Properties

Label 588.2.o.a.31.1
Level $588$
Weight $2$
Character 588.31
Analytic conductor $4.695$
Analytic rank $0$
Dimension $8$
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] = [588,2,Mod(19,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.o (of order \(6\), degree \(2\), not 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: \(4.69520363885\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.432972864.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(-1.41156 + 0.0865986i\) of defining polynomial
Character \(\chi\) \(=\) 588.31
Dual form 588.2.o.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41156 - 0.0865986i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.98500 + 0.244478i) q^{4} +(1.46890 - 0.848071i) q^{5} +(0.780776 - 1.17915i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.41156 - 0.0865986i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.98500 + 0.244478i) q^{4} +(1.46890 - 0.848071i) q^{5} +(0.780776 - 1.17915i) q^{6} +(-2.78078 - 0.516994i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.14688 + 1.06990i) q^{10} +(-2.61578 - 1.51022i) q^{11} +(-1.20422 + 1.59682i) q^{12} -6.04090i q^{13} +1.69614i q^{15} +(3.88046 + 0.970579i) q^{16} +(-3.76267 - 2.17238i) q^{17} +(0.630783 + 1.26575i) q^{18} +(-0.561553 - 0.972638i) q^{19} +(3.12311 - 1.32431i) q^{20} +(3.56155 + 2.35829i) q^{22} +(-2.61578 + 1.51022i) q^{23} +(1.83812 - 2.14973i) q^{24} +(-1.06155 + 1.83866i) q^{25} +(-0.523133 + 8.52708i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(0.146883 - 2.39420i) q^{30} +(-5.39345 - 1.70607i) q^{32} +(2.61578 - 1.51022i) q^{33} +(5.12311 + 3.39228i) q^{34} +(-0.780776 - 1.84130i) q^{36} +(3.56155 + 6.16879i) q^{37} +(0.708436 + 1.42157i) q^{38} +(5.23157 + 3.02045i) q^{39} +(-4.52313 + 1.59888i) q^{40} -7.73704i q^{41} -8.10887i q^{43} +(-4.82312 - 3.63730i) q^{44} +(-1.46890 - 0.848071i) q^{45} +(3.82312 - 1.90525i) q^{46} +(-5.12311 - 8.87348i) q^{47} +(-2.78078 + 2.87529i) q^{48} +(1.65767 - 2.50345i) q^{50} +(3.76267 - 2.17238i) q^{51} +(1.47687 - 11.9912i) q^{52} +(2.12311 - 3.67733i) q^{53} +(-1.41156 - 0.0865986i) q^{54} -5.12311 q^{55} +1.12311 q^{57} +(2.82312 + 0.173197i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-0.414669 + 3.36684i) q^{60} +(8.16937 - 4.71659i) q^{61} +(7.46543 + 2.87529i) q^{64} +(-5.12311 - 8.87348i) q^{65} +(-3.82312 + 1.90525i) q^{66} +(-1.79092 - 1.03399i) q^{67} +(-6.93780 - 5.23206i) q^{68} -3.02045i q^{69} +12.4536i q^{71} +(0.942658 + 2.66672i) q^{72} +(-2.93780 - 1.69614i) q^{73} +(-4.49314 - 9.01604i) q^{74} +(-1.06155 - 1.83866i) q^{75} +(-0.876894 - 2.06798i) q^{76} +(-7.12311 - 4.71659i) q^{78} +(4.08469 - 2.35829i) q^{79} +(6.52313 - 1.86522i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.670016 + 10.9213i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(-0.702217 + 11.4462i) q^{86} +(1.00000 - 1.73205i) q^{87} +(6.49314 + 5.55194i) q^{88} +(6.70047 - 3.86852i) q^{89} +(2.00000 + 1.32431i) q^{90} +(-5.56155 + 2.35829i) q^{92} +(6.46314 + 12.9691i) q^{94} +(-1.64973 - 0.952473i) q^{95} +(4.17423 - 3.81783i) q^{96} +8.68951i q^{97} +3.02045i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41156 0.0865986i −0.998123 0.0612344i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 1.98500 + 0.244478i 0.992501 + 0.122239i
\(5\) 1.46890 0.848071i 0.656913 0.379269i −0.134187 0.990956i \(-0.542842\pi\)
0.791100 + 0.611687i \(0.209509\pi\)
\(6\) 0.780776 1.17915i 0.318751 0.481385i
\(7\) 0 0
\(8\) −2.78078 0.516994i −0.983153 0.182785i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −2.14688 + 1.06990i −0.678904 + 0.338331i
\(11\) −2.61578 1.51022i −0.788689 0.455350i 0.0508120 0.998708i \(-0.483819\pi\)
−0.839501 + 0.543359i \(0.817152\pi\)
\(12\) −1.20422 + 1.59682i −0.347630 + 0.460963i
\(13\) 6.04090i 1.67544i −0.546098 0.837722i \(-0.683887\pi\)
0.546098 0.837722i \(-0.316113\pi\)
\(14\) 0 0
\(15\) 1.69614i 0.437942i
\(16\) 3.88046 + 0.970579i 0.970115 + 0.242645i
\(17\) −3.76267 2.17238i −0.912581 0.526879i −0.0313203 0.999509i \(-0.509971\pi\)
−0.881261 + 0.472630i \(0.843305\pi\)
\(18\) 0.630783 + 1.26575i 0.148677 + 0.298339i
\(19\) −0.561553 0.972638i −0.128829 0.223138i 0.794394 0.607403i \(-0.207789\pi\)
−0.923223 + 0.384264i \(0.874455\pi\)
\(20\) 3.12311 1.32431i 0.698348 0.296124i
\(21\) 0 0
\(22\) 3.56155 + 2.35829i 0.759326 + 0.502790i
