Properties

Label 336.2.bu.a.11.3
Level $336$
Weight $2$
Character 336.11
Analytic conductor $2.683$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(11,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 6, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bu (of order \(12\), degree \(4\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(60\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.3
Character \(\chi\) \(=\) 336.11
Dual form 336.2.bu.a.275.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37508 - 0.330401i) q^{2} +(1.72844 - 0.111804i) q^{3} +(1.78167 + 0.908653i) q^{4} +(-0.754514 - 0.202171i) q^{5} +(-2.41368 - 0.417338i) q^{6} +(-2.17010 + 1.51350i) q^{7} +(-2.14971 - 1.83813i) q^{8} +(2.97500 - 0.386494i) q^{9} +O(q^{10})\) \(q+(-1.37508 - 0.330401i) q^{2} +(1.72844 - 0.111804i) q^{3} +(1.78167 + 0.908653i) q^{4} +(-0.754514 - 0.202171i) q^{5} +(-2.41368 - 0.417338i) q^{6} +(-2.17010 + 1.51350i) q^{7} +(-2.14971 - 1.83813i) q^{8} +(2.97500 - 0.386494i) q^{9} +(0.970717 + 0.527293i) q^{10} +(5.08163 - 1.36162i) q^{11} +(3.18110 + 1.37135i) q^{12} +(1.87763 - 1.87763i) q^{13} +(3.48411 - 1.36417i) q^{14} +(-1.32673 - 0.265083i) q^{15} +(2.34870 + 3.23784i) q^{16} +(5.05298 + 2.91734i) q^{17} +(-4.21855 - 0.451484i) q^{18} +(0.230416 - 0.859925i) q^{19} +(-1.16059 - 1.04579i) q^{20} +(-3.58167 + 2.85861i) q^{21} +(-7.43751 + 0.193355i) q^{22} +(-2.30923 + 1.33323i) q^{23} +(-3.92116 - 2.93675i) q^{24} +(-3.80171 - 2.19492i) q^{25} +(-3.20225 + 1.96151i) q^{26} +(5.09889 - 1.00065i) q^{27} +(-5.24164 + 0.724684i) q^{28} +(2.32537 + 2.32537i) q^{29} +(1.73678 + 0.802864i) q^{30} +(6.21837 + 3.59018i) q^{31} +(-2.15986 - 5.22829i) q^{32} +(8.63106 - 2.92162i) q^{33} +(-5.98434 - 5.68107i) q^{34} +(1.94336 - 0.703222i) q^{35} +(5.65166 + 2.01464i) q^{36} +(0.780980 - 2.91466i) q^{37} +(-0.600960 + 1.10633i) q^{38} +(3.03544 - 3.45529i) q^{39} +(1.25037 + 1.82151i) q^{40} -4.47045 q^{41} +(5.86955 - 2.74742i) q^{42} +(-7.38377 + 7.38377i) q^{43} +(10.2910 + 2.19148i) q^{44} +(-2.32282 - 0.309845i) q^{45} +(3.61586 - 1.07033i) q^{46} +(-2.95041 - 5.11026i) q^{47} +(4.42159 + 5.33381i) q^{48} +(2.41866 - 6.56887i) q^{49} +(4.50244 + 4.27427i) q^{50} +(9.05994 + 4.47750i) q^{51} +(5.05142 - 1.63920i) q^{52} +(-2.40475 - 8.97464i) q^{53} +(-7.34198 - 0.308710i) q^{54} -4.10944 q^{55} +(7.44710 + 0.735348i) q^{56} +(0.302117 - 1.51209i) q^{57} +(-2.42926 - 3.96586i) q^{58} +(-1.93628 + 0.518825i) q^{59} +(-2.12294 - 1.67783i) q^{60} +(3.47073 + 0.929978i) q^{61} +(-7.36453 - 6.99132i) q^{62} +(-5.87109 + 5.34138i) q^{63} +(1.24254 + 7.90292i) q^{64} +(-1.79630 + 1.03709i) q^{65} +(-12.8337 + 1.16575i) q^{66} +(-3.49054 + 0.935287i) q^{67} +(6.35190 + 9.78914i) q^{68} +(-3.84229 + 2.56259i) q^{69} +(-2.90461 + 0.324897i) q^{70} +1.26188i q^{71} +(-7.10582 - 4.63759i) q^{72} +(-3.84560 - 2.22026i) q^{73} +(-2.03691 + 3.74984i) q^{74} +(-6.81642 - 3.36873i) q^{75} +(1.19190 - 1.32274i) q^{76} +(-8.96684 + 10.6459i) q^{77} +(-5.31559 + 3.74838i) q^{78} +(-13.8954 + 8.02251i) q^{79} +(-1.11753 - 2.91784i) q^{80} +(8.70125 - 2.29964i) q^{81} +(6.14721 + 1.47704i) q^{82} +(-6.66544 + 6.66544i) q^{83} +(-8.97884 + 1.83861i) q^{84} +(-3.22274 - 3.22274i) q^{85} +(12.5929 - 7.71365i) q^{86} +(4.27924 + 3.75927i) q^{87} +(-13.4269 - 6.41362i) q^{88} +(-7.91568 - 13.7104i) q^{89} +(3.09168 + 1.19352i) q^{90} +(-1.23286 + 6.91642i) q^{91} +(-5.32573 + 0.277096i) q^{92} +(11.1495 + 5.51016i) q^{93} +(2.36860 + 8.00181i) q^{94} +(-0.347705 + 0.602242i) q^{95} +(-4.31773 - 8.79530i) q^{96} -1.21416 q^{97} +(-5.49621 + 8.23357i) q^{98} +(14.5916 - 6.01484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37508 0.330401i −0.972326 0.233629i
\(3\) 1.72844 0.111804i 0.997914 0.0645502i
\(4\) 1.78167 + 0.908653i 0.890835 + 0.454326i
\(5\) −0.754514 0.202171i −0.337429 0.0904138i 0.0861259 0.996284i \(-0.472551\pi\)
−0.423555 + 0.905870i \(0.639218\pi\)
\(6\) −2.41368 0.417338i −0.985379 0.170378i
\(7\) −2.17010 + 1.51350i −0.820220 + 0.572048i
\(8\) −2.14971 1.83813i −0.760039 0.649878i
\(9\) 2.97500 0.386494i 0.991667 0.128831i
\(10\) 0.970717 + 0.527293i 0.306968 + 0.166745i
\(11\) 5.08163 1.36162i 1.53217 0.410544i 0.608444 0.793597i \(-0.291794\pi\)
0.923726 + 0.383053i \(0.125127\pi\)
\(12\) 3.18110 + 1.37135i 0.918304 + 0.395875i
\(13\) 1.87763 1.87763i 0.520760 0.520760i −0.397041 0.917801i \(-0.629963\pi\)
0.917801 + 0.397041i \(0.129963\pi\)
\(14\) 3.48411 1.36417i 0.931168 0.364590i
\(15\) −1.32673 0.265083i −0.342562 0.0684441i
\(16\) 2.34870 + 3.23784i 0.587175 + 0.809460i
\(17\) 5.05298 + 2.91734i 1.22553 + 0.707559i 0.966091 0.258202i \(-0.0831299\pi\)
0.259436 + 0.965760i \(0.416463\pi\)
\(18\) −4.21855 0.451484i −0.994322 0.106416i
\(19\) 0.230416 0.859925i 0.0528611 0.197280i −0.934446 0.356106i \(-0.884104\pi\)
0.987307 + 0.158826i \(0.0507708\pi\)
\(20\) −1.16059 1.04579i −0.259516 0.233847i
\(21\) −3.58167 + 2.85861i −0.781584 + 0.623800i
\(22\) −7.43751 + 0.193355i −1.58568 + 0.0412235i
\(23\) −2.30923 + 1.33323i −0.481507 + 0.277998i −0.721044 0.692889i \(-0.756338\pi\)
0.239537 + 0.970887i \(0.423004\pi\)
\(24\) −3.92116 2.93675i −0.800403 0.599462i
\(25\) −3.80171 2.19492i −0.760342 0.438984i
\(26\) −3.20225 + 1.96151i −0.628013 + 0.384684i
\(27\) 5.09889 1.00065i 0.981282 0.192575i
\(28\) −5.24164 + 0.724684i −0.990578 + 0.136952i
\(29\) 2.32537 + 2.32537i 0.431810 + 0.431810i 0.889244 0.457434i \(-0.151231\pi\)
−0.457434 + 0.889244i \(0.651231\pi\)
\(30\) 1.73678 + 0.802864i 0.317091 + 0.146582i
\(31\) 6.21837 + 3.59018i 1.11685 + 0.644815i 0.940595 0.339530i \(-0.110268\pi\)
0.176256 + 0.984344i \(0.443601\pi\)
\(32\) −2.15986 5.22829i −0.381812 0.924240i
\(33\) 8.63106 2.92162i 1.50247 0.508589i
\(34\) −5.98434 5.68107i −1.02631 0.974296i
\(35\) 1.94336 0.703222i 0.328487 0.118866i
\(36\) 5.65166 + 2.01464i 0.941943 + 0.335773i
\(37\) 0.780980 2.91466i 0.128392 0.479167i −0.871545 0.490315i \(-0.836882\pi\)
0.999938 + 0.0111478i \(0.00354853\pi\)
\(38\) −0.600960 + 1.10633i −0.0974886 + 0.179471i
\(39\) 3.03544 3.45529i 0.486059 0.553289i
\(40\) 1.25037 + 1.82151i 0.197701 + 0.288006i
\(41\) −4.47045 −0.698167 −0.349084 0.937092i \(-0.613507\pi\)
−0.349084 + 0.937092i \(0.613507\pi\)
\(42\) 5.86955 2.74742i 0.905692 0.423936i
\(43\) −7.38377 + 7.38377i −1.12602 + 1.12602i −0.135196 + 0.990819i \(0.543166\pi\)
−0.990819 + 0.135196i \(0.956834\pi\)
\(44\) 10.2910 + 2.19148i 1.55143 + 0.330378i
\(45\) −2.32282 0.309845i −0.346265 0.0461890i
\(46\) 3.61586 1.07033i 0.533130 0.157811i
\(47\) −2.95041 5.11026i −0.430361 0.745407i 0.566543 0.824032i \(-0.308280\pi\)
−0.996904 + 0.0786247i \(0.974947\pi\)
\(48\) 4.42159 + 5.33381i 0.638201 + 0.769870i
\(49\) 2.41866 6.56887i 0.345523 0.938410i
\(50\) 4.50244 + 4.27427i 0.636741 + 0.604473i
\(51\) 9.05994 + 4.47750i 1.26864 + 0.626975i
\(52\) 5.05142 1.63920i 0.700506 0.227316i
\(53\) −2.40475 8.97464i −0.330317 1.23276i −0.908857 0.417107i \(-0.863044\pi\)
0.578540 0.815654i \(-0.303623\pi\)
\(54\) −7.34198 0.308710i −0.999117 0.0420101i
\(55\) −4.10944 −0.554117
\(56\) 7.44710 + 0.735348i 0.995160 + 0.0982650i
\(57\) 0.302117 1.51209i 0.0400164 0.200281i
\(58\) −2.42926 3.96586i −0.318977 0.520743i
\(59\) −1.93628 + 0.518825i −0.252082 + 0.0675453i −0.382647 0.923894i \(-0.624988\pi\)
0.130565 + 0.991440i \(0.458321\pi\)
\(60\) −2.12294 1.67783i −0.274070 0.216607i
\(61\) 3.47073 + 0.929978i 0.444381 + 0.119072i 0.474069 0.880488i \(-0.342785\pi\)
−0.0296881 + 0.999559i \(0.509451\pi\)
\(62\) −7.36453 6.99132i −0.935297 0.887899i
\(63\) −5.87109 + 5.34138i −0.739688 + 0.672950i
\(64\) 1.24254 + 7.90292i 0.155317 + 0.987865i
\(65\) −1.79630 + 1.03709i −0.222803 + 0.128636i
\(66\) −12.8337 + 1.16575i −1.57972 + 0.143494i
\(67\) −3.49054 + 0.935287i −0.426437 + 0.114264i −0.465653 0.884967i \(-0.654181\pi\)
0.0392160 + 0.999231i \(0.487514\pi\)
