2726 12.5167i −0.697262 0.611482i 0.235543 0.971864i \(-0.424313\pi\)
−0.932805 + 0.360382i \(0.882646\pi\)
\(420\) 0.327222 8.21295i 0.0159668 0.400751i
\(421\) −2.18760 + 33.3764i −0.106617 + 1.62667i 0.524802 + 0.851224i \(0.324139\pi\)
−0.631419 + 0.775442i \(0.717527\pi\)
\(422\) 4.71164 0.0244851i 0.229359 0.00119192i
\(423\) 7.76671 + 25.8127i 0.377630 + 1.25506i
\(424\) −10.0425 + 0.156575i −0.487705 + 0.00760396i
\(425\) 0.520988 + 3.95730i 0.0252716 + 0.191957i
\(426\) 2.20943 1.54250i 0.107047 0.0747345i
\(427\) 11.3137 + 3.84048i 0.547507 + 0.185854i
\(428\) −29.6262 + 2.25126i −1.43203 + 0.108819i
\(429\) 1.93926 3.48029i 0.0936284 0.168030i
\(430\) −11.0370 + 22.6771i −0.532250 + 1.09359i
\(431\) 3.38734 + 3.38734i 0.163162 + 0.163162i 0.783966 0.620804i \(-0.213194\pi\)
−0.620804 + 0.783966i \(0.713194\pi\)
\(432\) −17.2697 + 11.5653i −0.830890 + 0.556437i
\(433\) −23.5186 + 23.5186i −1.13023 + 1.13023i −0.140094 + 0.990138i \(0.544741\pi\)
−0.990138 + 0.140094i \(0.955259\pi\)
\(434\) 0.878800 + 2.54533i 0.0421838 + 0.122180i
\(435\) 21.5830 + 12.0263i 1.03483 + 0.576618i
\(436\) 2.50990 1.27034i 0.120202 0.0608385i
\(437\) −0.283794 + 0.836031i −0.0135757 + 0.0399928i
\(438\) 21.3858 + 3.80144i 1.02185 + 0.181640i
\(439\) −13.5280 + 1.78099i −0.645654 + 0.0850020i −0.446240 0.894913i \(-0.647237\pi\)
−0.199414 + 0.979915i \(0.563904\pi\)
\(440\) −4.06140 + 6.28837i −0.193620 + 0.299786i
\(441\) 11.9809 + 11.2721i 0.570519 + 0.536769i
\(442\) −5.16247 + 5.21641i −0.245554 + 0.248119i
\(443\) 28.0055 + 1.83558i 1.33058 + 0.0872110i 0.714037 0.700108i \(-0.246865\pi\)
0.616546 + 0.787319i \(0.288531\pi\)
\(444\) −5.53376 2.55480i −0.262620 0.121245i
\(445\) −4.86419 + 5.54654i −0.230585 + 0.262931i
\(446\) −11.9524 23.9228i −0.565961 1.13278i
\(447\) −1.62240 0.0815367i −0.0767371 0.00385656i
\(448\) 8.37455 5.18971i 0.395660 0.245191i
\(449\) 2.50970i 0.118440i 0.998245 + 0.0592201i \(0.0188614\pi\)
−0.998245 + 0.0592201i \(0.981139\pi\)
\(450\) 0.874217 5.39376i 0.0412110 0.254264i
\(451\) 0.344774 1.73330i 0.0162348 0.0816177i
\(452\) −4.39731 + 0.625477i −0.206832 + 0.0294200i
\(453\) 6.65243 + 15.3928i 0.312558 + 0.723217i
\(454\) −16.3523 + 4.47280i −0.767452 + 0.209919i
\(455\) −0.518600 + 3.93916i −0.0243124 + 0.184671i
\(456\) −1.46725 1.79479i −0.0687101 0.0840485i
\(457\) −4.55856 34.6257i −0.213241 1.61972i −0.678535 0.734568i \(-0.737385\pi\)
0.465295 0.885156i \(-0.345948\pi\)
\(458\) 19.9977 8.40533i 0.934430 0.392755i
\(459\) 0.735782 + 16.0869i 0.0343434 + 0.750872i
\(460\) 6.01903 + 3.93192i 0.280639 + 0.183327i
\(461\) −29.2929 14.4457i −1.36431 0.672802i −0.395006 0.918679i \(-0.629257\pi\)
−0.969301 + 0.245877i \(0.920924\pi\)
\(462\) 1.15407 + 3.97995i 0.0536923 + 0.185164i
\(463\) 10.2144 2.73695i 0.474705 0.127197i −0.0135312 0.999908i \(-0.504307\pi\)
0.488236 + 0.872712i \(0.337641\pi\)
\(464\) 2.55077 + 29.5054i 0.118417 + 1.36975i
\(465\) −1.08355 5.04446i −0.0502484 0.233931i
\(466\) 1.61349 + 0.785286i 0.0747433 + 0.0363777i
\(467\) −22.0973 + 14.7649i −1.02254 + 0.683240i −0.949396 0.314081i \(-0.898304\pi\)
−0.0731452 + 0.997321i \(0.523304\pi\)
\(468\) 8.82176 4.80805i 0.407786 0.222252i
\(469\) −10.0826 + 2.00556i −0.465571 + 0.0926079i
\(470\) 3.32171 + 24.2561i 0.153219 + 1.11885i
\(471\) −33.8501 16.0566i −1.55973 0.739850i
\(472\) −10.6136 37.2761i −0.488532 1.71577i
\(473\) 1.65964 12.6062i 0.0763102 0.579634i
\(474\) −0.832540 + 18.4811i −0.0382398 + 0.848864i
\(475\) 0.608136 + 0.0398594i 0.0279032 + 0.00182887i
\(476\) −0.0793353 7.63299i −0.00363633 0.349858i
\(477\) 7.79159 7.26471i 0.356752 0.332628i
\(478\) 5.98704 1.22327i 0.273841 0.0559512i
\(479\) −8.82264 + 5.09375i −0.403117 + 0.232739i −0.687828 0.725874i \(-0.741436\pi\)
0.284711 + 0.958613i \(0.408102\pi\)
\(480\) −17.1280 + 7.93665i −0.781785 + 0.362257i
\(481\) 2.55151 + 1.47312i 0.116339 + 0.0671684i
\(482\) 34.9996 + 11.6783i 1.59419 + 0.531932i
\(483\) 3.82807 1.08850i 0.174183 0.0495284i
\(484\) −4.53400 + 17.6530i −0.206091 + 0.802408i
\(485\) 7.17187 10.7335i 0.325658 0.487381i
\(486\) 5.36598 21.3824i 0.243406 0.969925i
\(487\) −9.72605 + 4.02866i −0.440729 + 0.182556i −0.592003 0.805936i \(-0.701663\pi\)
0.151274 + 0.988492i \(0.451663\pi\)
\(488\) −4.00534 27.1463i −0.181313 1.22885i