\(23\) −2.61578 + 1.51022i −0.545429 + 0.314903i −0.747276 0.664514i \(-0.768639\pi\)
0.201847 + 0.979417i \(0.435305\pi\)
\(24\) 1.83812 2.14973i 0.375204 0.438811i
\(25\) −1.06155 + 1.83866i −0.212311 + 0.367733i
\(26\) −0.523133 + 8.52708i −0.102595 + 1.67230i
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0.146883 2.39420i 0.0268171 0.437120i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −5.39345 1.70607i −0.953436 0.301594i
\(33\) 2.61578 1.51022i 0.455350 0.262896i
\(34\) 5.12311 + 3.39228i 0.878605 + 0.581772i
\(35\) 0 0
\(36\) −0.780776 1.84130i −0.130129 0.306883i
\(37\) 3.56155 + 6.16879i 0.585516 + 1.01414i 0.994811 + 0.101741i \(0.0324413\pi\)
−0.409295 + 0.912402i \(0.634225\pi\)
\(38\) 0.708436 + 1.42157i 0.114924 + 0.230608i
\(39\) 5.23157 + 3.02045i 0.837722 + 0.483659i
\(40\) −4.52313 + 1.59888i −0.715170 + 0.252805i
\(41\) 7.73704i 1.20832i −0.796862 0.604161i \(-0.793508\pi\)
0.796862 0.604161i \(-0.206492\pi\)
\(42\) 0 0
\(43\) 8.10887i 1.23659i −0.785946 0.618296i \(-0.787823\pi\)
0.785946 0.618296i \(-0.212177\pi\)
\(44\) −4.82312 3.63730i −0.727113 0.548343i
\(45\) −1.46890 0.848071i −0.218971 0.126423i
\(46\) 3.82312 1.90525i 0.563688 0.280913i
\(47\) −5.12311 8.87348i −0.747282 1.29433i −0.949121 0.314911i \(-0.898025\pi\)
0.201839 0.979419i \(-0.435308\pi\)
\(48\) −2.78078 + 2.87529i −0.401371 + 0.415012i
\(49\) 0 0
\(50\) 1.65767 2.50345i 0.234430 0.354042i
\(51\) 3.76267 2.17238i 0.526879 0.304194i
\(52\) 1.47687 11.9912i 0.204805 1.66288i
\(53\) 2.12311 3.67733i 0.291631 0.505120i −0.682565 0.730825i \(-0.739135\pi\)
0.974196 + 0.225706i \(0.0724687\pi\)
\(54\) −1.41156 0.0865986i −0.192089 0.0117846i
\(55\) −5.12311 −0.690799
\(56\) 0 0
\(57\) 1.12311 0.148759
\(58\) 2.82312 + 0.173197i 0.370694 + 0.0227419i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −0.414669 + 3.36684i −0.0535336 + 0.434657i
\(61\) 8.16937 4.71659i 1.04598 0.603897i 0.124459 0.992225i \(-0.460280\pi\)
0.921521 + 0.388327i \(0.126947\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.46543 + 2.87529i 0.933179 + 0.359411i
\(65\) −5.12311 8.87348i −0.635443 1.10062i
\(66\) −3.82312 + 1.90525i −0.470593 + 0.234520i
\(67\) −1.79092 1.03399i −0.218796 0.126322i 0.386597 0.922249i \(-0.373650\pi\)
−0.605392 + 0.795927i \(0.706984\pi\)
\(68\) −6.93780 5.23206i −0.841332 0.634481i
\(69\) 3.02045i 0.363619i
\(70\) 0 0
\(71\) 12.4536i 1.47797i 0.673720 + 0.738987i \(0.264695\pi\)
−0.673720 + 0.738987i \(0.735305\pi\)
\(72\) 0.942658 + 2.66672i 0.111093 + 0.314276i
\(73\) −2.93780 1.69614i −0.343844 0.198518i 0.318127 0.948048i \(-0.396946\pi\)
−0.661970 + 0.749530i \(0.730280\pi\)
\(74\) −4.49314 9.01604i −0.522316 1.04809i
\(75\) −1.06155 1.83866i −0.122578 0.212311i
\(76\) −0.876894 2.06798i −0.100587 0.237213i
\(77\) 0 0
\(78\) −7.12311 4.71659i −0.806533 0.534049i
\(79\) 4.08469 2.35829i 0.459563 0.265329i −0.252297 0.967650i \(-0.581186\pi\)
0.711861 + 0.702321i \(0.247853\pi\)
\(80\) 6.52313 1.86522i 0.729308 0.208538i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.670016 + 10.9213i −0.0739909 + 1.20605i
\(83\) −6.24621 −0.685611 −0.342805 0.939406i \(-0.611377\pi\)
−0.342805 + 0.939406i \(0.611377\pi\)
\(84\) 0 0
\(85\) −7.36932 −0.799315
\(86\) −0.702217 + 11.4462i −0.0757220 + 1.23427i
\(87\) 1.00000 1.73205i 0.107211 0.185695i
\(88\) 6.49314 + 5.55194i 0.692171 + 0.591839i
\(89\) 6.70047 3.86852i 0.710248 0.410062i −0.100905 0.994896i \(-0.532174\pi\)
0.811153 + 0.584834i \(0.198840\pi\)
\(90\) 2.00000 + 1.32431i 0.210819 + 0.139594i
\(91\) 0 0
\(92\) −5.56155 + 2.35829i −0.579832 + 0.245869i
\(93\) 0 0
\(94\) 6.46314 + 12.9691i 0.666622 + 1.33766i
\(95\) −1.64973 0.952473i −0.169259 0.0977216i
\(96\) 4.17423 3.81783i 0.426030 0.389656i
\(97\) 8.68951i 0.882286i 0.897437 + 0.441143i \(0.145427\pi\)
−0.897437 + 0.441143i \(0.854573\pi\)
\(98\) 0 0
\(99\) 3.02045i 0.303566i
\(100\) −2.55670 + 3.39022i −0.255670 + 0.339022i
\(101\) 6.05643 + 3.49668i 0.602638 + 0.347933i 0.770079 0.637949i \(-0.220217\pi\)
−0.167441 + 0.985882i \(0.553550\pi\)
\(102\) −5.49936 + 2.74060i −0.544517 + 0.271360i
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) −3.12311 + 16.7984i −0.306246 + 1.64722i
\(105\) 0 0
\(106\) −3.31534 + 5.00691i −0.322014 + 0.486314i
\(107\) −4.90955 + 2.83453i −0.474624 + 0.274024i −0.718173 0.695864i \(-0.755022\pi\)
0.243549 + 0.969889i \(0.421688\pi\)