\(68\) 6.35190 + 9.78914i 0.770281 + 1.18711i
\(69\) −3.84229 + 2.56259i −0.462558 + 0.308500i
\(70\) −2.90461 + 0.324897i −0.347167 + 0.0388326i
\(71\) 1.26188i 0.149758i 0.997193 + 0.0748791i \(0.0238571\pi\)
−0.997193 + 0.0748791i \(0.976143\pi\)
\(72\) −7.10582 4.63759i −0.837429 0.546546i
\(73\) −3.84560 2.22026i −0.450094 0.259862i 0.257776 0.966205i \(-0.417010\pi\)
−0.707870 + 0.706343i \(0.750344\pi\)
\(74\) −2.03691 + 3.74984i −0.236786 + 0.435910i
\(75\) −6.81642 3.36873i −0.787093 0.388988i
\(76\) 1.19190 1.32274i 0.136720 0.151728i
\(77\) −8.96684 + 10.6459i −1.02187 + 1.21321i
\(78\) −5.31559 + 3.74838i −0.601872 + 0.424420i
\(79\) −13.8954 + 8.02251i −1.56335 + 0.902602i −0.566439 + 0.824104i \(0.691679\pi\)
−0.996914 + 0.0784990i \(0.974987\pi\)
\(80\) −1.11753 2.91784i −0.124944 0.326224i
\(81\) 8.70125 2.29964i 0.966805 0.255515i
\(82\) 6.14721 + 1.47704i 0.678846 + 0.163112i
\(83\) −6.66544 + 6.66544i −0.731627 + 0.731627i −0.970942 0.239315i \(-0.923077\pi\)
0.239315 + 0.970942i \(0.423077\pi\)
\(84\) −8.97884 + 1.83861i −0.979671 + 0.200609i
\(85\) −3.22274 3.22274i −0.349555 0.349555i
\(86\) 12.5929 7.71365i 1.35792 0.831784i
\(87\) 4.27924 + 3.75927i 0.458783 + 0.403036i
\(88\) −13.4269 6.41362i −1.43131 0.683694i
\(89\) −7.91568 13.7104i −0.839060 1.45330i −0.890681 0.454629i \(-0.849772\pi\)
0.0516207 0.998667i \(-0.483561\pi\)
\(90\) 3.09168 + 1.19352i 0.325892 + 0.125808i
\(91\) −1.23286 + 6.91642i −0.129239 + 0.725037i
\(92\) −5.32573 + 0.277096i −0.555245 + 0.0288893i
\(93\) 11.1495 + 5.51016i 1.15615 + 0.571377i
\(94\) 2.36860 + 8.00181i 0.244303 + 0.825324i
\(95\) −0.347705 + 0.602242i −0.0356737 + 0.0617887i
\(96\) −4.31773 8.79530i −0.440676 0.897666i
\(97\) −1.21416 −0.123279 −0.0616394 0.998098i \(-0.519633\pi\)
−0.0616394 + 0.998098i \(0.519633\pi\)
\(98\) −5.49621 + 8.23357i −0.555201 + 0.831716i
\(99\) 14.5916 6.01484i 1.46651 0.604514i
\(100\) −4.77897 7.36505i −0.477897 0.736505i
\(101\) 1.70137 + 6.34960i 0.169293 + 0.631808i 0.997454 + 0.0713182i \(0.0227206\pi\)
−0.828161 + 0.560490i \(0.810613\pi\)
\(102\) −10.9787 9.15031i −1.08706 0.906016i
\(103\) 3.18462 + 5.51593i 0.313790 + 0.543501i 0.979180 0.202996i \(-0.0650678\pi\)
−0.665389 + 0.746497i \(0.731734\pi\)
\(104\) −7.48769 + 0.585033i −0.734228 + 0.0573672i
\(105\) 3.28035 1.43275i 0.320129 0.139822i
\(106\) 0.341483 + 13.1353i 0.0331678 + 1.27582i
\(107\) −4.85135 + 18.1055i −0.468998 + 1.75032i 0.174285 + 0.984695i \(0.444239\pi\)
−0.643283 + 0.765629i \(0.722428\pi\)
\(108\) 9.99379 + 2.85030i 0.961653 + 0.274270i
\(109\) −3.78984 14.1439i −0.363001 1.35474i −0.870111 0.492856i \(-0.835953\pi\)
0.507110 0.861881i \(-0.330714\pi\)
\(110\) 5.65080 + 1.35776i 0.538783 + 0.129458i
\(111\) 1.02401 5.12512i 0.0971943 0.486455i
\(112\) −9.99737 3.47169i −0.944663 0.328044i
\(113\) 15.8670i 1.49264i −0.665587 0.746321i \(-0.731819\pi\)
0.665587 0.746321i \(-0.268181\pi\)
\(114\) −0.915030 + 1.97942i −0.0857004 + 0.185390i
\(115\) 2.01189 0.539083i 0.187609 0.0502698i
\(116\) 2.03009 + 6.25599i 0.188489 + 0.580854i
\(117\) 4.86025 6.31163i 0.449330 0.583510i
\(118\) 2.83395 0.0736751i 0.260887 0.00678235i
\(119\) −15.3808 + 1.31675i −1.40996 + 0.120706i
\(120\) 2.36484 + 3.00857i 0.215880 + 0.274643i
\(121\) 14.4427 8.33850i 1.31297 0.758046i
\(122\) −4.46525 2.42552i −0.404265 0.219596i
\(123\) −7.72690 + 0.499816i −0.696711 + 0.0450669i
\(124\) 7.81686 + 12.0468i 0.701975 + 1.08184i
\(125\) 5.18641 + 5.18641i 0.463886 + 0.463886i
\(126\) 9.83799 5.40499i 0.876438 0.481515i
\(127\) 1.55313i 0.137818i 0.997623 + 0.0689089i \(0.0219518\pi\)
−0.997623 + 0.0689089i \(0.978048\pi\)
\(128\) 0.902545 11.2777i 0.0797745 0.996813i
\(129\) −11.9369 + 13.5879i −1.05098 + 1.19635i
\(130\) 2.81270 0.832584i 0.246690 0.0730225i
\(131\) 8.93944 + 2.39532i 0.781043 + 0.209280i 0.627244 0.778823i \(-0.284183\pi\)
0.153798 + 0.988102i \(0.450849\pi\)
\(132\) 18.0324 + 2.63726i 1.56952 + 0.229544i
\(133\) 0.801467 + 2.21486i 0.0694960 + 0.192052i
\(134\) 5.10878 0.132814i 0.441331 0.0114734i
\(135\) −4.04949 0.275847i −0.348525 0.0237411i
\(136\) −5.50000 15.5595i −0.471621 1.33422i
\(137\) −4.59559 + 7.95980i −0.392628 + 0.680052i −0.992795 0.119823i \(-0.961767\pi\)
0.600167 + 0.799875i \(0.295101\pi\)
\(138\) 6.13013 2.25426i 0.521831 0.191896i
\(139\) 4.40063 4.40063i 0.373257 0.373257i −0.495405 0.868662i \(-0.664980\pi\)
0.868662 + 0.495405i \(0.164980\pi\)
\(140\) 4.10141 + 0.512927i 0.346632 + 0.0433502i
\(141\) −5.67095 8.50289i −0.477580 0.716073i
\(142\) 0.416928 1.73519i 0.0349878 0.145614i
\(143\) 6.98480 12.0980i 0.584098 1.01169i
\(144\) 8.23879 + 8.72481i 0.686566 + 0.727068i
\(145\) −1.28440 2.22465i −0.106664 0.184747i
\(146\) 4.55442 + 4.32362i 0.376927 + 0.357825i
\(147\) 3.44608 11.6243i 0.284228 0.958757i
\(148\) 4.03986 4.48332i 0.332075 0.368527i
\(149\) −13.6759 3.66445i −1.12037 0.300203i −0.349340 0.936996i \(-0.613594\pi\)
−0.771035 + 0.636793i \(0.780261\pi\)
\(150\) 8.26007 + 6.88442i 0.674432 + 0.562110i
\(151\) −4.32448 + 7.49022i −0.351921 + 0.609545i −0.986586 0.163242i \(-0.947805\pi\)
0.634665 + 0.772788i \(0.281138\pi\)
\(152\) −2.07599 + 1.42506i −0.168385 + 0.115587i
\(153\) 16.1601 + 6.72614i 1.30647 + 0.543776i
\(154\) 15.8475 11.6762i 1.27703 0.940899i
\(155\) −3.96602 3.96602i −0.318558 0.318558i
\(156\) 8.54780 3.39803i 0.684372 0.272060i
\(157\) 0.697413 + 2.60278i 0.0556596 + 0.207724i 0.988155 0.153456i \(-0.0490404\pi\)
−0.932496 + 0.361181i \(0.882374\pi\)
\(158\) 21.7579 6.44051i 1.73096 0.512380i
\(159\) −5.15986 15.2432i −0.409203 1.20887i
\(160\) 0.572632 + 4.38148i 0.0452705 + 0.346386i
\(161\) 2.99341 6.38825i 0.235914 0.503465i
\(162\) −12.7247 + 0.287278i −0.999745 + 0.0225707i
\(163\) −0.593685 + 2.21566i −0.0465010 + 0.173544i −0.985271 0.171001i \(-0.945300\pi\)
0.938770 + 0.344545i \(0.111967\pi\)
\(164\) −7.96487 4.06209i −0.621952 0.317196i
\(165\) −7.10292 + 0.459454i −0.552962 + 0.0357684i
\(166\) 11.3678 6.96323i 0.882309 0.540451i
\(167\) 19.3308i 1.49586i −0.663777 0.747931i \(-0.731047\pi\)
0.663777 0.747931i \(-0.268953\pi\)
\(168\) 12.9541 + 0.438386i 0.999428 + 0.0338222i
\(169\) 5.94904i 0.457618i
\(170\) 3.36672 + 5.49631i 0.258216 + 0.421548i
\(171\) 0.353133 2.64733i 0.0270047 0.202447i
\(172\) −19.8647 + 6.44617i −1.51467 + 0.491516i
\(173\) −5.68241 + 21.2070i −0.432025 + 1.61234i 0.316061 + 0.948739i \(0.397640\pi\)
−0.748086 + 0.663602i \(0.769027\pi\)
\(174\) −4.64222 6.58315i −0.351926 0.499067i
\(175\) 11.5721 0.990680i 0.874767 0.0748884i
\(176\) 16.3439 + 13.2555i 1.23197 + 0.999169i
\(177\) −3.28874 + 1.11324i −0.247197 + 0.0836764i
\(178\) 6.35475 + 21.4681i 0.476309 + 1.60911i
\(179\) 0.384389 + 1.43456i 0.0287306 + 0.107224i 0.978802 0.204808i \(-0.0656570\pi\)
−0.950072 + 0.312032i \(0.898990\pi\)
\(180\) −3.85695 2.66268i −0.287480 0.198464i
\(181\) 15.0817 + 15.0817i 1.12101 + 1.12101i 0.991589 + 0.129425i \(0.0413133\pi\)
0.129425 + 0.991589i \(0.458687\pi\)
\(182\) 3.98046 9.10326i 0.295051 0.674779i
\(183\) 6.10291 + 1.21937i 0.451140 + 0.0901383i
\(184\) 7.41483 + 1.37860i 0.546629 + 0.101631i
\(185\) −1.17852 + 2.04126i −0.0866466 + 0.150076i
\(186\) −13.5108 11.2607i −0.990660 0.825673i
\(187\) 29.6497 + 7.94461i 2.16820 + 0.580968i
\(188\) −0.613206 11.7857i −0.0447227 0.859560i
\(189\) −9.55063 + 9.88866i −0.694706 + 0.719294i
\(190\) 0.677102 0.713247i 0.0491221 0.0517444i
\(191\) −5.18582 8.98210i −0.375233 0.649922i 0.615129 0.788426i \(-0.289104\pi\)
−0.990362 + 0.138504i \(0.955770\pi\)
\(192\) 3.03123 + 13.5208i 0.218760 + 0.975779i
\(193\) −1.28842 + 2.23161i −0.0927427 + 0.160635i −0.908664 0.417528i \(-0.862897\pi\)
0.815922 + 0.578163i \(0.196230\pi\)
\(194\) 1.66956 + 0.401158i 0.119867 + 0.0288015i
\(195\) −2.98884 + 1.99339i −0.214035 + 0.142749i
\(196\) 10.2781 9.50584i 0.734149 0.678989i