\(489\) 1.79654 0.145269i 0.0812421 0.00656930i
\(490\) 9.15676 + 11.8058i 0.413660 + 0.533331i
\(491\) 1.35412 3.98912i 0.0611107 0.180026i −0.912087 0.409997i \(-0.865530\pi\)
0.973198 + 0.229971i \(0.0738631\pi\)
\(492\) 3.06948 3.23099i 0.138383 0.145664i
\(493\) 20.5794 + 10.1487i 0.926851 + 0.457073i
\(494\) 0.627394 + 0.928480i 0.0282278 + 0.0417743i
\(495\) −1.27573 7.83683i −0.0573396 0.352239i
\(496\) 4.28121 4.46300i 0.192232 0.200395i
\(497\) 0.350638 1.30860i 0.0157283 0.0586987i
\(498\) −26.4118 6.50170i −1.18354 0.291348i
\(499\) −0.584936 8.92439i −0.0261853 0.399511i −0.990753 0.135676i \(-0.956679\pi\)
0.964568 0.263835i \(-0.0849873\pi\)
\(500\) 7.54946 23.0234i 0.337622 1.02964i
\(501\) −31.9803 + 4.70700i −1.42878 + 0.210293i
\(502\) 20.8569 27.4757i 0.930890 1.22630i
\(503\) 24.1518 + 10.0040i 1.07688 + 0.446057i 0.849412 0.527730i \(-0.176957\pi\)
0.227464 + 0.973787i \(0.426957\pi\)
\(504\) −2.89981 + 10.0395i −0.129168 + 0.447193i
\(505\) −13.4567 + 5.57396i −0.598817 + 0.248038i
\(506\) −3.50594 0.919914i −0.155858 0.0408952i
\(507\) 16.2110 7.00603i 0.719956 0.311149i
\(508\) 2.87436 23.7368i 0.127529 1.05315i
\(509\) −27.3833 24.0145i −1.21374 1.06443i −0.996085 0.0884008i \(-0.971824\pi\)
−0.217660 0.976025i \(-0.569842\pi\)
\(510\) −1.61243 + 14.5370i −0.0713995 + 0.643708i
\(511\) 9.45758 5.46034i 0.418379 0.241551i
\(512\) −19.3812 11.6778i −0.856535 0.516089i
\(513\) 2.43098 + 0.369007i 0.107330 + 0.0162920i
\(514\) 15.7837 + 10.4281i 0.696188 + 0.459963i
\(515\) 0.578309 + 1.70364i 0.0254833 + 0.0750715i
\(516\) 20.5165 24.6408i 0.903189 1.08475i
\(517\) −5.45918 11.0701i −0.240094 0.486863i
\(518\) −2.95581 + 0.808495i −0.129871 + 0.0355232i
\(519\) 0.494962 2.70293i 0.0217264 0.118645i
\(520\) 8.59403 3.06751i 0.376873 0.134519i
\(521\) −8.39543 + 20.2684i −0.367810 + 0.887973i 0.626298 + 0.779584i \(0.284569\pi\)
−0.994109 + 0.108389i \(0.965431\pi\)
\(522\) −22.9895 21.4054i −1.00622 0.936889i
\(523\) 16.5472 3.29144i 0.723558 0.143925i 0.180446 0.983585i \(-0.442246\pi\)
0.543112 + 0.839660i \(0.317246\pi\)
\(524\) 21.8420 19.5602i 0.954172 0.854493i
\(525\) −1.40969 2.35794i −0.0615238 0.102909i
\(526\) −33.7093 29.2537i −1.46979 1.27552i
\(527\) −1.24017 4.62836i −0.0540225 0.201615i
\(528\) 6.92479 6.52876i 0.301363 0.284128i
\(529\) 5.05186 18.8538i 0.219646 0.819731i
\(530\) 8.01681 5.41714i 0.348228 0.235305i
\(531\) 34.8606 + 21.7868i 1.51282 + 0.945468i
\(532\) −1.14543 0.215489i −0.0496605 0.00934262i
\(533\) −1.61963 + 1.42038i −0.0701541 + 0.0615235i
\(534\) 7.69039 5.36902i 0.332796 0.232340i
\(535\) 22.7076 17.4242i 0.981735 0.753312i
\(536\) 14.6632 + 18.5049i 0.633356 + 0.799290i
\(537\) −18.0713 15.3675i −0.779836 0.663155i
\(538\) −11.6482 + 6.80603i −0.502188 + 0.293429i
\(539\) −6.26298 4.18479i −0.269766 0.180252i
\(540\) 7.83496 18.4260i 0.337163 0.792931i
\(541\) 6.42389 32.2951i 0.276185 1.38847i −0.554710 0.832044i \(-0.687171\pi\)
0.830894 0.556430i \(-0.187829\pi\)
\(542\) −22.1860 25.0346i −0.952970 1.07533i
\(543\) 8.06354 + 15.7420i 0.346040 + 0.675554i
\(544\) −15.5168 + 8.15988i −0.665276 + 0.349852i
\(545\) −1.35497 + 2.34688i −0.0580406 + 0.100529i
\(546\) 1.83729 4.70529i 0.0786289 0.201368i
\(547\) −9.03509 26.6165i −0.386313 1.13804i −0.950053 0.312089i \(-0.898971\pi\)
0.563740 0.825952i \(-0.309362\pi\)
\(548\) 25.0632 0.260501i 1.07065 0.0111280i
\(549\) 22.4566 + 18.5145i 0.958423 + 0.790180i
\(550\) 0.0130021 + 2.50198i 0.000554413 + 0.106685i
\(551\) 2.13281 2.77953i 0.0908606 0.118412i
\(552\) −6.23561 6.68309i −0.265405 0.284451i
\(553\) 5.66217 + 7.37909i 0.240780 + 0.313791i
\(554\) −6.78849 8.75237i −0.288415 0.371853i
\(555\) 5.80900 0.854994i 0.246578 0.0362925i
\(556\) 0.833311 1.73502i 0.0353402 0.0735811i
\(557\) −20.3822 30.5042i −0.863623 1.29250i −0.954976 0.296684i \(-0.904119\pi\)
0.0913529 0.995819i \(-0.470881\pi\)
\(558\) −0.195331 + 6.55667i −0.00826903 + 0.277566i
\(559\) −10.9596 + 10.9596i −0.463540 + 0.463540i
\(560\) −4.01994 + 8.59765i −0.169873 + 0.363317i
\(561\) −1.54858 7.20941i −0.0653811 0.304381i
\(562\) 7.12034 + 6.17921i 0.300353 + 0.260654i
\(563\) 11.9824 0.785371i 0.505000 0.0330994i 0.189225 0.981934i \(-0.439402\pi\)
0.315774 + 0.948834i \(0.397736\pi\)
\(564\) 3.27061 30.9536i 0.137717 1.30338i
\(565\) 3.21693 2.82117i 0.135337 0.118687i