\(108\) 1.98500 + 0.244478i 0.191007 + 0.0235249i
\(109\) −4.12311 + 7.14143i −0.394922 + 0.684025i −0.993091 0.117345i \(-0.962562\pi\)
0.598169 + 0.801370i \(0.295895\pi\)
\(110\) 7.23157 + 0.443654i 0.689503 + 0.0423007i
\(111\) −7.12311 −0.676095
\(112\) 0 0
\(113\) 12.2462 1.15203 0.576013 0.817440i \(-0.304608\pi\)
0.576013 + 0.817440i \(0.304608\pi\)
\(114\) −1.58533 0.0972594i −0.148480 0.00910917i
\(115\) −2.56155 + 4.43674i −0.238866 + 0.413728i
\(116\) −3.97000 0.488956i −0.368606 0.0453985i
\(117\) −5.23157 + 3.02045i −0.483659 + 0.279241i
\(118\) −3.12311 + 4.71659i −0.287505 + 0.434197i
\(119\) 0 0
\(120\) 0.876894 4.71659i 0.0800491 0.430564i
\(121\) −0.938447 1.62544i −0.0853134 0.147767i
\(122\) −11.9400 + 5.95029i −1.08100 + 0.538714i
\(123\) 6.70047 + 3.86852i 0.604161 + 0.348813i
\(124\) 0 0
\(125\) 12.0818i 1.08063i
\(126\) 0 0
\(127\) 19.4470i 1.72564i −0.505510 0.862821i \(-0.668696\pi\)
0.505510 0.862821i \(-0.331304\pi\)
\(128\) −10.2889 4.70514i −0.909420 0.415879i
\(129\) 7.02249 + 4.05444i 0.618296 + 0.356973i
\(130\) 6.46314 + 12.9691i 0.566855 + 1.13747i
\(131\) 11.1231 + 19.2658i 0.971830 + 1.68326i 0.690022 + 0.723789i \(0.257601\pi\)
0.281809 + 0.959471i \(0.409066\pi\)
\(132\) 5.56155 2.35829i 0.484071 0.205263i
\(133\) 0 0
\(134\) 2.43845 + 1.61463i 0.210650 + 0.139482i
\(135\) 1.46890 0.848071i 0.126423 0.0729903i
\(136\) 9.34003 + 7.98617i 0.800901 + 0.684809i
\(137\) 8.12311 14.0696i 0.694004 1.20205i −0.276512 0.961011i \(-0.589178\pi\)
0.970515 0.241039i \(-0.0774882\pi\)
\(138\) −0.261567 + 4.26354i −0.0222660 + 0.362937i
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 10.2462 0.862887
\(142\) 1.07847 17.5790i 0.0905029 1.47520i
\(143\) −9.12311 + 15.8017i −0.762912 + 1.32140i
\(144\) −1.09968 3.84587i −0.0916404 0.320489i
\(145\) −2.93780 + 1.69614i −0.243971 + 0.140857i
\(146\) 4.00000 + 2.64861i 0.331042 + 0.219201i
\(147\) 0 0
\(148\) 5.56155 + 13.1158i 0.457157 + 1.07811i
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 1.33922 + 2.68731i 0.109347 + 0.219418i
\(151\) −7.02249 4.05444i −0.571482 0.329945i 0.186259 0.982501i \(-0.440364\pi\)
−0.757741 + 0.652555i \(0.773697\pi\)
\(152\) 1.05871 + 2.99501i 0.0858723 + 0.242927i
\(153\) 4.34475i 0.351253i
\(154\) 0 0
\(155\) 0 0
\(156\) 9.64624 + 7.27460i 0.772317 + 0.582434i
\(157\) 3.58184 + 2.06798i 0.285862 + 0.165042i 0.636074 0.771628i \(-0.280557\pi\)
−0.350212 + 0.936670i \(0.613891\pi\)
\(158\) −5.97000 + 2.97515i −0.474948 + 0.236690i
\(159\) 2.12311 + 3.67733i 0.168373 + 0.291631i
\(160\) −9.36932 + 2.06798i −0.740710 + 0.163488i
\(161\) 0 0
\(162\) 0.780776 1.17915i 0.0613436 0.0926426i
\(163\) −9.96029 + 5.75058i −0.780150 + 0.450420i −0.836484 0.547992i \(-0.815392\pi\)
0.0563333 + 0.998412i \(0.482059\pi\)
\(164\) 1.89154 15.3580i 0.147704 1.19926i
\(165\) 2.56155 4.43674i 0.199417 0.345400i
\(166\) 8.81690 + 0.540913i 0.684324 + 0.0419830i
\(167\) 2.24621 0.173817 0.0869085 0.996216i \(-0.472301\pi\)
0.0869085 + 0.996216i \(0.472301\pi\)
\(168\) 0 0
\(169\) −23.4924 −1.80711
\(170\) 10.4022 + 0.638172i 0.797815 + 0.0489456i
\(171\) −0.561553 + 0.972638i −0.0429430 + 0.0743795i
\(172\) 1.98244 16.0961i 0.151160 1.22732i
\(173\) −7.34451 + 4.24035i −0.558392 + 0.322388i −0.752500 0.658592i \(-0.771152\pi\)
0.194108 + 0.980980i \(0.437819\pi\)
\(174\) −1.56155 + 2.35829i −0.118381 + 0.178782i
\(175\) 0 0
\(176\) −8.68466 8.39919i −0.654631 0.633113i
\(177\) 2.00000 + 3.46410i 0.150329 + 0.260378i
\(178\) −9.79312 + 4.88039i −0.734026 + 0.365801i
\(179\) 1.97175 + 1.13839i 0.147375 + 0.0850873i 0.571874 0.820341i \(-0.306216\pi\)
−0.424499 + 0.905428i \(0.639550\pi\)
\(180\) −2.70844 2.04254i −0.201875 0.152242i
\(181\) 6.04090i 0.449016i 0.974472 + 0.224508i \(0.0720775\pi\)
−0.974472 + 0.224508i \(0.927922\pi\)
\(182\) 0 0
\(183\) 9.43318i 0.697321i
\(184\) 8.05469 2.84725i 0.593800 0.209902i
\(185\) 10.4631 + 6.04090i 0.769265 + 0.444135i
\(186\) 0 0
\(187\) 6.56155 + 11.3649i 0.479828 + 0.831087i
\(188\) −8.00000 18.8664i −0.583460 1.37597i
\(189\) 0 0
\(190\) 2.24621 + 1.48734i 0.162957 + 0.107903i
\(191\) 7.84735 4.53067i 0.567815 0.327828i −0.188461 0.982081i \(-0.560350\pi\)
0.756276 + 0.654253i \(0.227017\pi\)
\(192\) −6.22279 + 5.02761i −0.449091 + 0.362837i
\(193\) −4.68466 + 8.11407i −0.337209 + 0.584063i −0.983907 0.178683i \(-0.942816\pi\)
0.646698 + 0.762747i \(0.276150\pi\)