\(197\) −2.81762 + 2.81762i −0.200747 + 0.200747i −0.800320 0.599573i \(-0.795337\pi\)
0.599573 + 0.800320i \(0.295337\pi\)
\(198\) −22.0519 + 3.44978i −1.56716 + 0.245165i
\(199\) 4.53162 7.84900i 0.321238 0.556401i −0.659506 0.751700i \(-0.729234\pi\)
0.980744 + 0.195299i \(0.0625677\pi\)
\(200\) 4.13804 + 11.7065i 0.292603 + 0.827774i
\(201\) −5.92861 + 2.00684i −0.418172 + 0.141552i
\(202\) −0.241601 9.29331i −0.0169990 0.653875i
\(203\) −8.56572 1.52685i −0.601195 0.107164i
\(204\) 12.0733 + 16.2098i 0.845302 + 1.13491i
\(205\) 3.37302 + 0.903798i 0.235582 + 0.0631240i
\(206\) −2.55663 8.63703i −0.178129 0.601770i
\(207\) −6.35466 + 4.85887i −0.441679 + 0.337715i
\(208\) 10.4894 + 1.66947i 0.727312 + 0.115757i
\(209\) 4.68356i 0.323969i
\(210\) −4.98411 + 0.886312i −0.343936 + 0.0611614i
\(211\) −5.89696 5.89696i −0.405964 0.405964i 0.474365 0.880328i \(-0.342678\pi\)
−0.880328 + 0.474365i \(0.842678\pi\)
\(212\) 3.87036 18.1749i 0.265818 1.24826i
\(213\) 0.141084 + 2.18109i 0.00966692 + 0.149446i
\(214\) 12.6530 23.2935i 0.864945 1.59231i
\(215\) 7.06395 4.07837i 0.481757 0.278143i
\(216\) −12.8005 7.22133i −0.870963 0.491349i
\(217\) −18.9282 + 1.62043i −1.28493 + 0.110002i
\(218\) 0.538172 + 20.7011i 0.0364496 + 1.40205i
\(219\) −6.89512 3.40763i −0.465929 0.230266i
\(220\) −7.32168 3.73406i −0.493627 0.251750i
\(221\) 14.9653 4.00994i 1.00667 0.269737i
\(222\) −3.10143 + 6.70911i −0.208154 + 0.450286i
\(223\) 26.6995i 1.78793i −0.448135 0.893966i \(-0.647912\pi\)
0.448135 0.893966i \(-0.352088\pi\)
\(224\) 12.6001 + 8.07697i 0.841880 + 0.539666i
\(225\) −12.1584 5.06054i −0.810560 0.337369i
\(226\) −5.24247 + 21.8183i −0.348724 + 1.45133i
\(227\) 4.43947 + 16.5683i 0.294658 + 1.09968i 0.941489 + 0.337045i \(0.109427\pi\)
−0.646831 + 0.762634i \(0.723906\pi\)
\(228\) 1.91224 2.41953i 0.126641 0.160237i
\(229\) 1.00246 3.74124i 0.0662446 0.247228i −0.924861 0.380305i \(-0.875819\pi\)
0.991106 + 0.133077i \(0.0424857\pi\)
\(230\) −2.94461 + 0.0765519i −0.194162 + 0.00504768i
\(231\) −14.3084 + 19.4033i −0.941423 + 1.27664i
\(232\) −0.724541 9.27321i −0.0475685 0.608816i
\(233\) −4.71826 8.17227i −0.309104 0.535383i 0.669063 0.743206i \(-0.266696\pi\)
−0.978167 + 0.207823i \(0.933362\pi\)
\(234\) −8.76858 + 7.07314i −0.573220 + 0.462386i
\(235\) 1.19298 + 4.45225i 0.0778212 + 0.290433i
\(236\) −3.92125 0.835032i −0.255251 0.0543560i
\(237\) −23.1204 + 15.4200i −1.50183 + 1.00163i
\(238\) 21.5849 + 3.27122i 1.39914 + 0.212042i
\(239\) −8.96265 −0.579746 −0.289873 0.957065i \(-0.593613\pi\)
−0.289873 + 0.957065i \(0.593613\pi\)
\(240\) −2.25781 4.91836i −0.145741 0.317479i
\(241\) 13.4509 23.2977i 0.866452 1.50074i 0.000852960 1.00000i \(-0.499728\pi\)
0.865599 0.500739i \(-0.166938\pi\)
\(242\) −22.6149 + 6.69420i −1.45374 + 0.430319i
\(243\) 14.7825 4.94762i 0.948295 0.317390i
\(244\) 5.33866 + 4.81060i 0.341773 + 0.307967i
\(245\) −3.15295 + 4.46732i −0.201435 + 0.285407i
\(246\) 10.7902 + 1.86569i 0.687959 + 0.118952i
\(247\) −1.18198 2.04725i −0.0752078 0.130264i
\(248\) −6.76849 19.1480i −0.429800 1.21590i
\(249\) −10.7756 + 12.2660i −0.682875 + 0.777328i
\(250\) −5.41811 8.84530i −0.342672 0.559426i
\(251\) 8.65499 + 8.65499i 0.546298 + 0.546298i 0.925368 0.379070i \(-0.123756\pi\)
−0.379070 + 0.925368i \(0.623756\pi\)
\(252\) −15.3138 + 4.18180i −0.964679 + 0.263428i
\(253\) −9.91929 + 9.91929i −0.623620 + 0.623620i
\(254\) 0.513155 2.13567i 0.0321982 0.134004i
\(255\) −5.93063 5.20999i −0.371390 0.326263i
\(256\) −4.96721 + 15.2094i −0.310451 + 0.950589i
\(257\) 4.68663 2.70583i 0.292344 0.168785i −0.346654 0.937993i \(-0.612682\pi\)
0.638999 + 0.769208i \(0.279349\pi\)
\(258\) 20.9036 14.7405i 1.30140 0.917704i
\(259\) 2.71652 + 7.50711i 0.168796 + 0.466469i
\(260\) −4.14277 + 0.215547i −0.256924 + 0.0133677i
\(261\) 7.81671 + 6.01923i 0.483842 + 0.372581i
\(262\) −11.5010 6.24734i −0.710534 0.385962i
\(263\) −8.16518 4.71417i −0.503487 0.290688i 0.226666 0.973973i \(-0.427218\pi\)
−0.730152 + 0.683284i \(0.760551\pi\)
\(264\) −23.9246 9.58437i −1.47246 0.589877i
\(265\) 7.25766i 0.445835i
\(266\) −0.370288 3.31040i −0.0227038 0.202974i
\(267\) −15.2146 22.8125i −0.931121 1.39610i
\(268\) −7.06884 1.50531i −0.431798 0.0919517i
\(269\) 22.4971 6.02807i 1.37167 0.367538i 0.503582 0.863948i \(-0.332015\pi\)
0.868088 + 0.496410i \(0.165349\pi\)
\(270\) 5.47722 + 1.71727i 0.333333 + 0.104509i
\(271\) −4.20629 + 2.42850i −0.255514 + 0.147521i −0.622286 0.782790i \(-0.713796\pi\)
0.366772 + 0.930311i \(0.380463\pi\)
\(272\) 2.42206 + 23.2127i 0.146859 + 1.40748i
\(273\) −1.35763 + 12.0924i −0.0821676 + 0.731868i
\(274\) 8.94922 9.42695i 0.540642 0.569503i
\(275\) −22.3075 5.97729i −1.34519 0.360444i
\(276\) −9.17421 + 1.07438i −0.552222 + 0.0646702i
\(277\) 1.55735 0.417290i 0.0935719 0.0250725i −0.211729 0.977328i \(-0.567910\pi\)
0.305301 + 0.952256i \(0.401243\pi\)
\(278\) −7.50518 + 4.59724i −0.450131 + 0.275724i
\(279\) 19.8872 + 8.27741i 1.19062 + 0.495556i
\(280\) −5.47027 2.06042i −0.326911 0.123134i
\(281\) −10.0515 −0.599621 −0.299811 0.953999i \(-0.596923\pi\)
−0.299811 + 0.953999i \(0.596923\pi\)
\(282\) 4.98862 + 13.5658i 0.297068 + 0.807832i
\(283\) −2.21053 8.24980i −0.131402 0.490399i 0.868585 0.495541i \(-0.165030\pi\)
−0.999987 + 0.00514138i \(0.998363\pi\)
\(284\) −1.14661 + 2.24826i −0.0680391 + 0.133410i
\(285\) −0.533653 + 1.07981i −0.0316109 + 0.0639626i
\(286\) −13.6018 + 14.3279i −0.804293 + 0.847228i
\(287\) 9.70133 6.76601i 0.572651 0.399385i
\(288\) −8.44628 14.7194i −0.497702 0.867348i
\(289\) 8.52173 + 14.7601i 0.501278 + 0.868240i
\(290\) 1.03112 + 3.48343i 0.0605497 + 0.204554i
\(291\) −2.09859 + 0.135748i −0.123022 + 0.00795768i
\(292\) −4.83415 7.45009i −0.282897 0.435984i
\(293\) 11.2904 11.2904i 0.659594 0.659594i −0.295690 0.955284i \(-0.595549\pi\)
0.955284 + 0.295690i \(0.0955495\pi\)
\(294\) −8.57931 + 14.8457i −0.500355 + 0.865820i
\(295\) 1.56584 0.0911669
\(296\) −7.03641 + 4.83014i −0.408983 + 0.280746i
\(297\) 24.5482 12.0277i 1.42443 0.697917i
\(298\) 17.5947 + 9.55743i 1.01923 + 0.553647i
\(299\) −1.83255 + 6.83918i −0.105979 + 0.395520i
\(300\) −9.08361 12.1957i −0.524442 0.704121i
\(301\) 4.84821 27.1988i 0.279446 1.56771i
\(302\) 8.42127 8.87081i 0.484589 0.510458i
\(303\) 3.65062 + 10.7847i 0.209723 + 0.619563i
\(304\) 3.32548 1.27366i 0.190729 0.0730492i
\(305\) −2.43070 1.40336i −0.139181 0.0803564i
\(306\) −19.9991 14.5883i −1.14327 0.833956i
\(307\) −5.34075 5.34075i −0.304813 0.304813i 0.538081 0.842893i \(-0.319150\pi\)
−0.842893 + 0.538081i \(0.819150\pi\)
\(308\) −25.6494 + 10.8197i −1.46151 + 0.616510i
\(309\) 6.12113 + 9.17789i 0.348219 + 0.522112i
\(310\) 4.14320 + 6.76395i 0.235318 + 0.384167i
\(311\) 24.0537 + 13.8874i 1.36396 + 0.787483i 0.990149 0.140021i \(-0.0447171\pi\)
0.373812 + 0.927504i \(0.378050\pi\)
\(312\) −12.8766 + 1.84835i −0.728994 + 0.104642i
\(313\) −13.9319 + 8.04359i −0.787478 + 0.454650i −0.839074 0.544018i \(-0.816902\pi\)
0.0515962 + 0.998668i \(0.483569\pi\)
\(314\) −0.0990353 3.80945i −0.00558889 0.214980i
\(315\) 5.50969 2.84318i 0.310436 0.160195i
\(316\) −32.0467 + 1.66738i −1.80277 + 0.0937975i
\(317\) −2.76754 + 10.3286i −0.155440 + 0.580111i 0.843627 + 0.536930i \(0.180416\pi\)
−0.999067 + 0.0431814i \(0.986251\pi\)
\(318\) 2.05882 + 22.6655i 0.115453 + 1.27102i
\(319\) 14.9829 + 8.65040i 0.838883 + 0.484330i
\(320\) 0.660232 6.21407i 0.0369081 0.347377i
\(321\) −6.36099 + 31.8366i −0.355036 + 1.77695i
\(322\) −6.22685 + 7.79531i −0.347009 + 0.434416i
\(323\) 3.67298 3.67298i 0.204370 0.204370i
\(324\) 17.5923 + 3.80921i 0.977351 + 0.211623i
\(325\) −11.2594 + 3.01695i −0.624561 + 0.167350i
\(326\) 1.54842 2.85055i 0.0857589 0.157877i
\(327\) −8.13185 24.0231i −0.449692 1.32848i
\(328\) 9.61019 + 8.21728i 0.530634 + 0.453724i
\(329\) 14.1370 + 6.62433i 0.779399 + 0.365211i
\(330\) 9.91887 + 1.71503i 0.546016 + 0.0944092i