\(566\) 1.84217 + 4.38283i 0.0774321 + 0.184224i
\(567\) −4.85735 9.96271i −0.203989 0.418394i
\(568\) −3.04184 + 0.654515i −0.127633 + 0.0274629i
\(569\) 3.75336 4.89148i 0.157349 0.205061i −0.708025 0.706187i \(-0.750414\pi\)
0.865375 + 0.501125i \(0.167080\pi\)
\(570\) 2.12892 + 0.674489i 0.0891708 + 0.0282512i
\(571\) 18.3458 9.04712i 0.767746 0.378610i −0.0158555 0.999874i \(-0.505047\pi\)
0.783601 + 0.621264i \(0.213381\pi\)
\(572\) −3.62049 + 2.83836i −0.151380 + 0.118678i
\(573\) −19.5287 18.9425i −0.815822 0.791335i
\(574\) 0.134923 2.23656i 0.00563157 0.0933520i
\(575\) 2.40295 0.100210
\(576\) 23.5565 4.59271i 0.981519 0.191363i
\(577\) 39.1554 1.63006 0.815030 0.579418i \(-0.196720\pi\)
0.815030 + 0.579418i \(0.196720\pi\)
\(578\) 0.629770 10.4394i 0.0261950 0.434222i
\(579\) 1.73153 6.87976i 0.0719601 0.285913i
\(580\) −17.6021 22.4524i −0.730887 0.932286i
\(581\) −12.2651 + 6.04850i −0.508844 + 0.250934i
\(582\) −12.1155 + 11.0710i −0.502203 + 0.458907i
\(583\) −2.96951 + 3.86994i −0.122984 + 0.160276i
\(584\) −21.0691 13.6076i −0.871844 0.563088i
\(585\) −4.58169 + 8.52545i −0.189429 + 0.352484i
\(586\) −11.4400 27.2176i −0.472580 1.12435i
\(587\) −25.3993 + 22.2746i −1.04834 + 0.919370i −0.996850 0.0793040i \(-0.974730\pi\)
−0.0514895 + 0.998674i \(0.516397\pi\)
\(588\) −7.71634 17.3569i −0.318216 0.715787i
\(589\) −0.730053 + 0.0478502i −0.0300813 + 0.00197163i
\(590\) 28.1988 + 24.4716i 1.16093 + 1.00748i
\(591\) 34.2474 + 11.0465i 1.40875 + 0.454391i
\(592\) 4.74942 + 5.19381i 0.195200 + 0.213464i
\(593\) 5.92112 5.92112i 0.243151 0.243151i −0.575001 0.818153i \(-0.694998\pi\)
0.818153 + 0.575001i \(0.194998\pi\)
\(594\) −0.806670 + 10.0622i −0.0330981 + 0.412859i
\(595\) 4.08542 + 6.11426i 0.167486 + 0.250660i
\(596\) 1.69085 + 0.812096i 0.0692597 + 0.0332648i
\(597\) −13.4212 16.9497i −0.549292 0.693707i
\(598\) 2.70787 + 3.49125i 0.110733 + 0.142768i
\(599\) −15.9809 20.8267i −0.652962 0.850957i 0.343129 0.939288i \(-0.388513\pi\)
−0.996091 + 0.0883316i \(0.971846\pi\)
\(600\) −3.34199 + 5.35166i −0.136436 + 0.218481i
\(601\) 11.1661 14.5519i 0.455473 0.593584i −0.508011 0.861351i \(-0.669619\pi\)
0.963484 + 0.267767i \(0.0862856\pi\)
\(602\) −0.0837740 16.1205i −0.00341437 0.657024i
\(603\) −24.6987 4.13498i −1.00581 0.168389i
\(604\) −0.201243 19.3619i −0.00818845 0.787825i
\(605\) −5.64376 16.6260i −0.229451 0.675942i
\(606\) 18.3062 2.79166i 0.743640 0.113403i
\(607\) −1.68346 + 2.91584i −0.0683295 + 0.118350i −0.898166 0.439656i \(-0.855100\pi\)
0.829837 + 0.558007i \(0.188434\pi\)
\(608\) 0.759756 + 2.56675i 0.0308122 + 0.104095i
\(609\) −15.7730 0.792701i −0.639156 0.0321219i
\(610\) 17.5323 + 19.7834i 0.709863 + 0.801008i
\(611\) −2.93528 + 14.7567i −0.118749 + 0.596990i
\(612\) 6.40822 17.4559i 0.259037 0.705612i
\(613\) 30.4720 + 20.3608i 1.23075 + 0.822363i 0.988991 0.147972i \(-0.0472747\pi\)
0.241762 + 0.970336i \(0.422275\pi\)
\(614\) −17.8022 + 10.4018i −0.718439 + 0.419784i
\(615\) −0.773312 + 4.22296i −0.0311829 + 0.170286i
\(616\) 0.550530 4.75318i 0.0221815 0.191511i
\(617\) −34.9523 + 26.8198i −1.40713 + 1.07973i −0.422248 + 0.906480i \(0.638759\pi\)
−0.984879 + 0.173246i \(0.944574\pi\)
\(618\) −0.196198 2.27889i −0.00789225 0.0916705i
\(619\) 35.7088 31.3158i 1.43526 1.25869i 0.521002 0.853556i \(-0.325558\pi\)
0.914258 0.405133i \(-0.132775\pi\)
\(620\) −1.10150 + 5.85499i −0.0442372 + 0.235142i
\(621\) 9.65967 + 0.824939i 0.387629 + 0.0331037i
\(622\) −38.3822 + 25.9357i −1.53899 + 1.03993i
\(623\) 1.22047 4.55487i 0.0488972 0.182487i
\(624\) −11.5415 + 1.17518i −0.462030 + 0.0470447i
\(625\) 4.37449 + 16.3258i 0.174980 + 0.653033i
\(626\) 10.9031 + 9.46198i 0.435775 + 0.378177i
\(627\) −1.12576 + 0.0171527i −0.0449585 + 0.000685012i
\(628\) 28.8605 + 32.2272i 1.15166 + 1.28601i
\(629\) 5.34815 1.06381i 0.213245 0.0424170i
\(630\) −2.95056 9.62464i −0.117553 0.383455i
\(631\) −7.79289 + 18.8137i −0.310230 + 0.748962i 0.689466 + 0.724318i \(0.257845\pi\)
−0.999696 + 0.0246440i \(0.992155\pi\)
\(632\) 9.14824 19.3037i 0.363897 0.767862i
\(633\) 5.43550 1.93794i 0.216042 0.0770263i
\(634\) −17.6126 + 4.81752i −0.699486 + 0.191328i
\(635\) 10.1875 + 20.6582i 0.404278 + 0.819796i
\(636\) −11.5430 + 4.25120i −0.457709 + 0.168571i
\(637\) 2.95139 + 8.69451i 0.116938 + 0.344489i