\(194\) 0.752499 12.2658i 0.0540263 0.880630i
\(195\) 10.2462 0.733746
\(196\) 0 0
\(197\) 0.246211 0.0175418 0.00877091 0.999962i \(-0.497208\pi\)
0.00877091 + 0.999962i \(0.497208\pi\)
\(198\) 0.261567 4.26354i 0.0185887 0.302997i
\(199\) 2.56155 4.43674i 0.181584 0.314512i −0.760836 0.648944i \(-0.775211\pi\)
0.942420 + 0.334432i \(0.108544\pi\)
\(200\) 3.90252 4.56410i 0.275950 0.322730i
\(201\) 1.79092 1.03399i 0.126322 0.0729319i
\(202\) −8.24621 5.46026i −0.580201 0.384182i
\(203\) 0 0
\(204\) 8.00000 3.39228i 0.560112 0.237507i
\(205\) −6.56155 11.3649i −0.458279 0.793762i
\(206\) 5.04627 + 10.1260i 0.351590 + 0.705510i
\(207\) 2.61578 + 1.51022i 0.181810 + 0.104968i
\(208\) 5.86317 23.4415i 0.406537 1.62537i
\(209\) 3.39228i 0.234649i
\(210\) 0 0
\(211\) 3.97292i 0.273507i 0.990605 + 0.136754i \(0.0436668\pi\)
−0.990605 + 0.136754i \(0.956333\pi\)
\(212\) 5.11339 6.78045i 0.351189 0.465683i
\(213\) −10.7852 6.22681i −0.738987 0.426654i
\(214\) 7.17559 3.57595i 0.490513 0.244447i
\(215\) −6.87689 11.9111i −0.469000 0.812332i
\(216\) −2.78078 0.516994i −0.189208 0.0351770i
\(217\) 0 0
\(218\) 6.43845 9.72350i 0.436067 0.658558i
\(219\) 2.93780 1.69614i 0.198518 0.114615i
\(220\) −10.1694 1.25249i −0.685619 0.0844427i
\(221\) −13.1231 + 22.7299i −0.882756 + 1.52898i
\(222\) 10.0547 + 0.616851i 0.674827 + 0.0414003i
\(223\) −18.8769 −1.26409 −0.632045 0.774932i \(-0.717784\pi\)
−0.632045 + 0.774932i \(0.717784\pi\)
\(224\) 0 0
\(225\) 2.12311 0.141540
\(226\) −17.2863 1.06050i −1.14986 0.0705437i
\(227\) 8.24621 14.2829i 0.547320 0.947987i −0.451137 0.892455i \(-0.648981\pi\)
0.998457 0.0555316i \(-0.0176854\pi\)
\(228\) 2.22937 + 0.274575i 0.147643 + 0.0181842i
\(229\) −15.6947 + 9.06134i −1.03714 + 0.598790i −0.919021 0.394209i \(-0.871018\pi\)
−0.118115 + 0.993000i \(0.537685\pi\)
\(230\) 4.00000 6.04090i 0.263752 0.398325i
\(231\) 0 0
\(232\) 5.56155 + 1.03399i 0.365134 + 0.0678846i
\(233\) 5.24621 + 9.08670i 0.343691 + 0.595290i 0.985115 0.171897i \(-0.0549895\pi\)
−0.641424 + 0.767186i \(0.721656\pi\)
\(234\) 7.64624 3.81050i 0.499850 0.249100i
\(235\) −15.0507 8.68951i −0.981798 0.566841i
\(236\) 4.81690 6.38729i 0.313553 0.415777i
\(237\) 4.71659i 0.306375i
\(238\) 0 0
\(239\) 2.27678i 0.147273i 0.997285 + 0.0736363i \(0.0234604\pi\)
−0.997285 + 0.0736363i \(0.976540\pi\)
\(240\) −1.64624 + 6.58181i −0.106264 + 0.424854i
\(241\) 1.64973 + 0.952473i 0.106269 + 0.0613542i 0.552192 0.833717i \(-0.313791\pi\)
−0.445924 + 0.895071i \(0.647125\pi\)
\(242\) 1.18391 + 2.37567i 0.0761048 + 0.152714i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 17.3693 7.36520i 1.11196 0.471509i
\(245\) 0 0
\(246\) −9.12311 6.04090i −0.581668 0.385153i
\(247\) −5.87560 + 3.39228i −0.373856 + 0.215846i
\(248\) 0 0
\(249\) 3.12311 5.40938i 0.197919 0.342805i
\(250\) 1.04627 17.0542i 0.0661717 1.07860i
\(251\) 22.2462 1.40417 0.702084 0.712094i \(-0.252253\pi\)
0.702084 + 0.712094i \(0.252253\pi\)
\(252\) 0 0
\(253\) 9.12311 0.573565
\(254\) −1.68408 + 27.4506i −0.105669 + 1.72240i
\(255\) 3.68466 6.38202i 0.230742 0.399657i
\(256\) 14.1160 + 7.53259i 0.882247 + 0.470787i
\(257\) −17.1636 + 9.90941i −1.07064 + 0.618132i −0.928355 0.371694i \(-0.878777\pi\)
−0.142281 + 0.989826i \(0.545444\pi\)
\(258\) −9.56155 6.33122i −0.595276 0.394164i
\(259\) 0 0
\(260\) −8.00000 18.8664i −0.496139 1.17004i
\(261\) 1.00000 + 1.73205i 0.0618984 + 0.107211i
\(262\) −14.0325 28.1580i −0.866933 1.73961i
\(263\) 4.26552 + 2.46270i 0.263023 + 0.151856i 0.625713 0.780054i \(-0.284808\pi\)
−0.362690 + 0.931910i \(0.618142\pi\)
\(264\) −8.05469 + 2.84725i −0.495732 + 0.175236i
\(265\) 7.20217i 0.442426i
\(266\) 0 0
\(267\) 7.73704i 0.473499i
\(268\) −3.30219 2.49031i −0.201713 0.152120i
\(269\) −19.4574 11.2337i −1.18634 0.684932i −0.228865 0.973458i \(-0.573501\pi\)
−0.957472 + 0.288526i \(0.906835\pi\)
\(270\) −2.14688 + 1.06990i −0.130655 + 0.0651119i
\(271\) 2.24621 + 3.89055i 0.136448 + 0.236334i 0.926150 0.377157i \(-0.123098\pi\)
−0.789702 + 0.613491i \(0.789765\pi\)
\(272\) −12.4924 12.0818i −0.757464 0.732566i
\(273\) 0 0
\(274\) −12.6847 + 19.1567i −0.766308 + 1.15730i
\(275\) 5.55359 3.20636i 0.334894 0.193351i
\(276\) 0.738433 5.99559i 0.0444485 0.360892i
\(277\) −1.56155 + 2.70469i −0.0938246 + 0.162509i −0.909117 0.416540i \(-0.863243\pi\)
0.815293 + 0.579049i \(0.196576\pi\)