\(331\) −26.8314 7.18946i −1.47479 0.395168i −0.570218 0.821493i \(-0.693141\pi\)
−0.904570 + 0.426325i \(0.859808\pi\)
\(332\) −17.9322 + 5.81905i −0.984157 + 0.319362i
\(333\) 1.19692 8.97295i 0.0655908 0.491715i
\(334\) −6.38691 + 26.5813i −0.349476 + 1.45447i
\(335\) 2.82275 0.154223
\(336\) −17.6680 4.88285i −0.963868 0.266381i
\(337\) −23.9919 −1.30692 −0.653461 0.756961i \(-0.726683\pi\)
−0.653461 + 0.756961i \(0.726683\pi\)
\(338\) 1.96557 8.18038i 0.106913 0.444954i
\(339\) −1.77400 27.4251i −0.0963503 1.48953i
\(340\) −2.81351 8.67022i −0.152584 0.470209i
\(341\) 36.4879 + 9.77691i 1.97593 + 0.529449i
\(342\) −1.36026 + 3.52361i −0.0735547 + 0.190535i
\(343\) 4.69322 + 17.9157i 0.253410 + 0.967359i
\(344\) 29.4454 2.30065i 1.58759 0.124042i
\(345\) 3.41715 1.15671i 0.183973 0.0622751i
\(346\) 14.8206 27.2838i 0.796758 1.46679i
\(347\) 25.5784 6.85371i 1.37312 0.367927i 0.504503 0.863410i \(-0.331676\pi\)
0.868618 + 0.495483i \(0.165009\pi\)
\(348\) 4.20833 + 10.5861i 0.225590 + 0.567476i
\(349\) −12.4422 + 12.4422i −0.666017 + 0.666017i −0.956792 0.290775i \(-0.906087\pi\)
0.290775 + 0.956792i \(0.406087\pi\)
\(350\) −16.2398 2.46117i −0.868055 0.131555i
\(351\) 7.69497 11.4527i 0.410727 0.611298i
\(352\) −18.0945 23.6273i −0.964443 1.25934i
\(353\) 16.8372 + 9.72097i 0.896154 + 0.517395i 0.875951 0.482401i \(-0.160235\pi\)
0.0202039 + 0.999796i \(0.493568\pi\)
\(354\) 4.89008 0.444191i 0.259905 0.0236085i
\(355\) 0.255117 0.952110i 0.0135402 0.0505327i
\(356\) −1.64518 31.6200i −0.0871943 1.67585i
\(357\) −26.4376 + 3.99556i −1.39923 + 0.211467i
\(358\) −0.0545848 2.09963i −0.00288490 0.110969i
\(359\) 16.1363 9.31629i 0.851640 0.491695i −0.00956358 0.999954i \(-0.503044\pi\)
0.861204 + 0.508259i \(0.169711\pi\)
\(360\) 4.42386 + 4.93572i 0.233158 + 0.260135i
\(361\) 15.7681 + 9.10372i 0.829900 + 0.479143i
\(362\) −15.7555 25.7215i −0.828090 1.35189i
\(363\) 24.0311 16.0273i 1.26130 0.841217i
\(364\) −8.48117 + 11.2025i −0.444534 + 0.587172i
\(365\) 2.45269 + 2.45269i 0.128380 + 0.128380i
\(366\) −7.98909 3.69313i −0.417596 0.193043i
\(367\) −19.7783 11.4190i −1.03242 0.596068i −0.114743 0.993395i \(-0.536605\pi\)
−0.917677 + 0.397327i \(0.869938\pi\)
\(368\) −9.74047 4.34554i −0.507757 0.226527i
\(369\) −13.2996 + 1.72780i −0.692349 + 0.0899458i
\(370\) 2.29499 2.41750i 0.119311 0.125680i
\(371\) 18.8016 + 15.8363i 0.976131 + 0.822179i
\(372\) 14.8579 + 19.9483i 0.770344 + 1.03427i
\(373\) 4.60599 17.1898i 0.238489 0.890053i −0.738056 0.674740i \(-0.764256\pi\)
0.976545 0.215314i \(-0.0690774\pi\)
\(374\) −38.1457 20.7207i −1.97247 1.07144i
\(375\) 9.54425 + 8.38452i 0.492863 + 0.432975i
\(376\) −3.05080 + 16.4088i −0.157333 + 0.846221i
\(377\) 8.73235 0.449739
\(378\) 16.4001 10.4421i 0.843528 0.537085i
\(379\) 16.6607 16.6607i 0.855805 0.855805i −0.135036 0.990841i \(-0.543115\pi\)
0.990841 + 0.135036i \(0.0431150\pi\)
\(380\) −1.16672 + 0.757054i −0.0598517 + 0.0388361i
\(381\) 0.173646 + 2.68449i 0.00889617 + 0.137530i
\(382\) 4.16320 + 14.0645i 0.213008 + 0.719601i
\(383\) 13.0339 + 22.5753i 0.666000 + 1.15355i 0.979013 + 0.203797i \(0.0653283\pi\)
−0.313013 + 0.949749i \(0.601338\pi\)
\(384\) 0.299105 19.5936i 0.0152636 0.999884i
\(385\) 8.91790 6.21963i 0.454498 0.316982i
\(386\) 2.50901 2.64294i 0.127705 0.134522i
\(387\) −19.1129 + 24.8205i −0.971566 + 1.26170i
\(388\) −2.16323 1.10325i −0.109821 0.0560088i
\(389\) −2.73878 10.2212i −0.138861 0.518238i −0.999952 0.00978648i \(-0.996885\pi\)
0.861091 0.508451i \(-0.169782\pi\)
\(390\) 4.76850 1.75354i 0.241462 0.0887941i
\(391\) −15.5580 −0.786800
\(392\) −17.2739 + 9.67537i −0.872463 + 0.488680i
\(393\) 15.7191 + 3.14069i 0.792923 + 0.158427i
\(394\) 4.80538 2.94350i 0.242092 0.148291i
\(395\) 12.1062 3.24384i 0.609129 0.163215i
\(396\) 31.4628 + 2.54224i 1.58107 + 0.127752i
\(397\) −14.0565 3.76642i −0.705474 0.189031i −0.111793 0.993732i \(-0.535659\pi\)
−0.593681 + 0.804700i \(0.702326\pi\)
\(398\) −8.82464 + 9.29572i −0.442339 + 0.465953i
\(399\) 1.63292 + 3.73864i 0.0817481 + 0.187166i
\(400\) −1.82228 17.4645i −0.0911141 0.873226i
\(401\) −2.81760 + 1.62674i −0.140704 + 0.0812358i −0.568700 0.822545i \(-0.692553\pi\)
0.427995 + 0.903781i \(0.359220\pi\)
\(402\) 8.81536 0.800745i 0.439670 0.0399375i
\(403\) 18.4168 4.93476i 0.917405 0.245818i
\(404\) −2.73830 + 12.8588i −0.136235 + 0.639751i
\(405\) −7.03013 0.0240346i −0.349330 0.00119429i
\(406\) 11.2740 + 4.92965i 0.559521 + 0.244654i
\(407\) 15.8746i 0.786876i
\(408\) −11.2460 26.2787i −0.556762 1.30099i
\(409\) 7.49505 + 4.32727i 0.370606 + 0.213970i 0.673723 0.738984i \(-0.264694\pi\)
−0.303117 + 0.952953i \(0.598027\pi\)
\(410\) −4.33954 2.35724i −0.214315 0.116416i
\(411\) −7.05326 + 14.2718i −0.347912 + 0.703978i
\(412\) 0.661885 + 12.7213i 0.0326087 + 0.626733i
\(413\) 3.41668 4.05645i 0.168124 0.199605i
\(414\) 10.3435 4.58173i 0.508356 0.225180i
\(415\) 6.37673 3.68161i 0.313021 0.180723i
\(416\) −13.8722 5.76137i −0.680140 0.282474i
\(417\) 7.11422 8.09824i 0.348385 0.396572i
\(418\) −1.54745 + 6.44026i −0.0756884 + 0.315003i
\(419\) −14.2915 + 14.2915i −0.698188 + 0.698188i −0.964019 0.265832i \(-0.914353\pi\)
0.265832 + 0.964019i \(0.414353\pi\)
\(420\) 7.14637 + 0.428008i 0.348707 + 0.0208846i
\(421\) 8.62897 + 8.62897i 0.420550 + 0.420550i 0.885393 0.464843i \(-0.153889\pi\)
−0.464843 + 0.885393i \(0.653889\pi\)
\(422\) 6.16041 + 10.0571i 0.299884 + 0.489574i
\(423\) −10.7525 14.0627i −0.522806 0.683752i
\(424\) −11.3271 + 23.7131i −0.550090 + 1.15161i
\(425\) −12.8066 22.1817i −0.621213 1.07597i
\(426\) 0.526632 3.04578i 0.0255154 0.147569i
\(427\) −8.93934 + 3.23478i −0.432605 + 0.156542i
\(428\) −25.0951 + 27.8498i −1.21302 + 1.34617i
\(429\) 10.7202 21.6916i 0.517575 1.04728i
\(430\) −11.0610 + 3.27414i −0.533407 + 0.157893i
\(431\) −3.88398 + 6.72725i −0.187085 + 0.324040i −0.944277 0.329152i \(-0.893237\pi\)
0.757192 + 0.653192i \(0.226571\pi\)
\(432\) 15.2157 + 14.1592i 0.732066 + 0.681234i
\(433\) 6.45634 0.310272 0.155136 0.987893i \(-0.450418\pi\)
0.155136 + 0.987893i \(0.450418\pi\)
\(434\) 26.5631 + 4.02567i 1.27507 + 0.193238i
\(435\) −2.46873 3.70156i −0.118367 0.177476i
\(436\) 6.09963 28.6434i 0.292119 1.37177i
\(437\) 0.614397 + 2.29296i 0.0293906 + 0.109687i
\(438\) 8.35544 + 6.96390i 0.399238 + 0.332748i
\(439\) 14.0248 + 24.2917i 0.669368 + 1.15938i 0.978081 + 0.208224i \(0.0667682\pi\)
−0.308713 + 0.951155i \(0.599898\pi\)
\(440\) 8.83413 + 7.55370i 0.421151 + 0.360109i
\(441\) 4.65669 20.4772i 0.221747 0.975104i
\(442\) −21.9033 + 0.569426i −1.04183 + 0.0270848i
\(443\) 0.228326 0.852124i 0.0108481 0.0404856i −0.960290 0.279005i \(-0.909995\pi\)
0.971138 + 0.238519i \(0.0766621\pi\)
\(444\) 6.48140 8.20082i 0.307594 0.389194i
\(445\) 3.20065 + 11.9450i 0.151725 + 0.566247i
\(446\) −8.82154 + 36.7139i −0.417712 + 1.73845i
\(447\) −24.0477 4.80475i −1.13742 0.227257i
\(448\) −14.6575 15.2695i −0.692500 0.721418i
\(449\) 0.897513i 0.0423563i −0.999776 0.0211781i \(-0.993258\pi\)
0.999776 0.0211781i \(-0.00674171\pi\)
\(450\) 15.0467 + 10.9758i 0.709310 + 0.517403i
\(451\) −22.7172 + 6.08706i −1.06971 + 0.286628i
\(452\) 14.4176 28.2698i 0.678146 1.32970i
\(453\) −6.63716 + 13.4299i −0.311841 + 0.630991i
\(454\) −0.630422 24.2495i −0.0295872 1.13809i
\(455\) 2.32851 4.96929i 0.109162 0.232964i
\(456\) −3.42889 + 2.69523i −0.160572 + 0.126216i
\(457\) 4.51144 2.60468i 0.211036 0.121842i −0.390757 0.920494i \(-0.627787\pi\)
0.601793 + 0.798652i \(0.294453\pi\)
\(458\) −2.61457 + 4.81328i −0.122171 + 0.224910i
\(459\) 28.6838 + 9.81894i 1.33885 + 0.458309i
\(460\) 4.07436 + 0.867637i 0.189968 + 0.0404538i
\(461\) −11.8421 11.8421i −0.551540 0.551540i 0.375345 0.926885i \(-0.377524\pi\)
−0.926885 + 0.375345i \(0.877524\pi\)
\(462\) 26.0860 21.9535i 1.21363 1.02137i
\(463\) 13.2191i 0.614344i 0.951654 + 0.307172i \(0.0993826\pi\)
−0.951654 + 0.307172i \(0.900617\pi\)