\(638\) 12.0008 + 7.92875i 0.475115 + 0.313902i
\(639\) 1.92833 2.67822i 0.0762837 0.105949i
\(640\) 21.7835 0.792762i 0.861067 0.0313367i
\(641\) −26.9327 + 15.5496i −1.06378 + 0.614171i −0.926474 0.376358i \(-0.877176\pi\)
−0.137302 + 0.990529i \(0.543843\pi\)
\(642\) −33.3276 + 14.6095i −1.31534 + 0.576589i
\(643\) 33.8327 + 29.6705i 1.33423 + 1.17009i 0.971187 + 0.238319i \(0.0765963\pi\)
0.363045 + 0.931771i \(0.381737\pi\)
\(644\) −4.56217 0.552447i −0.179775 0.0217695i
\(645\) −3.56473 + 30.6821i −0.140361 + 1.20810i
\(646\) 2.00608 + 0.526368i 0.0789280 + 0.0207097i
\(647\) 0.0953182 0.0394821i 0.00374734 0.00155220i −0.380809 0.924654i \(-0.624354\pi\)
0.384556 + 0.923102i \(0.374354\pi\)
\(648\) −15.2718 + 20.3660i −0.599933 + 0.800051i
\(649\) −17.3907 7.20347i −0.682645 0.282761i
\(650\) 1.84405 2.42925i 0.0723296 0.0952830i
\(651\) 2.04729 + 2.58555i 0.0802397 + 0.101336i
\(652\) −1.97763 0.648471i −0.0774499 0.0253961i
\(653\) 2.42674 + 37.0250i 0.0949659 + 1.44890i 0.733701 + 0.679472i \(0.237791\pi\)
−0.638735 + 0.769427i \(0.720542\pi\)
\(654\) 2.38591 2.48546i 0.0932965 0.0971890i
\(655\) −7.31043 + 27.2829i −0.285642 + 1.06603i
\(656\) −4.71232 + 2.06768i −0.183985 + 0.0807294i
\(657\) 26.2571 4.27429i 1.02439 0.166756i
\(658\) −8.76170 12.9664i −0.341567 0.505484i
\(659\) −16.2990 8.03776i −0.634918 0.313107i 0.0961960 0.995362i \(-0.469332\pi\)
−0.731114 + 0.682256i \(0.760999\pi\)
\(660\) −2.14521 + 8.91380i −0.0835023 + 0.346969i
\(661\) 0.401001 1.18131i 0.0155971 0.0459477i −0.938853 0.344319i \(-0.888110\pi\)
0.954450 + 0.298371i \(0.0964433\pi\)
\(662\) 21.4083 + 27.6016i 0.832056 + 1.07277i
\(663\) −3.85223 + 8.12116i −0.149608 + 0.315400i
\(664\) 25.2128 + 18.7293i 0.978447 + 0.726838i
\(665\) 1.03732 0.429674i 0.0402257 0.0166620i
\(666\) −7.43104 0.709822i −0.287947 0.0275050i
\(667\) 7.67460 11.4859i 0.297162 0.444734i
\(668\) 36.1521 + 9.28532i 1.39877 + 0.359260i
\(669\) −23.5098 22.8041i −0.908941 0.881659i
\(670\) −21.5753 7.19900i −0.833526 0.278122i
\(671\) −11.5415 6.66348i −0.445554 0.257241i
\(672\) 7.57537 9.39218i 0.292226 0.362311i
\(673\) −26.2437 + 15.1518i −1.01162 + 0.584059i −0.911665 0.410934i \(-0.865203\pi\)
−0.0999538 + 0.994992i \(0.531869\pi\)
\(674\) 43.0300 8.79189i 1.65745 0.338651i
\(675\) −1.17574 6.58809i −0.0452544 0.253576i
\(676\) −20.3911 + 0.211940i −0.784272 + 0.00815152i
\(677\) −1.15610 0.0757746i −0.0444324 0.00291225i 0.0431707 0.999068i \(-0.486254\pi\)
−0.0876031 + 0.996155i \(0.527921\pi\)
\(678\) −4.82863 + 2.50513i −0.185442 + 0.0962090i
\(679\) −1.07702 + 8.18082i −0.0413324 + 0.313951i
\(680\) 8.21535 14.7560i 0.315044 0.565866i
\(681\) −17.0861 + 11.7970i −0.654742 + 0.452063i
\(682\) −0.407520 2.97584i −0.0156047 0.113951i
\(683\) −7.19152 + 1.43048i −0.275176 + 0.0547359i −0.330749 0.943719i \(-0.607301\pi\)
0.0555731 + 0.998455i \(0.482301\pi\)
\(684\) −2.42318 1.47962i −0.0926527 0.0565747i
\(685\) −20.0764 + 13.4146i −0.767080 + 0.512547i
\(686\) −19.5491 9.51457i −0.746387 0.363268i
\(687\) 19.7054 17.8195i 0.751806 0.679856i
\(688\) −32.8585 + 17.0621i −1.25272 + 0.650485i
\(689\) 5.74346 1.53896i 0.218808 0.0586295i
\(690\) 8.55003 + 2.10473i 0.325494 + 0.0801257i
\(691\) 21.9898 + 10.8441i 0.836530 + 0.412531i 0.809511 0.587104i \(-0.199732\pi\)
0.0270184 + 0.999635i \(0.491399\pi\)
\(692\) −1.73529 + 2.65641i −0.0659659 + 0.100981i
\(693\) 2.94689 + 4.13203i 0.111943 + 0.156963i
\(694\) 26.9780 11.3393i 1.02407 0.430433i
\(695\) 0.242021 + 1.83833i 0.00918037 + 0.0697318i
\(696\) 14.9067 + 33.0667i 0.565036 + 1.25339i
\(697\) −0.520417 + 3.95296i −0.0197122 + 0.149729i
\(698\) −40.7207 + 11.1382i −1.54130 + 0.421587i
\(699\) 2.18305 + 0.253633i 0.0825704 + 0.00959326i
\(700\) 0.446719 + 3.14058i 0.0168844 + 0.118703i
\(701\) 0.293804 1.47705i 0.0110968 0.0557875i −0.974840 0.222905i \(-0.928446\pi\)
0.985937 + 0.167118i \(0.0534460\pi\)
\(702\) 8.24691 9.13233i 0.311260 0.344678i
\(703\) 0.832590i 0.0314017i
\(704\) −10.2911 + 3.85517i −0.387862 + 0.145297i
\(705\) 13.6701 + 26.6874i 0.514846 + 1.00511i
\(706\) −4.96714 9.94178i −0.186941 0.374164i
\(707\) 6.13865 6.99978i 0.230868 0.263254i
\(708\) −27.3747 38.7797i −1.02880 1.45743i
\(709\) −30.7589 2.01604i −1.15517 0.0757141i −0.524254 0.851562i \(-0.675656\pi\)