\(278\) −16.9387 1.03918i −1.01592 0.0623261i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.246211 −0.0146877 −0.00734387 0.999973i \(-0.502338\pi\)
−0.00734387 + 0.999973i \(0.502338\pi\)
\(282\) −14.4631 0.887307i −0.861267 0.0528384i
\(283\) 8.56155 14.8290i 0.508931 0.881495i −0.491015 0.871151i \(-0.663374\pi\)
0.999946 0.0103441i \(-0.00329268\pi\)
\(284\) −3.04464 + 24.7205i −0.180666 + 1.46689i
\(285\) 1.64973 0.952473i 0.0977216 0.0564196i
\(286\) 14.2462 21.5150i 0.842396 1.27221i
\(287\) 0 0
\(288\) 1.21922 + 5.52390i 0.0718434 + 0.325499i
\(289\) 0.938447 + 1.62544i 0.0552028 + 0.0956140i
\(290\) 4.29377 2.13979i 0.252139 0.125653i
\(291\) −7.52534 4.34475i −0.441143 0.254694i
\(292\) −5.41687 4.08507i −0.316998 0.239061i
\(293\) 6.99337i 0.408557i −0.978913 0.204278i \(-0.934515\pi\)
0.978913 0.204278i \(-0.0654848\pi\)
\(294\) 0 0
\(295\) 6.78456i 0.395013i
\(296\) −6.71466 18.9953i −0.390281 1.10408i
\(297\) −2.61578 1.51022i −0.151783 0.0876321i
\(298\) −6.30783 12.6575i −0.365403 0.733227i
\(299\) 9.12311 + 15.8017i 0.527603 + 0.913835i
\(300\) −1.65767 3.90928i −0.0957057 0.225702i
\(301\) 0 0
\(302\) 9.56155 + 6.33122i 0.550206 + 0.364320i
\(303\) −6.05643 + 3.49668i −0.347933 + 0.200879i
\(304\) −1.23506 4.31932i −0.0708357 0.247730i
\(305\) 8.00000 13.8564i 0.458079 0.793416i
\(306\) 0.376250 6.13288i 0.0215088 0.350593i
\(307\) 21.6155 1.23366 0.616832 0.787095i \(-0.288416\pi\)
0.616832 + 0.787095i \(0.288416\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) −12.9863 11.1039i −0.735203 0.628633i
\(313\) −22.2143 + 12.8255i −1.25563 + 0.724938i −0.972222 0.234062i \(-0.924798\pi\)
−0.283407 + 0.959000i \(0.591465\pi\)
\(314\) −4.87689 3.22925i −0.275219 0.182237i
\(315\) 0 0
\(316\) 8.68466 3.68260i 0.488550 0.207163i
\(317\) −9.24621 16.0149i −0.519319 0.899487i −0.999748 0.0224532i \(-0.992852\pi\)
0.480429 0.877034i \(-0.340481\pi\)
\(318\) −2.67844 5.37462i −0.150199 0.301394i
\(319\) 5.23157 + 3.02045i 0.292912 + 0.169113i
\(320\) 13.4044 2.10770i 0.749331 0.117824i
\(321\) 5.66906i 0.316416i
\(322\) 0 0
\(323\) 4.87962i 0.271509i
\(324\) −1.20422 + 1.59682i −0.0669014 + 0.0887124i
\(325\) 11.1072 + 6.41273i 0.616115 + 0.355714i
\(326\) 14.5575 7.25473i 0.806267 0.401803i
\(327\) −4.12311 7.14143i −0.228008 0.394922i
\(328\) −4.00000 + 21.5150i −0.220863 + 1.18797i
\(329\) 0 0
\(330\) −4.00000 + 6.04090i −0.220193 + 0.332540i
\(331\) 4.72872 2.73013i 0.259914 0.150061i −0.364381 0.931250i \(-0.618720\pi\)
0.624295 + 0.781188i \(0.285386\pi\)
\(332\) −12.3987 1.52706i −0.680469 0.0838084i
\(333\) 3.56155 6.16879i 0.195172 0.338048i
\(334\) −3.17066 0.194519i −0.173491 0.0106436i
\(335\) −3.50758 −0.191639
\(336\) 0 0
\(337\) −8.24621 −0.449200 −0.224600 0.974451i \(-0.572108\pi\)
−0.224600 + 0.974451i \(0.572108\pi\)
\(338\) 33.1610 + 2.03441i 1.80372 + 0.110657i
\(339\) −6.12311 + 10.6055i −0.332561 + 0.576013i
\(340\) −14.6281 1.80164i −0.793320 0.0977075i
\(341\) 0 0
\(342\) 0.876894 1.32431i 0.0474170 0.0716103i
\(343\) 0 0
\(344\) −4.19224 + 22.5490i −0.226030 + 1.21576i
\(345\) −2.56155 4.43674i −0.137909 0.238866i
\(346\) 10.7344 5.34949i 0.577086 0.287590i
\(347\) 30.0617 + 17.3561i 1.61380 + 0.931726i 0.988479 + 0.151355i \(0.0483638\pi\)
0.625317 + 0.780371i \(0.284970\pi\)
\(348\) 2.40845 3.19365i 0.129106 0.171197i
\(349\) 4.13595i 0.221392i −0.993854 0.110696i \(-0.964692\pi\)
0.993854 0.110696i \(-0.0353080\pi\)
\(350\) 0 0
\(351\) 6.04090i 0.322439i
\(352\) 11.5316 + 12.6080i 0.614634 + 0.672011i
\(353\) −5.41240 3.12485i −0.288073 0.166319i 0.349000 0.937123i \(-0.386521\pi\)
−0.637072 + 0.770804i \(0.719855\pi\)
\(354\) −2.52313 5.06298i −0.134103 0.269095i
\(355\) 10.5616 + 18.2931i 0.560549 + 0.970899i
\(356\) 14.2462 6.04090i 0.755048 0.320167i
\(357\) 0 0
\(358\) −2.68466 1.77766i −0.141889 0.0939520i
\(359\) −0.966053 + 0.557751i −0.0509863 + 0.0294370i −0.525276 0.850932i \(-0.676038\pi\)
0.474290 + 0.880369i \(0.342705\pi\)
\(360\) 3.64624 + 3.11771i 0.192174 + 0.164318i
\(361\) 8.86932 15.3621i 0.466806 0.808532i
\(362\) 0.523133 8.52708i 0.0274953 0.448174i
\(363\) 1.87689 0.0985114
\(364\) 0 0
\(365\) −5.75379 −0.301167
\(366\) 0.816900 13.3155i 0.0427000 0.696012i
\(367\) −4.31534 + 7.47439i −0.225259 + 0.390160i −0.956397 0.292069i \(-0.905656\pi\)
0.731138 + 0.682229i \(0.238989\pi\)
\(368\) −11.6162 + 3.32154i −0.605538 + 0.173147i
\(369\) −6.70047 + 3.86852i −0.348813 + 0.201387i