\(464\) −2.06758 + 12.9908i −0.0959849 + 0.603081i
\(465\) −7.29843 6.41160i −0.338457 0.297331i
\(466\) 3.78785 + 12.7964i 0.175469 + 0.592782i
\(467\) −38.0314 10.1905i −1.75988 0.471560i −0.773194 0.634169i \(-0.781342\pi\)
−0.986690 + 0.162610i \(0.948009\pi\)
\(468\) 14.3944 6.82897i 0.665383 0.315669i
\(469\) 6.15926 7.31258i 0.284408 0.337664i
\(470\) −0.169407 6.51634i −0.00781417 0.300576i
\(471\) 1.49644 + 4.42077i 0.0689522 + 0.203698i
\(472\) 5.11612 + 2.44382i 0.235488 + 0.112486i
\(473\) −27.4677 + 47.5755i −1.26297 + 2.18752i
\(474\) 36.8871 13.5647i 1.69428 0.623045i
\(475\) −2.76344 + 2.76344i −0.126795 + 0.126795i
\(476\) −28.6001 11.6298i −1.31088 0.533053i
\(477\) −10.6228 25.7701i −0.486383 1.17993i
\(478\) 12.3243 + 2.96127i 0.563702 + 0.135445i
\(479\) −13.8376 + 23.9674i −0.632255 + 1.09510i 0.354834 + 0.934929i \(0.384537\pi\)
−0.987090 + 0.160169i \(0.948796\pi\)
\(480\) 1.47963 + 7.50910i 0.0675355 + 0.342742i
\(481\) −4.00625 6.93903i −0.182669 0.316392i
\(482\) −26.1937 + 27.5919i −1.19309 + 1.25678i
\(483\) 4.45969 11.3764i 0.202923 0.517643i
\(484\) 33.3090 1.73306i 1.51404 0.0787753i
\(485\) 0.916098 + 0.245468i 0.0415979 + 0.0111461i
\(486\) −21.9617 + 1.91922i −0.996203 + 0.0870575i
\(487\) 0.692794 1.19995i 0.0313935 0.0543751i −0.849902 0.526941i \(-0.823339\pi\)
0.881295 + 0.472566i \(0.156672\pi\)
\(488\) −5.75164 8.37884i −0.260365 0.379292i
\(489\) −0.778427 + 3.89601i −0.0352017 + 0.176184i
\(490\) 5.81156 5.10117i 0.262539 0.230447i
\(491\) −13.8726 13.8726i −0.626063 0.626063i 0.321012 0.947075i \(-0.395977\pi\)
−0.947075 + 0.321012i \(0.895977\pi\)
\(492\) −14.2210 6.13056i −0.641130 0.276387i
\(493\) 4.96615 + 18.5339i 0.223664 + 0.834726i
\(494\) 0.948902 + 3.20566i 0.0426931 + 0.144229i
\(495\) −12.2256 + 1.58827i −0.549500 + 0.0713876i
\(496\) 2.98067 + 28.5663i 0.133836 + 1.28267i
\(497\) −1.90986 2.73842i −0.0856688 0.122835i
\(498\) 18.8700 13.3065i 0.845583 0.596277i
\(499\) −0.888961 + 3.31765i −0.0397954 + 0.148518i −0.982965 0.183794i \(-0.941162\pi\)
0.943169 + 0.332312i \(0.107829\pi\)
\(500\) 4.52783 + 13.9531i 0.202491 + 0.624002i
\(501\) −2.16127 33.4121i −0.0965582 1.49274i
\(502\) −9.04166 14.7609i −0.403549 0.658811i
\(503\) 35.2193i 1.57035i −0.619273 0.785176i \(-0.712572\pi\)
0.619273 0.785176i \(-0.287428\pi\)
\(504\) 22.4393 0.690596i 0.999527 0.0307616i
\(505\) 5.13483i 0.228497i
\(506\) 16.9171 10.3624i 0.752058 0.460666i
\(507\) 0.665128 + 10.2825i 0.0295394 + 0.456664i
\(508\) −1.41125 + 2.76716i −0.0626143 + 0.122773i
\(509\) 4.86113 18.1420i 0.215466 0.804129i −0.770536 0.637396i \(-0.780012\pi\)
0.986002 0.166733i \(-0.0533217\pi\)
\(510\) 6.43368 + 9.12363i 0.284888 + 0.404001i
\(511\) 11.7057 1.00212i 0.517829 0.0443311i
\(512\) 11.8555 19.2730i 0.523944 0.851752i
\(513\) 0.314385 4.61523i 0.0138804 0.203767i
\(514\) −7.33849 + 2.17225i −0.323687 + 0.0958140i
\(515\) −1.28768 4.80569i −0.0567420 0.211764i
\(516\) −33.6143 + 13.3628i −1.47979 + 0.588263i
\(517\) −21.9511 21.9511i −0.965409 0.965409i
\(518\) −1.25506 11.2204i −0.0551444 0.492996i
\(519\) −7.45065 + 37.2904i −0.327047 + 1.63687i
\(520\) 5.76784 + 1.07238i 0.252937 + 0.0470270i
\(521\) −7.50479 + 12.9987i −0.328791 + 0.569482i −0.982272 0.187460i \(-0.939974\pi\)
0.653481 + 0.756943i \(0.273308\pi\)
\(522\) −8.75982 10.8596i −0.383407 0.475310i
\(523\) −13.9931 3.74944i −0.611876 0.163952i −0.0604439 0.998172i \(-0.519252\pi\)
−0.551432 + 0.834220i \(0.685918\pi\)
\(524\) 13.7506 + 12.3905i 0.600699 + 0.541282i
\(525\) 19.8909 3.00614i 0.868109 0.131199i
\(526\) 9.67018 + 9.18013i 0.421640 + 0.400273i
\(527\) 20.9475 + 36.2822i 0.912488 + 1.58048i
\(528\) 29.7315 + 21.0840i 1.29390 + 0.917561i
\(529\) −7.94498 + 13.7611i −0.345434 + 0.598309i
\(530\) 2.39794 9.97984i 0.104160 0.433497i
\(531\) −5.55991 + 2.29186i −0.241280 + 0.0994585i
\(532\) −0.584586 + 4.67440i −0.0253450 + 0.202661i
\(533\) −8.39384 + 8.39384i −0.363578 + 0.363578i
\(534\) 13.3840 + 36.3959i 0.579184 + 1.57500i
\(535\) 7.32083 12.6800i 0.316507 0.548206i
\(536\) 9.22284 + 4.40547i 0.398366 + 0.190288i
\(537\) 0.824784 + 2.43657i 0.0355920 + 0.105146i
\(538\) −32.9269 + 0.856009i −1.41958 + 0.0369052i
\(539\) 3.34645 36.6739i 0.144142 1.57966i
\(540\) −6.96421 4.17105i −0.299692 0.179493i
\(541\) 15.6520 + 4.19395i 0.672933 + 0.180312i 0.579076 0.815274i \(-0.303414\pi\)
0.0938574 + 0.995586i \(0.470080\pi\)
\(542\) 6.58635 1.94962i 0.282908 0.0837432i
\(543\) 27.7540 + 24.3816i 1.19104 + 1.04631i
\(544\) 4.33898 32.7195i 0.186032 1.40284i
\(545\) 11.4380i 0.489948i
\(546\) 5.86220 16.1795i 0.250879 0.692417i
\(547\) −15.1724 15.1724i −0.648727 0.648727i 0.303959 0.952685i \(-0.401692\pi\)
−0.952685 + 0.303959i \(0.901692\pi\)
\(548\) −15.4205 + 10.0059i −0.658733 + 0.427433i
\(549\) 10.6848 + 1.42527i 0.456018 + 0.0608291i
\(550\) 28.6997 + 15.5897i 1.22376 + 0.664745i
\(551\) 2.53545 1.46384i 0.108014 0.0623617i
\(552\) 12.9702 + 1.55381i 0.552049 + 0.0661345i
\(553\) 18.0123 38.4402i 0.765963 1.63465i
\(554\) −2.27934 + 0.0592568i −0.0968401 + 0.00251758i
\(555\) −1.80878 + 3.65995i −0.0767784 + 0.155356i
\(556\) 11.8391 3.84183i 0.502091 0.162930i
\(557\) 27.8755 7.46921i 1.18112 0.316481i 0.385751 0.922603i \(-0.373942\pi\)
0.795372 + 0.606122i \(0.207276\pi\)
\(558\) −24.6116 17.9528i −1.04189 0.760004i
\(559\) 27.7279i 1.17277i
\(560\) 6.84128 + 4.64062i 0.289097 + 0.196102i
\(561\) 52.1359 + 10.4168i 2.20118 + 0.439798i
\(562\) 13.8216 + 3.32102i 0.583027 + 0.140089i
\(563\) −1.46912 5.48281i −0.0619158 0.231073i 0.928033 0.372497i \(-0.121498\pi\)
−0.989949 + 0.141424i \(0.954832\pi\)
\(564\) −2.37758 20.3023i −0.100114 0.854880i
\(565\) −3.20785 + 11.9719i −0.134955 + 0.503660i
\(566\) 0.313903 + 12.0745i 0.0131943 + 0.507527i
\(567\) −15.4021 + 18.1597i −0.646826 + 0.762637i
\(568\) 2.31951 2.71269i 0.0973245 0.113822i
\(569\) 0.764734 + 1.32456i 0.0320593 + 0.0555284i 0.881610 0.471979i \(-0.156460\pi\)
−0.849551 + 0.527507i \(0.823127\pi\)
\(570\) 1.09058 1.30851i 0.0456796 0.0548073i
\(571\) 6.67118 + 24.8972i 0.279180 + 1.04192i 0.952988 + 0.303008i \(0.0979911\pi\)
−0.673807 + 0.738907i \(0.735342\pi\)
\(572\) 23.4375 15.2079i 0.979971 0.635876i
\(573\) −9.96760 14.9452i −0.416403 0.624345i
\(574\) −15.5756 + 6.09846i −0.650111 + 0.254545i
\(575\) 11.7053 0.488146
\(576\) 6.75098 + 23.0309i 0.281291 + 0.959623i
\(577\) −11.1059 + 19.2360i −0.462344 + 0.800803i −0.999077 0.0429487i \(-0.986325\pi\)
0.536733 + 0.843752i \(0.319658\pi\)
\(578\) −6.84129 23.1118i −0.284560 0.961325i
\(579\) −1.97746 + 4.00126i −0.0821802 + 0.166287i
\(580\) −0.266947 5.13066i −0.0110844 0.213039i
\(581\) 4.37655 24.5528i 0.181570 1.01862i
\(582\) 2.93058 + 0.506714i 0.121476 + 0.0210040i
\(583\) −24.4401 42.3315i −1.01220 1.75319i
\(584\) 4.18581 + 11.8417i 0.173210 + 0.490011i
\(585\) −4.94316 + 3.77961i −0.204374 + 0.156268i
\(586\) −19.2556 + 11.7948i −0.795441 + 0.487240i
\(587\) 10.9206 + 10.9206i 0.450740 + 0.450740i 0.895600 0.444860i \(-0.146747\pi\)
−0.444860 + 0.895600i \(0.646747\pi\)
\(588\) 16.7022 17.5794i 0.688789 0.724962i
\(589\) 4.52010 4.52010i 0.186247 0.186247i
\(590\) −2.15315 0.517356i −0.0886440 0.0212992i
\(591\) −4.55505 + 5.18510i −0.187370 + 0.213286i
\(592\) 11.2715 4.31697i 0.463255 0.177426i
\(593\) −33.2636 + 19.2048i −1.36597 + 0.788645i −0.990411 0.138151i \(-0.955884\pi\)
−0.375563 + 0.926797i \(0.622551\pi\)
\(594\) −37.7296 + 8.42823i −1.54806 + 0.345815i
\(595\) 11.8713 + 2.11606i 0.486675 + 0.0867502i
\(596\) −21.0363 18.9555i −0.861679 0.776448i
\(597\) 6.95508 14.0732i 0.284652 0.575976i
\(598\) 4.77957 8.79891i 0.195451 0.359814i
\(599\) −39.5224 22.8183i −1.61484 0.932330i −0.988226 0.153001i \(-0.951106\pi\)
−0.626616 0.779328i \(-0.715561\pi\)
\(600\) 8.46118 + 19.7713i 0.345426 + 0.807160i
\(601\) 20.8527i 0.850599i 0.905053 + 0.425300i \(0.139831\pi\)