−0.630920 + 0.775848i \(0.717323\pi\)
\(710\) 2.10843 2.13046i 0.0791280 0.0799547i
\(711\) 6.52825 + 21.6967i 0.244829 + 0.813690i
\(712\) −10.5878 + 2.27818i −0.396794 + 0.0853786i
\(713\) −2.86000 + 0.376527i −0.107108 + 0.0141010i
\(714\) −3.18537 8.78958i −0.119209 0.328942i
\(715\) 1.42456 4.19661i 0.0532754 0.156944i
\(716\) 12.3698 + 24.4397i 0.462279 + 0.913355i
\(717\) 6.42365 3.84035i 0.239896 0.143421i
\(718\) 5.26179 + 15.2401i 0.196368 + 0.568755i
\(719\) −17.8291 + 17.8291i −0.664914 + 0.664914i −0.956534 0.291620i \(-0.905806\pi\)
0.291620 + 0.956534i \(0.405806\pi\)
\(720\) −16.5788 + 16.1147i −0.617854 + 0.600561i
\(721\) −0.813169 0.813169i −0.0302840 0.0302840i
\(722\) −11.6203 + 23.8757i −0.432465 + 0.888562i
\(723\) 45.1837 0.688443i 1.68040 0.0256035i
\(724\) −1.54748 20.3645i −0.0575116 0.756842i
\(725\) −9.02947 3.06509i −0.335346 0.113835i
\(726\) 1.91471 + 22.2399i 0.0710616 + 0.825399i
\(727\) −5.82411 44.2385i −0.216004 1.64072i −0.664757 0.747060i \(-0.731465\pi\)
0.448753 0.893656i \(-0.351868\pi\)
\(728\) −4.05956 + 4.18815i −0.150457 + 0.155223i
\(729\) −2.46469 26.8873i −0.0912849 0.995825i
\(730\) 24.1615 0.125561i 0.894257 0.00464721i
\(731\) −1.87616 + 28.6246i −0.0693922 + 1.05872i
\(732\) −15.6316 29.7506i −0.577761 1.09961i
\(733\) 16.3078 + 14.3016i 0.602343 + 0.528241i 0.905305 0.424762i \(-0.139642\pi\)
−0.302962 + 0.953003i \(0.597976\pi\)
\(734\) 11.3337 + 3.78170i 0.418334 + 0.139585i
\(735\) 15.3677 + 9.93312i 0.566848 + 0.366389i
\(736\) 3.65111 + 9.90276i 0.134582 + 0.365021i
\(737\) 11.4669 0.422387
\(738\) 2.23798 4.97824i 0.0823812 0.183252i
\(739\) −17.9871 3.57786i −0.661667 0.131614i −0.147177 0.989110i \(-0.547019\pi\)
−0.514490 + 0.857496i \(0.672019\pi\)
\(740\) −6.56678 1.68661i −0.241400 0.0620012i
\(741\) 1.10142 + 0.818794i 0.0404617 + 0.0300792i
\(742\) −3.06439 + 5.37196i −0.112497 + 0.197211i
\(743\) 20.4815 + 2.69644i 0.751393 + 0.0989227i 0.496488 0.868044i \(-0.334623\pi\)
0.254905 + 0.966966i \(0.417956\pi\)
\(744\) 3.13909 6.89325i 0.115084 0.252719i
\(745\) −1.79153 + 0.235859i −0.0656366 + 0.00864122i
\(746\) 15.2449 + 6.22202i 0.558155 + 0.227804i
\(747\) −33.1603 + 3.19054i −1.21327 + 0.116736i
\(748\) −1.57423 + 8.36780i −0.0575596 + 0.305957i
\(749\) −8.09180 + 16.4086i −0.295668 + 0.599556i
\(750\) −0.606280 29.6688i −0.0221382 1.08335i
\(751\) 6.53144 + 24.3757i 0.238336 + 0.889481i 0.976617 + 0.214988i \(0.0689711\pi\)
−0.738281 + 0.674493i \(0.764362\pi\)
\(752\) −17.3197 + 31.4927i −0.631586 + 1.14842i
\(753\) 12.9691 40.2081i 0.472621 1.46527i
\(754\) −5.72199 16.5730i −0.208383 0.603552i
\(755\) 10.3631 + 15.5095i 0.377152 + 0.564448i
\(756\) 0.717607 + 12.7783i 0.0260991 + 0.464741i
\(757\) 5.99028 + 30.1152i 0.217720 + 1.09455i 0.922757 + 0.385383i \(0.125931\pi\)
−0.705036 + 0.709171i \(0.749069\pi\)
\(758\) 26.4654 + 20.0900i 0.961268 + 0.729701i
\(759\) −4.42480 + 0.357792i −0.160610 + 0.0129870i
\(760\) −1.96504 1.66982i −0.0712793 0.0605708i
\(761\) 49.1741 + 6.47389i 1.78256 + 0.234678i 0.948451 0.316924i \(-0.102650\pi\)
0.834107 + 0.551602i \(0.185983\pi\)
\(762\) −6.29859 28.5985i −0.228174 1.03601i
\(763\) 0.113290 1.72848i 0.00410139 0.0625751i
\(764\) 12.3231 + 28.8974i 0.445834 + 1.04547i
\(765\) 4.02834 + 17.4544i 0.145645 + 0.631067i
\(766\) −16.9105 + 25.5954i −0.611003 + 0.924798i
\(767\) 11.4727 + 19.8713i 0.414254 + 0.717510i
\(768\) −27.1326 5.64116i −0.979063 0.203558i
\(769\) 9.08274 15.7318i 0.327532 0.567302i −0.654490 0.756071i \(-0.727116\pi\)
0.982022 + 0.188769i \(0.0604498\pi\)
\(770\) 2.06020 + 4.12352i 0.0742446 + 0.148601i
\(771\) 22.4683 + 5.65494i 0.809177 + 0.203658i
\(772\) −4.91904 + 6.55048i −0.177040 + 0.235757i
\(773\) −18.9905 12.6891i −0.683043 0.456394i 0.165020 0.986290i \(-0.447231\pi\)
−0.848063 + 0.529896i \(0.822231\pi\)
\(774\) 13.7247 36.7937i 0.493324 1.32252i
\(775\) 0.762018 + 1.83967i 0.0273725 + 0.0660830i
\(776\) 17.8480 6.37057i 0.640706 0.228690i
\(777\) −3.08846 + 2.13241i −0.110798 + 0.0764998i
\(778\) −2.87391 + 22.7421i −0.103035 + 0.815345i
\(779\) 0.576465 + 0.195684i 0.0206540 + 0.00701109i
\(780\) 8.68917 7.02842i 0.311122 0.251658i
\(781\) −0.668366 + 1.35531i −0.0239160 + 0.0484969i
\(782\) 8.02850 + 1.55364i 0.287099 + 0.0555581i
\(783\) −35.2455 15.4213i −1.25957 0.551112i