\(370\) −14.2462 9.43318i −0.740625 0.490408i
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) −8.27784 16.6105i −0.428037 0.858909i
\(375\) −10.4631 6.04090i −0.540314 0.311951i
\(376\) 9.65868 + 27.3238i 0.498108 + 1.40912i
\(377\) 12.0818i 0.622244i
\(378\) 0 0
\(379\) 18.7033i 0.960725i −0.877070 0.480363i \(-0.840505\pi\)
0.877070 0.480363i \(-0.159495\pi\)
\(380\) −3.04186 2.29398i −0.156044 0.117679i
\(381\) 16.8416 + 9.72350i 0.862821 + 0.498150i
\(382\) −11.4694 + 5.71574i −0.586823 + 0.292443i
\(383\) −13.1231 22.7299i −0.670559 1.16144i −0.977746 0.209794i \(-0.932721\pi\)
0.307186 0.951649i \(-0.400613\pi\)
\(384\) 9.21922 6.55789i 0.470467 0.334656i
\(385\) 0 0
\(386\) 7.31534 11.0478i 0.372341 0.562318i
\(387\) −7.02249 + 4.05444i −0.356973 + 0.206099i
\(388\) −2.12440 + 17.2487i −0.107850 + 0.875669i
\(389\) −0.123106 + 0.213225i −0.00624170 + 0.0108109i −0.869129 0.494585i \(-0.835320\pi\)
0.862888 + 0.505396i \(0.168653\pi\)
\(390\) −14.4631 0.887307i −0.732369 0.0449306i
\(391\) 13.1231 0.663664
\(392\) 0 0
\(393\) −22.2462 −1.12217
\(394\) −0.347542 0.0213215i −0.0175089 0.00107416i
\(395\) 4.00000 6.92820i 0.201262 0.348596i
\(396\) −0.738433 + 5.99559i −0.0371077 + 0.301290i
\(397\) 14.0450 8.10887i 0.704897 0.406973i −0.104272 0.994549i \(-0.533251\pi\)
0.809169 + 0.587576i \(0.199918\pi\)
\(398\) −4.00000 + 6.04090i −0.200502 + 0.302803i
\(399\) 0 0
\(400\) −5.90388 + 6.10454i −0.295194 + 0.305227i
\(401\) 4.12311 + 7.14143i 0.205898 + 0.356626i 0.950418 0.310974i \(-0.100655\pi\)
−0.744520 + 0.667600i \(0.767322\pi\)
\(402\) −2.61753 + 1.30444i −0.130551 + 0.0650598i
\(403\) 0 0
\(404\) 11.1672 + 8.42159i 0.555587 + 0.418990i
\(405\) 1.69614i 0.0842819i
\(406\) 0 0
\(407\) 21.5150i 1.06646i
\(408\) −11.5862 + 4.09562i −0.573605 + 0.202763i
\(409\) −23.8641 13.7779i −1.18000 0.681275i −0.223988 0.974592i \(-0.571908\pi\)
−0.956015 + 0.293317i \(0.905241\pi\)
\(410\) 8.27784 + 16.6105i 0.408813 + 0.820335i
\(411\) 8.12311 + 14.0696i 0.400683 + 0.694004i
\(412\) −6.24621 14.7304i −0.307729 0.725715i
\(413\) 0 0
\(414\) −3.56155 2.35829i −0.175041 0.115904i
\(415\) −9.17507 + 5.29723i −0.450386 + 0.260031i
\(416\) −10.3062 + 32.5813i −0.505303 + 1.59743i
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) 0.293767 4.78841i 0.0143686 0.234209i
\(419\) −16.4924 −0.805708 −0.402854 0.915264i \(-0.631982\pi\)
−0.402854 + 0.915264i \(0.631982\pi\)
\(420\) 0 0
\(421\) 19.1231 0.932003 0.466002 0.884784i \(-0.345694\pi\)
0.466002 + 0.884784i \(0.345694\pi\)
\(422\) 0.344049 5.60801i 0.0167481 0.272994i
\(423\) −5.12311 + 8.87348i −0.249094 + 0.431443i
\(424\) −7.80504 + 9.12819i −0.379046 + 0.443304i
\(425\) 7.98854 4.61219i 0.387501 0.223724i
\(426\) 14.6847 + 9.72350i 0.711474 + 0.471105i
\(427\) 0 0
\(428\) −10.4384 + 4.42627i −0.504561 + 0.213952i
\(429\) −9.12311 15.8017i −0.440468 0.762912i
\(430\) 8.67566 + 17.4088i 0.418377 + 0.839527i
\(431\) 13.0789 + 7.55112i 0.629990 + 0.363725i 0.780748 0.624846i \(-0.214838\pi\)
−0.150758 + 0.988571i \(0.548172\pi\)
\(432\) 3.88046 + 0.970579i 0.186699 + 0.0466970i
\(433\) 6.78456i 0.326045i −0.986622 0.163023i \(-0.947876\pi\)
0.986622 0.163023i \(-0.0521244\pi\)
\(434\) 0 0
\(435\) 3.39228i 0.162647i
\(436\) −9.93029 + 13.1677i −0.475575 + 0.630620i
\(437\) 2.93780 + 1.69614i 0.140534 + 0.0811374i
\(438\) −4.29377 + 2.13979i −0.205164 + 0.102243i
\(439\) −15.6847 27.1666i −0.748588 1.29659i −0.948500 0.316778i \(-0.897399\pi\)
0.199912 0.979814i \(-0.435934\pi\)
\(440\) 14.2462 + 2.64861i 0.679161 + 0.126268i
\(441\) 0 0
\(442\) 20.4924 30.9481i 0.974725 1.47205i
\(443\) 31.0674 17.9368i 1.47606 0.852202i 0.476422 0.879217i \(-0.341934\pi\)
0.999635 + 0.0270153i \(0.00860028\pi\)
\(444\) −14.1394 1.74144i −0.671025 0.0826453i
\(445\) 6.56155 11.3649i 0.311047 0.538750i
\(446\) 26.6459 + 1.63471i 1.26172 + 0.0774059i
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) 28.2462 1.33302 0.666511 0.745496i \(-0.267787\pi\)
0.666511 + 0.745496i \(0.267787\pi\)
\(450\) −2.99689 0.183858i −0.141275 0.00866715i
\(451\) −11.6847 + 20.2384i −0.550209 + 0.952990i
\(452\) 24.3087 + 2.99393i 1.14339 + 0.140823i
\(453\) 7.02249 4.05444i 0.329945 0.190494i
\(454\) −12.8769 + 19.4470i −0.604343 + 0.912693i
\(455\) 0 0
\(456\) −3.12311 0.580639i −0.146253 0.0271909i
\(457\) 8.12311 + 14.0696i 0.379983 + 0.658150i 0.991059 0.133422i \(-0.0425966\pi\)