−0.905053 + 0.425300i \(0.860169\pi\)
\(602\) −15.6532 + 35.7986i −0.637976 + 1.45904i
\(603\) −10.0229 + 4.13155i −0.408163 + 0.168250i
\(604\) −14.5108 + 9.41565i −0.590436 + 0.383117i
\(605\) −12.5830 + 3.37161i −0.511573 + 0.137076i
\(606\) −1.45662 16.0359i −0.0591713 0.651414i
\(607\) 19.5717 11.2997i 0.794390 0.458641i −0.0471158 0.998889i \(-0.515003\pi\)
0.841506 + 0.540248i \(0.181670\pi\)
\(608\) −4.99361 + 0.652633i −0.202517 + 0.0264678i
\(609\) −14.9760 1.68138i −0.606859 0.0681328i
\(610\) 2.87872 + 2.73284i 0.116556 + 0.110649i
\(611\) −15.1349 4.05539i −0.612293 0.164063i
\(612\) 22.6803 + 26.6677i 0.916798 + 1.07798i
\(613\) −42.1602 + 11.2968i −1.70283 + 0.456273i −0.973650 0.228047i \(-0.926766\pi\)
−0.729182 + 0.684320i \(0.760099\pi\)
\(614\) 5.57935 + 9.10853i 0.225164 + 0.367590i
\(615\) 5.93111 + 1.18504i 0.239165 + 0.0477855i
\(616\) 38.8447 6.40334i 1.56510 0.257998i
\(617\) 14.9563 0.602116 0.301058 0.953606i \(-0.402660\pi\)
0.301058 + 0.953606i \(0.402660\pi\)
\(618\) −5.38464 14.6427i −0.216602 0.589017i
\(619\) −6.01129 22.4344i −0.241614 0.901716i −0.975055 0.221963i \(-0.928754\pi\)
0.733441 0.679753i \(-0.237913\pi\)
\(620\) −3.46240 10.6699i −0.139053 0.428512i
\(621\) −10.4404 + 9.10873i −0.418959 + 0.365521i
\(622\) −28.4873 27.0436i −1.14224 1.08435i
\(623\) 37.9284 + 17.7725i 1.51957 + 0.712040i
\(624\) 18.3170 + 1.71282i 0.733267 + 0.0685675i
\(625\) 8.10991 + 14.0468i 0.324397 + 0.561871i
\(626\) 21.8150 6.45744i 0.871904 0.258091i
\(627\) −0.523643 8.09525i −0.0209123 0.323293i
\(628\) −1.12246 + 5.27100i −0.0447912 + 0.210336i
\(629\) 12.4493 12.4493i 0.496387 0.496387i
\(630\) −8.51564 + 2.08918i −0.339271 + 0.0832350i
\(631\) 8.01029 0.318885 0.159442 0.987207i \(-0.449030\pi\)
0.159442 + 0.987207i \(0.449030\pi\)
\(632\) 44.6175 + 8.29547i 1.77479 + 0.329976i
\(633\) −10.8518 9.53323i −0.431322 0.378912i
\(634\) 7.21815 13.2882i 0.286669 0.527742i
\(635\) 0.313998 1.17186i 0.0124606 0.0465037i
\(636\) 4.65765 31.8470i 0.184688 1.26281i
\(637\) −7.79254 16.8752i −0.308752 0.668621i
\(638\) −17.7446 16.8453i −0.702515 0.666913i
\(639\) 0.487710 + 3.75411i 0.0192935 + 0.148510i
\(640\) −2.96100 + 8.32668i −0.117044 + 0.329141i
\(641\) −19.7846 11.4227i −0.781445 0.451168i 0.0554969 0.998459i \(-0.482326\pi\)
−0.836942 + 0.547291i \(0.815659\pi\)
\(642\) 19.2657 41.6761i 0.760356 1.64483i
\(643\) 25.9448 + 25.9448i 1.02316 + 1.02316i 0.999725 + 0.0234396i \(0.00746173\pi\)
0.0234396 + 0.999725i \(0.492538\pi\)
\(644\) 11.1380 8.66179i 0.438898 0.341322i
\(645\) 11.7536 7.83900i 0.462799 0.308660i
\(646\) −6.26419 + 3.83708i −0.246461 + 0.150968i
\(647\) 15.2965 + 8.83145i 0.601368 + 0.347200i 0.769580 0.638551i \(-0.220466\pi\)
−0.168211 + 0.985751i \(0.553799\pi\)
\(648\) −22.9322 11.0505i −0.900863 0.434104i
\(649\) −9.13303 + 5.27296i −0.358503 + 0.206982i
\(650\) 16.4794 0.428419i 0.646374 0.0168040i
\(651\) −32.5350 + 4.91707i −1.27515 + 0.192715i
\(652\) −3.07102 + 3.40812i −0.120270 + 0.133472i
\(653\) −0.168923 + 0.630428i −0.00661046 + 0.0246706i −0.969152 0.246463i \(-0.920732\pi\)
0.962542 + 0.271133i \(0.0873984\pi\)
\(654\) 3.24467 + 35.7204i 0.126876 + 1.39678i
\(655\) −6.26067 3.61460i −0.244625 0.141234i
\(656\) −10.4998 14.4746i −0.409947 0.565139i
\(657\) −12.2988 5.11897i −0.479821 0.199710i
\(658\) −17.2508 13.7798i −0.672506 0.537194i
\(659\) −9.00214 + 9.00214i −0.350674 + 0.350674i −0.860360 0.509687i \(-0.829761\pi\)
0.509687 + 0.860360i \(0.329761\pi\)
\(660\) −13.0726 5.63550i −0.508848 0.219361i
\(661\) 30.3861 8.14194i 1.18188 0.316685i 0.386211 0.922411i \(-0.373784\pi\)
0.795673 + 0.605726i \(0.207117\pi\)
\(662\) 34.5199 + 18.7512i 1.34165 + 0.728785i
\(663\) 25.4182 8.60411i 0.987163 0.334156i
\(664\) 26.5808 2.07683i 1.03153 0.0805965i
\(665\) −0.156937 1.83317i −0.00608576 0.0710875i
\(666\) −4.61053 + 11.9430i −0.178654 + 0.462783i
\(667\) −8.47006 2.26955i −0.327962 0.0878772i
\(668\) 17.5650 34.4411i 0.679609 1.33257i
\(669\) −2.98512 46.1485i −0.115411 1.78420i
\(670\) −3.88150 0.932639i −0.149955 0.0360310i
\(671\) 18.9032 0.729751
\(672\) 22.6815 + 12.5518i 0.874959 + 0.484197i
\(673\) −3.76513 −0.145135 −0.0725675 0.997364i \(-0.523119\pi\)
−0.0725675 + 0.997364i \(0.523119\pi\)
\(674\) 32.9907 + 7.92694i 1.27075 + 0.305334i
\(675\) −21.5808 7.38747i −0.830647 0.284344i
\(676\) −5.40561 + 10.5992i −0.207908 + 0.407662i
\(677\) 42.6400 + 11.4254i 1.63879 + 0.439112i 0.956443 0.291918i \(-0.0942933\pi\)
0.682346 + 0.731030i \(0.260960\pi\)
\(678\) −6.62190 + 38.2978i −0.254313 + 1.47082i
\(679\) 2.63484 1.83762i 0.101116 0.0705214i
\(680\) 1.00415 + 12.8518i 0.0385072 + 0.492844i
\(681\) 9.52576 + 28.1410i 0.365028 + 1.07837i
\(682\) −46.9434 25.4996i −1.79756 0.976432i
\(683\) 20.1789 5.40692i 0.772125 0.206890i 0.148815 0.988865i \(-0.452454\pi\)
0.623310 + 0.781975i \(0.285788\pi\)
\(684\) 3.03467 4.39580i 0.116034 0.168078i
\(685\) 5.07669 5.07669i 0.193970 0.193970i
\(686\) −0.534161 26.1862i −0.0203944 0.999792i
\(687\) 1.31441 6.57858i 0.0501478 0.250989i
\(688\) −41.2498 6.56521i −1.57263 0.250296i
\(689\) −21.3662 12.3358i −0.813989 0.469957i
\(690\) −5.08102 + 0.461535i −0.193431 + 0.0175703i
\(691\) −0.181851 + 0.678676i −0.00691793 + 0.0258180i −0.969299 0.245887i \(-0.920921\pi\)
0.962381 + 0.271705i \(0.0875875\pi\)
\(692\) −29.3940 + 32.6206i −1.11739 + 1.24005i
\(693\) −22.5618 + 35.1371i −0.857052 + 1.33475i
\(694\) −37.4367 + 0.973254i −1.42108 + 0.0369442i
\(695\) −4.21002 + 2.43066i −0.159695 + 0.0922001i
\(696\) −2.28911 15.9472i −0.0867685 0.604476i
\(697\) −22.5891 13.0418i −0.855623 0.493994i
\(698\) 21.2199 12.9981i 0.803186 0.491985i
\(699\) −9.06892 13.5977i −0.343018 0.514314i
\(700\) 21.5178 + 8.74994i 0.813297 + 0.330717i
\(701\) 4.40327 + 4.40327i 0.166309 + 0.166309i 0.785355 0.619046i \(-0.212480\pi\)
−0.619046 + 0.785355i \(0.712480\pi\)
\(702\) −14.3651 + 13.2059i −0.542177 + 0.498423i
\(703\) −2.32644 1.34317i −0.0877433 0.0506586i
\(704\) 17.0749 + 38.4679i 0.643534 + 1.44981i
\(705\) 2.55977 + 7.56206i 0.0964064 + 0.284804i
\(706\) −19.9406 18.9301i −0.750476 0.712444i
\(707\) −13.3022 11.2042i −0.500282 0.421379i
\(708\) −6.87099 1.00489i −0.258228 0.0377661i
\(709\) −7.88738 + 29.4361i −0.296217 + 1.10550i 0.644030 + 0.765001i \(0.277261\pi\)
−0.940246 + 0.340495i \(0.889405\pi\)
\(710\) −0.665383 + 1.22493i −0.0249714 + 0.0459709i
\(711\) −38.2381 + 29.2374i −1.43404 + 1.09649i
\(712\) −8.18501 + 44.0234i −0.306746 + 1.64985i
\(713\) −19.1462 −0.717029
\(714\) 37.6739 + 3.24081i 1.40991 + 0.121284i
\(715\) −7.71600 + 7.71600i −0.288562 + 0.288562i
\(716\) −0.618662 + 2.90519i −0.0231205 + 0.108572i
\(717\) −15.4914 + 1.00206i −0.578537 + 0.0374227i
\(718\) −25.2667 + 7.47917i −0.942946 + 0.279120i
\(719\) −15.0012 25.9829i −0.559452 0.968999i −0.997542 0.0700683i \(-0.977678\pi\)
0.438090 0.898931i \(-0.355655\pi\)
\(720\) −4.45237 8.24864i −0.165930 0.307409i
\(721\) −15.2593 7.15020i −0.568286 0.266287i
\(722\) −18.6745 17.7281i −0.694992 0.659772i
\(723\) 20.6443 41.7726i 0.767772 1.55354i
\(724\) 13.1666 + 40.5747i 0.489333 + 1.50795i
\(725\) −3.73638 13.9444i −0.138766 0.517881i
\(726\) −38.3400 + 14.0989i −1.42293 + 0.523261i
\(727\) −19.2765 −0.714926 −0.357463 0.933927i \(-0.616358\pi\)
−0.357463 + 0.933927i \(0.616358\pi\)
\(728\) 15.3636 12.6022i 0.569412 0.467067i
\(729\) 24.9974 10.2044i 0.925830 0.377941i
\(730\) −2.56226 4.18300i −0.0948337 0.154820i
\(731\) −58.8510 + 15.7691i −2.17668 + 0.583241i
\(732\) 9.76540 + 7.71794i 0.360939 + 0.285263i
\(733\) −7.97924 2.13803i −0.294720 0.0789700i 0.108429 0.994104i \(-0.465418\pi\)
−0.403149 + 0.915134i \(0.632085\pi\)
\(734\) 23.4239 + 22.2368i 0.864590 + 0.820776i
\(735\) −4.95022 + 8.07401i −0.182592 + 0.297814i
\(736\) 11.9581 + 9.19371i 0.440782 + 0.338885i
\(737\) −16.4641 + 9.50557i −0.606464 + 0.350142i
\(738\) 18.8588 + 2.01834i 0.694203 + 0.0742960i