\(784\) 0.455890 + 21.9286i 0.0162818 + 0.783165i
\(785\) −40.2551 10.7863i −1.43677 0.384980i
\(786\) 17.3158 31.4591i 0.617633 1.12211i
\(787\) 7.20787 0.472429i 0.256933 0.0168403i 0.0636076 0.997975i \(-0.479739\pi\)
0.193325 + 0.981135i \(0.438073\pi\)
\(788\) −31.5233 27.0708i −1.12297 0.964356i
\(789\) −50.8157 20.1471i −1.80909 0.717257i
\(790\) 2.79204 + 20.3883i 0.0993362 + 0.725384i
\(791\) −1.04662 + 2.52677i −0.0372136 + 0.0898416i
\(792\) 5.35710 10.3522i 0.190356 0.367849i
\(793\) 6.21675 + 15.0086i 0.220763 + 0.532970i
\(794\) 8.93537 + 15.2924i 0.317104 + 0.542708i
\(795\) 7.06975 9.51003i 0.250738 0.337286i
\(796\) 6.71157 + 24.0455i 0.237885 + 0.852268i
\(797\) −7.58163 + 8.64519i −0.268555 + 0.306228i −0.870361 0.492414i \(-0.836115\pi\)
0.601806 + 0.798642i \(0.294448\pi\)
\(798\) −1.41115 + 0.215197i −0.0499542 + 0.00761790i
\(799\) 13.9234 + 24.1161i 0.492575 + 0.853166i
\(800\) 5.95049 4.20364i 0.210382 0.148621i
\(801\) 6.71199 9.32212i 0.237157 0.329381i
\(802\) 3.45963 + 16.9324i 0.122164 + 0.597902i
\(803\) −11.5349 + 3.91556i −0.407057 + 0.138177i
\(804\) 24.4470 + 15.4437i 0.862178 + 0.544658i
\(805\) 3.97047 1.95802i 0.139941 0.0690112i
\(806\) −1.81415 + 3.18026i −0.0639008 + 0.112020i
\(807\) −10.7037 + 12.5870i −0.376789 + 0.443084i
\(808\) −20.7378 5.21157i −0.729552 0.183342i
\(809\) 45.2831 + 18.7569i 1.59207 + 0.659457i 0.990266 0.139188i \(-0.0444493\pi\)
0.601803 + 0.798645i \(0.294449\pi\)
\(810\) 1.58701 24.4712i 0.0557619 0.859830i
\(811\) −3.35656 16.8746i −0.117865 0.592546i −0.993899 0.110297i \(-0.964820\pi\)
0.876034 0.482249i \(-0.160180\pi\)
\(812\) 16.4384 + 7.89521i 0.576876 + 0.277068i
\(813\) −35.7878 19.9414i −1.25513 0.699375i
\(814\) 3.40961 0.241279i 0.119507 0.00845682i
\(815\) 1.93662 0.518914i 0.0678367 0.0181768i
\(816\) −14.6261 + 15.7197i −0.512015 + 0.550299i
\(817\) 4.23074 + 1.13362i 0.148015 + 0.0396604i
\(818\) −21.7579 4.21050i −0.760748 0.147217i
\(819\) 0.216355 6.18275i 0.00756006 0.216043i
\(820\) 2.71116 4.15028i 0.0946779 0.144934i
\(821\) −36.5043 41.6252i −1.27401 1.45273i −0.831059 0.556185i \(-0.812265\pi\)
−0.442952 0.896545i \(-0.646069\pi\)
\(822\) 28.8609 10.4593i 1.00664 0.364810i
\(823\) −2.33771 3.04656i −0.0814873 0.106196i 0.750831 0.660495i \(-0.229653\pi\)
−0.832318 + 0.554298i \(0.812987\pi\)
\(824\) −0.809884 + 2.51394i −0.0282137 + 0.0875771i
\(825\) 1.02909 + 2.88637i 0.0358283 + 0.100490i
\(826\) −23.0842 6.05699i −0.803201 0.210749i
\(827\) −21.8040 + 32.6320i −0.758199 + 1.13473i 0.228717 + 0.973493i \(0.426547\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(828\) −9.91540 5.19658i −0.344584 0.180594i
\(829\) 15.4774 + 3.07864i 0.537552 + 0.106926i 0.456398 0.889776i \(-0.349139\pi\)
0.0811541 + 0.996702i \(0.474139\pi\)
\(830\) −30.2018 1.82196i −1.04832 0.0632412i
\(831\) −11.3931 7.36405i −0.395221 0.255456i
\(832\) 12.8131 + 3.90842i 0.444213 + 0.135500i
\(833\) 14.7170 + 8.49688i 0.509915 + 0.294399i
\(834\) 0.259880 2.34297i 0.00899891 0.0811303i
\(835\) −34.0489 + 11.5580i −1.17831 + 0.399983i
\(836\) 1.20621 + 0.485003i 0.0417176 + 0.0167742i
\(837\) 2.43169 + 7.65695i 0.0840515 + 0.264663i
\(838\) 19.0820 + 18.8847i 0.659175 + 0.652359i
\(839\) −13.7738 10.5690i −0.475526 0.364884i 0.343017 0.939329i \(-0.388551\pi\)
−0.818543 + 0.574445i \(0.805218\pi\)
\(840\) −1.16133 + 11.5659i −0.0400697 + 0.399062i
\(841\) −20.4822 + 15.7165i −0.706282 + 0.541949i
\(842\) 5.93044 46.9294i 0.204376 1.61729i
\(843\) 10.7337 + 4.25564i 0.369688 + 0.146572i
\(844\) −6.65326 0.366676i −0.229015 0.0126215i
\(845\) 16.3339 10.9139i 0.561902 0.375451i
\(846\) −8.76565 37.0999i −0.301369 1.27552i
\(847\) 7.93577 + 7.93577i 0.272676 + 0.272676i
\(848\) 14.1897 + 0.634180i 0.487278 + 0.0217778i
\(849\) 3.90544 + 4.31876i 0.134034 + 0.148219i
\(850\) −0.398451 5.63068i −0.0136668 0.193131i
\(851\) −0.214705 3.27577i −0.00736000 0.112292i
\(852\) −3.25029 + 1.98932i −0.111353 + 0.0681529i
\(853\) −4.79682 5.46972i −0.164240 0.187280i 0.663866 0.747852i \(-0.268915\pi\)
−0.828106 + 0.560572i \(0.810581\pi\)
\(854\) −15.6439 6.38486i −0.535322 0.218486i
\(855\) 2.73385 0.0833282i 0.0934957 0.00284976i
\(856\) 42.0134 0.655044i 1.43599 0.0223889i
\(857\) 8.10797 + 6.22146i 0.276963 + 0.212521i 0.737897 0.674913i \(-0.235819\pi\)