−0.611076 + 0.791572i \(0.709263\pi\)
\(458\) 22.9387 11.4315i 1.07186 0.534158i
\(459\) −3.76267 2.17238i −0.175626 0.101398i
\(460\) −6.16937 + 8.18069i −0.287648 + 0.381427i
\(461\) 17.1702i 0.799697i −0.916581 0.399848i \(-0.869063\pi\)
0.916581 0.399848i \(-0.130937\pi\)
\(462\) 0 0
\(463\) 39.4746i 1.83454i 0.398264 + 0.917271i \(0.369613\pi\)
−0.398264 + 0.917271i \(0.630387\pi\)
\(464\) −7.76092 1.94116i −0.360292 0.0901160i
\(465\) 0 0
\(466\) −6.61844 13.2807i −0.306594 0.615218i
\(467\) 8.87689 + 15.3752i 0.410774 + 0.711481i 0.994975 0.100128i \(-0.0319253\pi\)
−0.584201 + 0.811609i \(0.698592\pi\)
\(468\) −11.1231 + 4.71659i −0.514166 + 0.218024i
\(469\) 0 0
\(470\) 20.4924 + 13.5691i 0.945245 + 0.625897i
\(471\) −3.58184 + 2.06798i −0.165042 + 0.0952873i
\(472\) −7.35247 + 8.59890i −0.338425 + 0.395797i
\(473\) −12.2462 + 21.2111i −0.563081 + 0.975286i
\(474\) 0.408450 6.65775i 0.0187607 0.305800i
\(475\) 2.38447 0.109407
\(476\) 0 0
\(477\) −4.24621 −0.194421
\(478\) 0.197166 3.21381i 0.00901816 0.146996i
\(479\) −10.2462 + 17.7470i −0.468161 + 0.810879i −0.999338 0.0363819i \(-0.988417\pi\)
0.531177 + 0.847261i \(0.321750\pi\)
\(480\) 2.89374 9.14805i 0.132081 0.417550i
\(481\) 37.2650 21.5150i 1.69914 0.980998i
\(482\) −2.24621 1.48734i −0.102312 0.0677463i
\(483\) 0 0
\(484\) −1.46543 3.45593i −0.0666107 0.157088i
\(485\) 7.36932 + 12.7640i 0.334623 + 0.579585i
\(486\) 0.630783 + 1.26575i 0.0286129 + 0.0574154i
\(487\) −27.9488 16.1362i −1.26648 0.731202i −0.292159 0.956370i \(-0.594374\pi\)
−0.974320 + 0.225167i \(0.927707\pi\)
\(488\) −25.1556 + 8.89226i −1.13874 + 0.402534i
\(489\) 11.5012i 0.520100i
\(490\) 0 0
\(491\) 11.7100i 0.528463i 0.964459 + 0.264231i \(0.0851183\pi\)
−0.964459 + 0.264231i \(0.914882\pi\)
\(492\) 12.3547 + 9.31713i 0.556992 + 0.420049i
\(493\) 7.52534 + 4.34475i 0.338924 + 0.195678i
\(494\) 8.58753 4.27959i 0.386371 0.192548i
\(495\) 2.56155 + 4.43674i 0.115133 + 0.199417i
\(496\) 0 0
\(497\) 0 0
\(498\) −4.87689 + 7.36520i −0.218539 + 0.330043i
\(499\) 15.1919 8.77102i 0.680081 0.392645i −0.119805 0.992797i \(-0.538227\pi\)
0.799886 + 0.600153i \(0.204893\pi\)
\(500\) −2.95373 + 23.9824i −0.132095 + 1.07252i
\(501\) −1.12311 + 1.94528i −0.0501767 + 0.0869085i
\(502\) −31.4019 1.92649i −1.40153 0.0859835i
\(503\) −22.7386 −1.01387 −0.506933 0.861986i \(-0.669221\pi\)
−0.506933 + 0.861986i \(0.669221\pi\)
\(504\) 0 0
\(505\) 11.8617 0.527840
\(506\) −12.8778 0.790048i −0.572488 0.0351219i
\(507\) 11.7462 20.3450i 0.521668 0.903555i
\(508\) 4.75436 38.6023i 0.210941 1.71270i
\(509\) −1.46890 + 0.848071i −0.0651079 + 0.0375901i −0.532201 0.846618i \(-0.678635\pi\)
0.467093 + 0.884208i \(0.345301\pi\)
\(510\) −5.75379 + 8.68951i −0.254782 + 0.384778i
\(511\) 0 0
\(512\) −19.2732 11.8551i −0.851763 0.523927i
\(513\) −0.561553 0.972638i −0.0247932 0.0429430i
\(514\) 25.0856 12.5014i 1.10648 0.551412i
\(515\) −11.7512 6.78456i −0.517820 0.298964i
\(516\) 12.9484 + 9.76490i 0.570023 + 0.429876i
\(517\) 30.9481i 1.36110i
\(518\) 0 0
\(519\) 8.48071i 0.372262i
\(520\) 9.65868 + 27.3238i 0.423561 + 1.19823i
\(521\) 29.2765 + 16.9028i 1.28263 + 0.740524i 0.977328 0.211732i \(-0.0679105\pi\)
0.305298 + 0.952257i \(0.401244\pi\)
\(522\) −1.26157 2.53149i −0.0552173 0.110800i
\(523\) −0.246211 0.426450i −0.0107661 0.0186474i 0.860592 0.509295i \(-0.170094\pi\)
−0.871358 + 0.490647i \(0.836760\pi\)
\(524\) 17.3693 + 40.9620i 0.758782 + 1.78943i
\(525\) 0 0
\(526\) −5.80776 3.84563i −0.253231 0.167677i
\(527\) 0 0
\(528\) 11.6162 3.32154i 0.505532 0.144551i
\(529\) −6.93845 + 12.0177i −0.301672 + 0.522511i
\(530\) −0.623698 + 10.1663i −0.0270917 + 0.441596i
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −46.7386 −2.02447
\(534\) 0.670016 10.9213i 0.0289944 0.472610i
\(535\) −4.80776 + 8.32729i −0.207858 + 0.360020i
\(536\) 4.44558 + 3.80118i 0.192020 + 0.164186i
\(537\) −1.97175 + 1.13839i −0.0850873 + 0.0491251i
\(538\) 26.4924 + 17.5420i 1.14217 + 0.756291i
\(539\) 0 0
\(540\) 3.12311 1.32431i 0.134397 0.0569891i
\(541\) −5.56155 9.63289i −0.239110 0.414150i 0.721349 0.692571i \(-0.243522\pi\)
−0.960459 + 0.278421i \(0.910189\pi\)
\(542\) −2.83374 5.68627i −0.121720 0.244246i
\(543\) −5.23157 3.02045i −0.224508 0.129620i
\(544\) 16.5875 + 18.1360i 0.711185 + 0.777574i
\(545\) 13.9867i 0.599126i
\(546\) 0 0