\(739\) −2.34221 + 0.627593i −0.0861595 + 0.0230864i −0.301641 0.953421i \(-0.597534\pi\)
0.215482 + 0.976508i \(0.430868\pi\)
\(740\) −3.95453 + 2.56598i −0.145372 + 0.0943275i
\(741\) −2.27188 3.40640i −0.0834595 0.125137i
\(742\) −20.6213 27.9882i −0.757033 1.02748i
\(743\) 46.1287i 1.69230i 0.532946 + 0.846149i \(0.321085\pi\)
−0.532946 + 0.846149i \(0.678915\pi\)
\(744\) −13.8398 32.3395i −0.507390 1.18562i
\(745\) 9.57782 + 5.52976i 0.350904 + 0.202595i
\(746\) −12.0131 + 22.1154i −0.439831 + 0.809704i
\(747\) −17.2535 + 22.4058i −0.631274 + 0.819787i
\(748\) 45.6071 + 41.0960i 1.66756 + 1.50262i
\(749\) −16.8747 46.6332i −0.616587 1.70394i
\(750\) −10.3538 14.6828i −0.378068 0.536140i
\(751\) −31.4473 + 18.1561i −1.14753 + 0.662526i −0.948284 0.317424i \(-0.897182\pi\)
−0.199245 + 0.979950i \(0.563849\pi\)
\(752\) 9.61657 21.5554i 0.350680 0.786045i
\(753\) 15.9273 + 13.9920i 0.580422 + 0.509895i
\(754\) −12.0076 2.88517i −0.437293 0.105072i
\(755\) 4.77719 4.77719i 0.173860 0.173860i
\(756\) −26.0014 + 8.94013i −0.945663 + 0.325149i
\(757\) −4.85696 4.85696i −0.176529 0.176529i 0.613312 0.789841i \(-0.289837\pi\)
−0.789841 + 0.613312i \(0.789837\pi\)
\(758\) −28.4145 + 17.4051i −1.03206 + 0.632181i
\(759\) −16.0359 + 18.2539i −0.582065 + 0.662574i
\(760\) 1.85447 0.655521i 0.0672686 0.0237782i
\(761\) −7.69024 13.3199i −0.278771 0.482846i 0.692309 0.721602i \(-0.256594\pi\)
−0.971080 + 0.238756i \(0.923260\pi\)
\(762\) 0.648179 3.74875i 0.0234811 0.135803i
\(763\) 29.6310 + 24.9577i 1.07272 + 0.903530i
\(764\) −1.07781 20.7152i −0.0389938 0.749451i
\(765\) −10.8332 8.34209i −0.391676 0.301609i
\(766\) −10.4637 35.3492i −0.378068 1.27722i
\(767\) −2.66145 + 4.60977i −0.0960995 + 0.166449i
\(768\) −6.88504 + 26.8439i −0.248443 + 0.968647i
\(769\) 25.5362 0.920858 0.460429 0.887696i \(-0.347696\pi\)
0.460429 + 0.887696i \(0.347696\pi\)
\(770\) −14.3178 + 5.60598i −0.515977 + 0.202025i
\(771\) 7.79803 5.20084i 0.280839 0.187304i
\(772\) −4.32331 + 2.80527i −0.155599 + 0.100964i
\(773\) 4.00618 + 14.9513i 0.144092 + 0.537760i 0.999794 + 0.0202907i \(0.00645919\pi\)
−0.855702 + 0.517469i \(0.826874\pi\)
\(774\) 34.4825 27.8152i 1.23945 0.999795i
\(775\) −15.7603 27.2976i −0.566126 0.980559i
\(776\) 2.61009 + 2.23178i 0.0936967 + 0.0801162i
\(777\) 5.53466 + 12.6719i 0.198555 + 0.454600i
\(778\) 0.388917 + 14.9599i 0.0139433 + 0.536338i
\(779\) −1.03007 + 3.84426i −0.0369059 + 0.137735i
\(780\) −7.13642 + 0.835740i −0.255525 + 0.0299243i
\(781\) 1.71821 + 6.41243i 0.0614823 + 0.229455i
\(782\) 21.3934 + 5.14036i 0.765026 + 0.183819i
\(783\) 14.1837 + 9.52993i 0.506883 + 0.340572i
\(784\) 26.9497 7.59707i 0.962488 0.271324i
\(785\) 2.10483i 0.0751247i
\(786\) −20.5773 9.51228i −0.733966 0.339292i
\(787\) 16.5900 4.44528i 0.591369 0.158457i 0.0492904 0.998784i \(-0.484304\pi\)
0.542079 + 0.840328i \(0.317637\pi\)
\(788\) −7.58030 + 2.45983i −0.270037 + 0.0876278i
\(789\) −14.6401 7.23525i −0.521201 0.257582i
\(790\) −17.7187 + 0.460638i −0.630403 + 0.0163888i
\(791\) 24.0146 + 34.4330i 0.853862 + 1.22429i
\(792\) −42.4238 13.8911i −1.50747 0.493599i
\(793\) 8.26288 4.77058i 0.293423 0.169408i
\(794\) 18.0843 + 9.82338i 0.641787 + 0.348619i
\(795\) 0.811438 + 12.5444i 0.0287787 + 0.444905i
\(796\) 15.2059 9.86666i 0.538958 0.349715i
\(797\) 24.5223 + 24.5223i 0.868625 + 0.868625i 0.992320 0.123695i \(-0.0394745\pi\)
−0.123695 + 0.992320i \(0.539475\pi\)
\(798\) −1.01014 5.68043i −0.0357584 0.201085i
\(799\) 34.4294i 1.21802i
\(800\) −3.26452 + 24.6171i −0.115418 + 0.870347i
\(801\) −28.8481 37.7290i −1.01930 1.33309i
\(802\) 4.41190 1.30596i 0.155790 0.0461150i
\(803\) −22.5651 6.04630i −0.796305 0.213369i
\(804\) −12.3864 1.81152i −0.436833 0.0638873i
\(805\) −3.55009 + 4.21484i −0.125124 + 0.148554i
\(806\) −26.9549 + 0.700755i −0.949447 + 0.0246831i
\(807\) 38.2108 12.9344i 1.34508 0.455313i
\(808\) 8.01394 16.7772i 0.281929 0.590218i
\(809\) 2.00663 3.47558i 0.0705492 0.122195i −0.828593 0.559852i \(-0.810858\pi\)
0.899142 + 0.437657i \(0.144191\pi\)
\(810\) 9.65903 + 2.35581i 0.339384 + 0.0827748i
\(811\) −17.0041 + 17.0041i −0.597096 + 0.597096i −0.939539 0.342443i \(-0.888746\pi\)
0.342443 + 0.939539i \(0.388746\pi\)
\(812\) −13.8739 10.5036i −0.486879 0.368604i
\(813\) −6.99880 + 4.66780i −0.245459 + 0.163707i
\(814\) −5.24499 + 21.8288i −0.183837 + 0.765100i
\(815\) 0.895887 1.55172i 0.0313815 0.0543544i
\(816\) 6.78166 + 39.8509i 0.237405 + 1.39506i
\(817\) 4.64815 + 8.05084i 0.162618 + 0.281663i
\(818\) −8.87653 8.42669i −0.310361 0.294632i
\(819\) −0.994598 + 21.0528i −0.0347540 + 0.735645i
\(820\) 5.18837 + 4.67517i 0.181186 + 0.163264i
\(821\) 23.9229 + 6.41013i 0.834915 + 0.223715i 0.650857 0.759200i \(-0.274410\pi\)
0.184058 + 0.982915i \(0.441076\pi\)
\(822\) 14.4142 17.2945i 0.502753 0.603214i
\(823\) 17.5032 30.3164i 0.610122 1.05676i −0.381097 0.924535i \(-0.624454\pi\)
0.991219 0.132228i \(-0.0422131\pi\)
\(824\) 3.29298 17.7114i 0.114716 0.617007i
\(825\) −39.2255 7.83729i −1.36566 0.272859i
\(826\) −6.03846 + 4.44906i −0.210105 + 0.154803i
\(827\) 22.5742 + 22.5742i 0.784981 + 0.784981i 0.980667 0.195686i \(-0.0626934\pi\)
−0.195686 + 0.980667i \(0.562693\pi\)
\(828\) −15.7369 + 2.88272i −0.546896 + 0.100181i
\(829\) 0.0390009 + 0.145553i 0.00135456 + 0.00505528i 0.966600 0.256291i \(-0.0825004\pi\)
−0.965245 + 0.261346i \(0.915834\pi\)
\(830\) −9.98490 + 2.95562i −0.346581 + 0.102591i
\(831\) 2.64512 0.895378i 0.0917583 0.0310603i
\(832\) 17.1718 + 12.5057i 0.595323 + 0.433557i
\(833\) 31.3851 26.1363i 1.08743 0.905570i
\(834\) −12.4583 + 8.78515i −0.431394 + 0.304205i
\(835\) −3.90813 + 14.5854i −0.135247 + 0.504747i
\(836\) 4.25573 8.34457i 0.147188 0.288603i
\(837\) 35.2993 + 12.0835i 1.22012 + 0.417668i
\(838\) 24.3739 14.9300i 0.841983 0.515749i
\(839\) 26.4389i 0.912773i −0.889782 0.456386i \(-0.849143\pi\)
0.889782 0.456386i \(-0.150857\pi\)
\(840\) −9.68540 2.94971i −0.334178 0.101775i
\(841\) 18.1853i 0.627080i
\(842\) −9.01448 14.7165i −0.310659 0.507165i
\(843\) −17.3734 + 1.12380i −0.598371 + 0.0387057i
\(844\) −5.14815 15.8647i −0.177207 0.546087i
\(845\) 1.20273 4.48863i 0.0413750 0.154414i
\(846\) 10.1392 + 22.8899i 0.348594 + 0.786972i
\(847\) −18.7218 + 39.9544i −0.643290 + 1.37285i
\(848\) 23.4104 28.8649i 0.803917 0.991225i
\(849\) −4.74312 14.0121i −0.162783 0.480895i
\(850\) 10.2812 + 34.7329i 0.352644 + 1.19133i
\(851\) 2.08246 + 7.77183i 0.0713857 + 0.266415i
\(852\) −1.73049 + 4.01418i −0.0592855 + 0.137524i
\(853\) 20.4506 + 20.4506i 0.700215 + 0.700215i 0.964457 0.264241i \(-0.0851215\pi\)
−0.264241 + 0.964457i \(0.585122\pi\)
\(854\) 13.3610 1.49451i 0.457206 0.0511411i
\(855\) −0.801659 + 1.92606i −0.0274161 + 0.0658697i
\(856\) 43.7093 30.0042i 1.49395 1.02552i
\(857\) 18.7287 32.4390i 0.639759 1.10809i −0.345727 0.938335i \(-0.612368\pi\)
0.985486 0.169759i \(-0.0542990\pi\)
\(858\) −21.9080 + 26.2857i −0.747927 + 0.897378i
\(859\) 4.39190 + 1.17681i 0.149850 + 0.0401521i 0.332964 0.942940i \(-0.391951\pi\)
−0.183114 + 0.983092i \(0.558618\pi\)
\(860\) 16.2915 0.847640i 0.555534 0.0289043i
\(861\) 16.0117 12.7793i 0.545677 0.435517i
\(862\) 7.56346 7.96722i 0.257612 0.271364i
\(863\) −18.7789 32.5260i −0.639241 1.10720i −0.985600 0.169096i \(-0.945915\pi\)
0.346359 0.938102i \(-0.387418\pi\)
\(864\) −16.2446 24.4972i −0.552651 0.833413i
\(865\) 8.57491 14.8522i 0.291556 0.504989i
\(866\) −8.87796 2.13318i −0.301685 0.0724884i
\(867\) 16.3795 + 24.5591i 0.556278 + 0.834071i
\(868\) −35.1962 14.3121i −1.19464 0.485784i
\(869\) −59.6877 + 59.6877i −2.02477 + 2.02477i
\(870\) 2.17170 + 5.90560i 0.0736274 + 0.200219i
\(871\) −4.79781 + 8.31005i −0.162568 + 0.281575i
\(872\) −17.8512 + 37.3715i −0.604519 + 1.26556i
\(873\) −3.61211 + 0.469264i −0.122252 + 0.0158822i
\(874\) −0.0872467 3.35599i −0.00295116 0.113518i
\(875\) −19.1046 3.40541i −0.645854 0.115124i