−0.460934 + 0.887434i \(0.652486\pi\)
\(858\) −3.03393 + 4.74780i −0.103577 + 0.162087i
\(859\) 19.1774 + 38.8879i 0.654324 + 1.32684i 0.930698 + 0.365788i \(0.119201\pi\)
−0.276374 + 0.961050i \(0.589133\pi\)
\(860\) 17.5115 31.0721i 0.597136 1.05955i
\(861\) −0.750549 2.63956i −0.0255786 0.0899558i
\(862\) −4.49326 5.07019i −0.153041 0.172691i
\(863\) 2.97783i 0.101367i −0.998715 0.0506833i \(-0.983860\pi\)
0.998715 0.0506833i \(-0.0161399\pi\)
\(864\) 25.3636 14.8555i 0.862889 0.505394i
\(865\) 3.05665i 0.103929i
\(866\) 35.2028 31.1972i 1.19624 1.06012i
\(867\) −3.50328 12.3205i −0.118978 0.418425i
\(868\) −1.02380 3.66794i −0.0347499 0.124498i
\(869\) −4.58867 9.30491i −0.155660 0.315647i
\(870\) −29.4435 18.8149i −0.998227 0.637885i
\(871\) −11.0893 8.50911i −0.375746 0.288320i
\(872\) −3.65128 + 1.57954i −0.123648 + 0.0534899i
\(873\) −9.51521 + 17.7056i −0.322041 + 0.599243i
\(874\) 0.471813 1.15601i 0.0159593 0.0391027i
\(875\) −9.83723 11.2172i −0.332559 0.379211i
\(876\) −29.8655 7.18749i −1.00906 0.242843i
\(877\) −2.56832 39.1849i −0.0867258 1.32318i −0.790371 0.612629i \(-0.790112\pi\)
0.703645 0.710552i \(-0.251555\pi\)
\(878\) 19.2484 1.36210i 0.649601 0.0459686i
\(879\) −24.2530 26.8197i −0.818033 0.904607i
\(880\) 6.26878 8.53109i 0.211320 0.287583i
\(881\) 29.4301 + 29.4301i 0.991524 + 0.991524i 0.999964 0.00844056i \(-0.00268675\pi\)
−0.00844056 + 0.999964i \(0.502687\pi\)
\(882\) −15.9529 16.9326i −0.537161 0.570150i
\(883\) 43.3815 28.9866i 1.45990 0.975475i 0.463924 0.885875i \(-0.346441\pi\)
0.995978 0.0896006i \(-0.0285591\pi\)
\(884\) 7.73181 6.92409i 0.260049 0.232882i
\(885\) 42.5089 + 16.8537i 1.42892 + 0.566531i
\(886\) −39.3776 4.97612i −1.32292 0.167176i
\(887\) −7.45308 + 5.71895i −0.250250 + 0.192024i −0.726267 0.687412i \(-0.758747\pi\)
0.476017 + 0.879436i \(0.342080\pi\)
\(888\) 7.59415 + 4.07772i 0.254843 + 0.136839i
\(889\) −11.6805 8.96280i −0.391753 0.300603i
\(890\) 7.33886 7.41553i 0.245999 0.248569i
\(891\) 3.14597 + 11.9563i 0.105394 + 0.400550i
\(892\) 14.8353 + 34.7884i 0.496722 + 1.16480i
\(893\) 4.02620 1.36671i 0.134732 0.0457353i
\(894\) 2.28332 + 0.253264i 0.0763656 + 0.00847041i
\(895\) −22.8523 13.1938i −0.763868 0.441020i
\(896\) −12.2639 + 6.61287i −0.409707 + 0.220920i
\(897\) 4.54460 + 2.93746i 0.151740 + 0.0980789i
\(898\) 0.213724 3.54281i 0.00713208 0.118225i
\(899\) 11.2272 + 2.23323i 0.374448 + 0.0744824i
\(900\) −1.69342 + 7.53964i −0.0564472 + 0.251321i
\(901\) 6.11408 9.15037i 0.203689 0.304843i
\(902\) −0.634305 + 2.41744i −0.0211201 + 0.0804920i
\(903\) −6.63053 18.5971i −0.220650 0.618874i
\(904\) 6.26071 0.508481i 0.208228 0.0169118i
\(905\) 11.9771 + 15.6088i 0.398132 + 0.518855i
\(906\) −8.08004 22.2957i −0.268441 0.740726i
\(907\) −13.6325 15.5449i −0.452661 0.516161i 0.479826 0.877364i \(-0.340700\pi\)
−0.932488 + 0.361202i \(0.882366\pi\)
\(908\) 23.4646 4.92146i 0.778700 0.163324i
\(909\) 20.0257 10.6460i 0.664211 0.353106i
\(910\) 1.06754 5.51654i 0.0353885 0.182872i
\(911\) −36.5211 9.78580i −1.21000 0.324218i −0.403237 0.915095i \(-0.632115\pi\)
−0.806761 + 0.590877i \(0.798782\pi\)
\(912\) 1.91839 + 2.65855i 0.0635243 + 0.0880335i
\(913\) 14.7343 3.94806i 0.487636 0.130662i
\(914\) 3.48638 + 49.2675i 0.115319 + 1.62962i
\(915\) 28.2811 + 15.7585i 0.934943 + 0.520962i
\(916\) −28.9455 + 10.1624i −0.956385 + 0.335774i
\(917\) −3.52222 17.7074i −0.116314 0.584750i
\(918\) 0.331285 22.7717i 0.0109340 0.751578i
\(919\) 7.85946 + 3.25549i 0.259260 + 0.107389i 0.508528 0.861046i \(-0.330190\pi\)
−0.249268 + 0.968435i \(0.580190\pi\)
\(920\) −8.16190 6.06306i −0.269090 0.199893i
\(921\) −16.3588 + 19.2371i −0.539040 + 0.633884i
\(922\) 40.1211 + 22.8867i 1.32132 + 0.753735i
\(923\) 1.65208 0.814717i 0.0543790 0.0268167i
\(924\) −1.29021 5.71656i −0.0424449 0.188061i
\(925\) −2.14580 + 0.728401i −0.0705535 + 0.0239497i
\(926\) −14.6522 + 2.99375i −0.481503 + 0.0983808i
\(927\) −1.15040 2.55428i −0.0377840 0.0838936i
\(928\) −1.08813 41.8684i −0.0357196 1.37440i
\(929\) −16.5607 28.6839i −0.543338 0.941090i −0.998709 0.0507880i \(-0.983827\pi\)
0.455371 0.890302i \(-0.349507\pi\)
\(930\) 1.10001 + 7.21327i 0.0360706 + 0.236532i
\(931\) 1.71082 1.95082i 0.0560699 0.0639354i
\(932\) −2.21080 1.24595i −0.0724171 0.0408125i
\(933\) −33.8480 + 45.5313i −1.10813 + 1.49063i
\(934\) 32.4510 18.9611i 1.06183 0.620426i
\(935\) −3.13894 7.57806i −0.102654 0.247829i
\(936\) −12.8627 + 6.03601i −0.420429 + 0.197293i
\(937\) 3.29889 7.96422i 0.107770 0.260180i −0.860790 0.508961i \(-0.830030\pi\)
0.968560 + 0.248781i \(0.0800299\pi\)
\(938\) 14.4039 1.97251i 0.470303 0.0644047i
\(939\) 16.4361 + 6.51649i 0.536371 + 0.212658i
\(940\) −2.62344 34.5240i −0.0855672 1.12605i
\(941\) −35.5190 + 2.32804i −1.15789 + 0.0758919i −0.632213 0.774795i \(-0.717853\pi\)
−0.525673 + 0.850687i \(0.676187\pi\)
\(942\) 46.4170 + 25.5489i 1.51235 + 0.832429i
\(943\) 2.31852 + 0.621247i 0.0755015 + 0.0202306i
\(944\) 11.8083 + 53.5246i 0.384327 + 1.74208i
\(945\) −7.31097 9.92769i −0.237826 0.322948i
\(946\) −3.41636 + 17.6542i −0.111075 + 0.573987i
\(947\) 2.87025 5.82030i 0.0932707 0.189134i −0.845238 0.534390i \(-0.820541\pi\)
0.938509 + 0.345256i \(0.112208\pi\)
\(948\) 2.74909 26.0179i 0.0892862 0.845021i
\(949\) 14.0607 + 4.77295i 0.456428 + 0.154936i
\(950\) −0.855080 0.108056i −0.0277424 0.00350579i
\(951\) −18.4030 + 12.7062i −0.596757 + 0.412028i
\(952\) −0.538027 + 10.7818i −0.0174375 + 0.349442i
\(953\) 19.2800 + 46.5461i 0.624542 + 1.50778i 0.846317 + 0.532679i \(0.178815\pi\)
−0.221775 + 0.975098i \(0.571185\pi\)
\(954\) −11.6176 + 9.59169i −0.376135 + 0.310542i
\(955\) −25.1632 16.8135i −0.814262 0.544073i
\(956\) −8.55576 + 1.21698i −0.276713 + 0.0393599i
\(957\) 17.0833 + 4.29961i 0.552224 + 0.138987i
\(958\) 12.8882 6.43925i 0.416400 0.208043i
\(959\) 7.71693 13.3661i 0.249193 0.431614i
\(960\) 24.8546 9.74514i 0.802180 0.314523i
\(961\) 14.3048 + 24.7766i 0.461444 + 0.799245i
\(962\) −3.47639 2.29681i −0.112083 0.0740521i
\(963\) −32.5967 + 30.3925i −1.05041 + 0.979384i
\(964\) −48.4126 19.4662i −1.55927 0.626963i
\(965\) 0.516128 7.87459i 0.0166148 0.253492i
\(966\) −5.49658 + 1.21058i −0.176850 + 0.0389498i
\(967\) −57.1170 7.51960i −1.83676 0.241814i −0.869200 0.494460i \(-0.835366\pi\)
−0.967559 + 0.252646i \(0.918699\pi\)
\(968\) 7.90372 24.5337i 0.254035 0.788542i
\(969\) 2.53184 0.204726i 0.0813343 0.00657675i
\(970\) −11.0382 + 14.5411i −0.354415 + 0.466887i
\(971\) −8.87799 44.6327i −0.284908 1.43233i −0.812564 0.582872i \(-0.801929\pi\)
0.527656 0.849458i \(-0.323071\pi\)
\(972\) −9.39578 + 29.7274i −0.301370 + 0.953507i
\(973\) −0.658459 0.985454i −0.0211092 0.0315922i
\(974\) 14.0728 4.85878i 0.450922 0.155685i
\(975\) 1.14666 3.55498i 0.0367224 0.113850i
\(976\) 3.34237 + 38.6621i 0.106987 + 1.23754i
\(977\) 2.22360 + 8.29858i 0.0711392 + 0.265495i 0.992330 0.123616i \(-0.0394490\pi\)
−0.921191 + 0.389111i \(0.872782\pi\)
\(978\) −2.54845 + 0.0520772i −0.0814903 + 0.00166525i
\(979\) −2.32639 + 4.71746i −0.0743519 + 0.150771i
\(980\) −11.9207 17.4454i −0.380794 0.557273i
\(981\) 1.75012 3.83955i 0.0558771 0.122588i
\(982\) −2.25125 + 5.51591i −0.0718404 + 0.176020i
\(983\) −2.44192 + 0.321485i −0.0778852 + 0.0102538i −0.169368 0.985553i \(-0.554173\pi\)
0.0914829 + 0.995807i \(0.470839\pi\)
\(984\) −4.60817 + 4.29962i −0.146903 + 0.137067i
\(985\) 39.6859 + 5.22475i 1.26450 + 0.166474i
\(986\) −28.1867 16.0789i −0.897646 0.512055i
\(987\) −15.3816 11.4346i −0.489601 0.363969i
\(988\) −0.806591 1.36411i −0.0256611 0.0433983i
\(989\) 16.9379 + 3.36915i 0.538593 + 0.107133i
\(990\) 1.13350 + 11.1715i 0.0360248 + 0.355053i
\(991\) 31.1462 0.989392 0.494696 0.869066i \(-0.335279\pi\)
0.494696 + 0.869066i \(0.335279\pi\)
\(992\) −6.42363 + 5.93560i −0.203950 + 0.188455i
\(993\) 35.9294 + 23.2234i 1.14018 + 0.736971i
\(994\) −0.606417 + 1.81742i −0.0192344 + 0.0576451i
\(995\) −18.0812 15.8568i −0.573214 0.502695i
\(996\) 36.7305 + 11.4273i 1.16385 + 0.362088i
\(997\) 1.50167 22.9111i 0.0475584 0.725601i −0.905790 0.423727i \(-0.860721\pi\)
0.953348 0.301873i \(-0.0976119\pi\)
\(998\) 0.0657277 + 12.6479i 0.00208058 + 0.400362i
\(999\) −8.87602 + 2.19146i −0.280825 + 0.0693347i
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 576.2.bl.a.419.2 yes 1504
9.2 odd 6 inner 576.2.bl.a.227.36 yes 1504
64.11 odd 16 inner 576.2.bl.a.203.36 yes 1504
576.11 even 48 inner 576.2.bl.a.11.2 1504
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.bl.a.11.2 1504 576.11 even 48 inner
576.2.bl.a.203.36 yes 1504 64.11 odd 16 inner
576.2.bl.a.227.36 yes 1504 9.2 odd 6 inner
576.2.bl.a.419.2 yes 1504 1.1 even 1 trivial