\(876\) −9.18849 12.3365i −0.310450 0.416813i
\(877\) 34.8510 + 9.33830i 1.17684 + 0.315332i 0.793670 0.608348i \(-0.208167\pi\)
0.383165 + 0.923680i \(0.374834\pi\)
\(878\) −11.2592 38.0367i −0.379979 1.28368i
\(879\) 18.2525 20.7771i 0.615642 0.700796i
\(880\) −9.65185 13.3057i −0.325364 0.448536i
\(881\) 3.11993i 0.105113i −0.998618 0.0525566i \(-0.983263\pi\)
0.998618 0.0525566i \(-0.0167370\pi\)
\(882\) −13.1690 + 26.6191i −0.443423 + 0.896313i
\(883\) 23.0064 + 23.0064i 0.774227 + 0.774227i 0.978842 0.204615i \(-0.0655943\pi\)
−0.204615 + 0.978842i \(0.565594\pi\)
\(884\) 30.3068 + 6.45386i 1.01933 + 0.217067i
\(885\) 2.70646 0.175068i 0.0909768 0.00588485i
\(886\) −0.595508 + 1.09630i −0.0200065 + 0.0368308i
\(887\) 38.8285 22.4176i 1.30373 0.752710i 0.322690 0.946505i \(-0.395413\pi\)
0.981042 + 0.193795i \(0.0620795\pi\)
\(888\) −11.6220 + 9.13529i −0.390008 + 0.306560i
\(889\) −2.35065 3.37044i −0.0788383 0.113041i
\(890\) −0.454504 17.4828i −0.0152350 0.586024i
\(891\) 41.0853 23.5337i 1.37641 0.788409i
\(892\) 24.2606 47.5697i 0.812305 1.59275i
\(893\) −5.07426 + 1.35964i −0.169804 + 0.0454987i
\(894\) 31.4799 + 14.5523i 1.05285 + 0.486701i
\(895\) 1.16011i 0.0387782i
\(896\) 15.1101 + 25.8396i 0.504792 + 0.863241i
\(897\) −2.40280 + 12.0260i −0.0802273 + 0.401536i
\(898\) −0.296539 + 1.23415i −0.00989564 + 0.0411841i
\(899\) 6.11151 + 22.8085i 0.203830 + 0.760705i
\(900\) −17.0640 20.0640i −0.568800 0.668800i
\(901\) 14.0309 52.3641i 0.467438 1.74450i
\(902\) 33.2491 0.864385i 1.10707 0.0287809i
\(903\) 5.33889 47.5536i 0.177667 1.58248i
\(904\) −29.1656 + 34.1095i −0.970035 + 1.13446i
\(905\) −8.33027 14.4285i −0.276908 0.479618i
\(906\) 13.5638 16.2742i 0.450629 0.540674i
\(907\) −15.0607 56.2074i −0.500083 1.86634i −0.499463 0.866335i \(-0.666469\pi\)
−0.000620375 1.00000i \(-0.500197\pi\)
\(908\) −7.14519 + 33.5532i −0.237121 + 1.11350i
\(909\) 7.51565 + 18.2325i 0.249278 + 0.604733i
\(910\) −4.84373 + 6.06381i −0.160568 + 0.201013i
\(911\) 0.821005 0.0272011 0.0136006 0.999908i \(-0.495671\pi\)
0.0136006 + 0.999908i \(0.495671\pi\)
\(912\) 5.60549 2.57324i 0.185616 0.0852084i
\(913\) −24.7955 + 42.9471i −0.820612 + 1.42134i
\(914\) −7.06417 + 2.09105i −0.233662 + 0.0691659i
\(915\) −4.35821 2.15387i −0.144078 0.0712046i
\(916\) 5.18554 5.75477i 0.171335 0.190143i
\(917\) −23.0248 + 8.33173i −0.760345 + 0.275138i
\(918\) −36.1983 22.9790i −1.19472 0.758419i
\(919\) 9.52088 + 16.4906i 0.314065 + 0.543976i 0.979238 0.202713i \(-0.0649758\pi\)
−0.665173 + 0.746689i \(0.731642\pi\)
\(920\) −5.31588 2.53924i −0.175259 0.0837162i
\(921\) −9.82828 8.63404i −0.323853 0.284501i
\(922\) 12.3711 + 20.1964i 0.407421 + 0.665132i
\(923\) 2.36935 + 2.36935i 0.0779880 + 0.0779880i
\(924\) −43.1237 + 21.5689i −1.41866 + 0.709565i
\(925\) −9.36649 + 9.36649i −0.307968 + 0.307968i
\(926\) 4.36760 18.1773i 0.143528 0.597342i
\(927\) 11.6061 + 15.1791i 0.381195 + 0.498546i
\(928\) 7.13524 17.1802i 0.234226 0.563967i
\(929\) −41.5872 + 24.0104i −1.36443 + 0.787755i −0.990210 0.139585i \(-0.955423\pi\)
−0.374221 + 0.927339i \(0.622090\pi\)
\(930\) 7.91751 + 11.2278i 0.259625 + 0.368175i
\(931\) −5.09144 3.59344i −0.166865 0.117770i
\(932\) −0.980633 18.8476i −0.0321217 0.617372i
\(933\) 43.1280 + 21.3142i 1.41195 + 0.697797i
\(934\) 48.9292 + 26.5783i 1.60101 + 0.869669i
\(935\) −20.7649 11.9886i −0.679086 0.392071i
\(936\) −22.0498 + 4.63442i −0.720719 + 0.151481i
\(937\) 39.8484i 1.30179i −0.759168 0.650895i \(-0.774394\pi\)
0.759168 0.650895i \(-0.225606\pi\)
\(938\) −10.8855 + 8.02033i −0.355426 + 0.261873i
\(939\) −23.1811 + 15.4605i −0.756487 + 0.504534i
\(940\) −1.92006 + 9.01644i −0.0626253 + 0.294084i
\(941\) −22.9847 + 6.15874i −0.749281 + 0.200769i −0.613199 0.789928i \(-0.710118\pi\)
−0.136082 + 0.990698i \(0.543451\pi\)
\(942\) −0.597089 6.57332i −0.0194542 0.214170i
\(943\) 10.3233 5.96015i 0.336172 0.194089i
\(944\) −6.22762 5.05080i −0.202692 0.164390i
\(945\) 9.20529 5.53027i 0.299448 0.179900i
\(946\) 53.4892 56.3446i 1.73909 1.83192i
\(947\) 13.3126 + 3.56711i 0.432602 + 0.115915i 0.468548 0.883438i \(-0.344777\pi\)
−0.0359451 + 0.999354i \(0.511444\pi\)
\(948\) −55.2043 + 6.46492i −1.79295 + 0.209971i
\(949\) −11.3894 + 3.05179i −0.369716 + 0.0990652i
\(950\) 4.71299 2.88690i 0.152909 0.0936634i
\(951\) −3.62874 + 18.1617i −0.117670 + 0.588935i
\(952\) 35.4848 + 25.4414i 1.15007 + 0.824561i
\(953\) 51.0166 1.65259 0.826295 0.563238i \(-0.190445\pi\)
0.826295 + 0.563238i \(0.190445\pi\)
\(954\) 6.09264 + 38.9457i 0.197256 + 1.26091i
\(955\) 2.09685 + 7.82555i 0.0678524 + 0.253229i
\(956\) −15.9685 8.14394i −0.516458 0.263394i
\(957\) 26.8642 + 13.2765i 0.868398 + 0.429169i
\(958\) 26.9466 28.3850i 0.870604 0.917079i
\(959\) −2.07423 24.2290i −0.0669804 0.782394i
\(960\) 0.446410 10.8145i 0.0144078 0.349035i
\(961\) 10.2787 + 17.8033i 0.331572 + 0.574300i
\(962\) 3.21624 + 10.8654i 0.103696 + 0.350313i
\(963\) −7.43511 + 55.7388i −0.239593 + 1.79616i
\(964\) 45.1347 29.2866i 1.45369 0.943259i
\(965\) 1.42330 1.42330i 0.0458177 0.0458177i
\(966\) −9.89118 + 14.1699i −0.318243 + 0.455909i
\(967\) 25.7161 0.826974 0.413487 0.910510i \(-0.364311\pi\)
0.413487 + 0.910510i \(0.364311\pi\)
\(968\) −46.3750 8.62222i −1.49055 0.277129i
\(969\) 5.93787 6.75918i 0.190752 0.217136i
\(970\) −1.17860 0.640216i −0.0378426 0.0205561i
\(971\) −1.77838 + 6.63699i −0.0570708 + 0.212991i −0.988573 0.150746i \(-0.951833\pi\)
0.931502 + 0.363737i \(0.118499\pi\)
\(972\) 30.8331 + 4.61710i 0.988973 + 0.148093i
\(973\) −2.88947 + 16.2102i −0.0926323 + 0.519674i
\(974\) −1.34911 + 1.42113i −0.0432283 + 0.0455359i
\(975\) −19.1239 + 6.47347i −0.612455 + 0.207317i
\(976\) 5.14057 + 13.4219i 0.164546 + 0.429624i
\(977\) 22.7924 + 13.1592i 0.729192 + 0.420999i 0.818127 0.575038i \(-0.195013\pi\)
−0.0889342 + 0.996037i \(0.528346\pi\)
\(978\) 2.35764 5.10012i 0.0753891 0.163084i
\(979\) −58.8929 58.8929i −1.88222 1.88222i
\(980\) −9.67677 + 5.09436i −0.309113 + 0.162733i
\(981\) −16.7413 40.6133i −0.534508 1.29668i
\(982\) 14.4924 + 23.6594i 0.462471 + 0.755003i
\(983\) 1.85155 + 1.06899i 0.0590552 + 0.0340955i 0.529237 0.848474i \(-0.322478\pi\)
−0.470182 + 0.882570i \(0.655812\pi\)
\(984\) 17.5294 + 13.1286i 0.558815 + 0.418525i
\(985\) 2.69557 1.55629i 0.0858881 0.0495875i
\(986\) −0.705213 27.1264i −0.0224585 0.863880i
\(987\) 25.1756 + 9.86917i 0.801348 + 0.314139i
\(988\) −0.245661 4.72154i −0.00781551 0.150212i
\(989\) 7.20652 26.8951i 0.229154 0.855214i
\(990\) 17.3359 + 1.85535i 0.550971 + 0.0589668i
\(991\) 6.78484 + 3.91723i 0.215528 + 0.124435i 0.603878 0.797077i \(-0.293622\pi\)
−0.388350 + 0.921512i \(0.626955\pi\)
\(992\) 5.33969 40.2657i 0.169535 1.27844i
\(993\) −47.1803 9.42667i −1.49722 0.299146i
\(994\) 1.72142 + 4.39655i 0.0546003 + 0.139450i
\(995\) −5.00602 + 5.00602i −0.158701 + 0.158701i
\(996\) −30.3441 + 12.0628i −0.961490 + 0.382223i
\(997\) 33.4779 8.97039i 1.06026 0.284095i 0.313773 0.949498i \(-0.398407\pi\)
0.746484 + 0.665403i \(0.231740\pi\)
\(998\) 2.31854 4.26831i 0.0733922 0.135111i
\(999\) 1.06559 15.6430i 0.0337137 0.494923i
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 336.2.bu.a.11.3 240
3.2 odd 2 inner 336.2.bu.a.11.58 yes 240
7.2 even 3 inner 336.2.bu.a.107.37 yes 240
16.3 odd 4 inner 336.2.bu.a.179.24 yes 240
21.2 odd 6 inner 336.2.bu.a.107.24 yes 240
48.35 even 4 inner 336.2.bu.a.179.37 yes 240
112.51 odd 12 inner 336.2.bu.a.275.58 yes 240
336.275 even 12 inner 336.2.bu.a.275.3 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bu.a.11.3 240 1.1 even 1 trivial
336.2.bu.a.11.58 yes 240 3.2 odd 2 inner
336.2.bu.a.107.24 yes 240 21.2 odd 6 inner
336.2.bu.a.107.37 yes 240 7.2 even 3 inner
336.2.bu.a.179.24 yes 240 16.3 odd 4 inner
336.2.bu.a.179.37 yes 240 48.35 even 4 inner
336.2.bu.a.275.3 yes 240 336.275 even 12 inner
336.2.bu.a.275.58 yes 240 112.51 odd 12 inner