\(547\) 33.0161i 1.41167i 0.708378 + 0.705834i \(0.249427\pi\)
−0.708378 + 0.705834i \(0.750573\pi\)
\(548\) 19.5641 25.9423i 0.835737 1.10820i
\(549\) −8.16937 4.71659i −0.348660 0.201299i
\(550\) −8.11689 + 4.04504i −0.346105 + 0.172481i
\(551\) 1.12311 + 1.94528i 0.0478459 + 0.0828715i
\(552\) −1.56155 + 8.39919i −0.0664641 + 0.357493i
\(553\) 0 0
\(554\) 2.43845 3.68260i 0.103600 0.156459i
\(555\) −10.4631 + 6.04090i −0.444135 + 0.256422i
\(556\) 23.8200 + 2.93374i 1.01019 + 0.124418i
\(557\) −7.00000 + 12.1244i −0.296600 + 0.513725i −0.975356 0.220638i \(-0.929186\pi\)
0.678756 + 0.734364i \(0.262519\pi\)
\(558\) 0 0
\(559\) −48.9848 −2.07184
\(560\) 0 0
\(561\) −13.1231 −0.554058
\(562\) 0.347542 + 0.0213215i 0.0146602 + 0.000899395i
\(563\) −7.12311 + 12.3376i −0.300203 + 0.519967i −0.976182 0.216954i \(-0.930388\pi\)
0.675979 + 0.736921i \(0.263721\pi\)
\(564\) 20.3387 + 2.50497i 0.856416 + 0.105478i
\(565\) 17.9885 10.3857i 0.756781 0.436928i
\(566\) −13.3693 + 20.1907i −0.561954 + 0.848677i
\(567\) 0 0
\(568\) 6.43845 34.6307i 0.270151 1.45307i
\(569\) −17.4924 30.2978i −0.733320 1.27015i −0.955456 0.295133i \(-0.904636\pi\)
0.222136 0.975016i \(-0.428697\pi\)
\(570\) −2.41118 + 1.20161i −0.100993 + 0.0503298i
\(571\) 35.4741 + 20.4810i 1.48454 + 0.857102i 0.999845 0.0175783i \(-0.00559565\pi\)
0.484699 + 0.874681i \(0.338929\pi\)
\(572\) −21.9725 + 29.1360i −0.918718 + 1.21824i
\(573\) 9.06134i 0.378543i
\(574\) 0 0
\(575\) 6.41273i 0.267429i
\(576\) −1.24264 7.90290i −0.0517769 0.329288i
\(577\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) −1.18391 2.37567i −0.0492443 0.0988149i
\(579\) −4.68466 8.11407i −0.194688 0.337209i
\(580\) −6.24621 + 2.64861i −0.259360 + 0.109978i
\(581\) 0 0
\(582\) 10.2462 + 6.78456i 0.424719 + 0.281229i
\(583\) −11.1072 + 6.41273i −0.460012 + 0.265588i
\(584\) 7.29248 + 6.23541i 0.301765 + 0.258023i
\(585\) −5.12311 + 8.87348i −0.211814 + 0.366873i
\(586\) −0.605616 + 9.87156i −0.0250178 + 0.407790i
\(587\) 38.2462 1.57859 0.789295 0.614014i \(-0.210446\pi\)
0.789295 + 0.614014i \(0.210446\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −0.587534 + 9.57682i −0.0241884 + 0.394271i
\(591\) −0.123106 + 0.213225i −0.00506389 + 0.00877091i
\(592\) 7.83317 + 27.3945i 0.321941 + 1.12591i
\(593\) 18.8133 10.8619i 0.772571 0.446044i −0.0612198 0.998124i \(-0.519499\pi\)
0.833791 + 0.552080i \(0.186166\pi\)
\(594\) 3.56155 + 2.35829i 0.146132 + 0.0967620i
\(595\) 0 0
\(596\) 7.80776 + 18.4130i 0.319818 + 0.754226i
\(597\) 2.56155 + 4.43674i 0.104837 + 0.181584i
\(598\) −11.5094 23.0951i −0.470655 0.944427i
\(599\) −16.6608 9.61909i −0.680740 0.393026i 0.119394 0.992847i \(-0.461905\pi\)
−0.800134 + 0.599821i \(0.795238\pi\)
\(600\) 2.00136 + 5.66173i 0.0817053 + 0.231139i
\(601\) 5.29723i 0.216078i 0.994147 + 0.108039i \(0.0344572\pi\)
−0.994147 + 0.108039i \(0.965543\pi\)
\(602\) 0 0
\(603\) 2.06798i 0.0842145i
\(604\) −12.9484 9.76490i −0.526864 0.397328i
\(605\) −2.75697 1.59174i −0.112087 0.0647134i
\(606\) 8.85183 4.41130i 0.359581 0.179197i
\(607\) −16.8078 29.1119i −0.682206 1.18162i −0.974306 0.225228i \(-0.927687\pi\)
0.292100 0.956388i \(-0.405646\pi\)
\(608\) 1.36932 + 6.20393i 0.0555331 + 0.251602i
\(609\) 0 0
\(610\) −12.4924 + 18.8664i −0.505803 + 0.763876i
\(611\) −53.6038 + 30.9481i −2.16858 + 1.25203i
\(612\) −1.06220 + 8.62434i −0.0429368 + 0.348618i
\(613\) 20.3693 35.2807i 0.822709 1.42497i −0.0809488 0.996718i \(-0.525795\pi\)
0.903658 0.428255i \(-0.140872\pi\)
\(614\) −30.5116 1.87187i −1.23135 0.0755427i
\(615\) 13.1231 0.529175
\(616\) 0 0
\(617\) 15.7538 0.634224 0.317112 0.948388i \(-0.397287\pi\)
0.317112 + 0.948388i \(0.397287\pi\)
\(618\) −11.2925 0.692789i −0.454250 0.0278680i
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 0 0
\(621\) −2.61578 + 1.51022i −0.104968 + 0.0606032i
\(622\) −6.24621 + 9.43318i −0.250450 + 0.378236i
\(623\) 0 0
\(624\) 17.3693 + 16.7984i 0.695329 + 0.672473i
\(625\) 4.93845 + 8.55364i 0.197538 + 0.342146i
\(626\) 32.4675 16.1802i 1.29766 0.646690i
\(627\) −2.93780 1.69614i −0.117325 0.0677373i
\(628\) 6.60438 + 4.98061i 0.263543 + 0.198748i
\(629\) 30.9481i 1.23398i
\(630\) 0 0
\(631\) 17.9597i 0.714963i −0.933920 0.357481i \(-0.883636\pi\)
0.933920 0.357481i \(-0.116364\pi\)
\(632\) −12.5778 + 4.44613i −0.500319 + 0.176858i
\(633\) −3.44065 1.98646i −0.136754 0.0789547i
\(634\) 11.6647 + 23.4067i 0.463265 + 0.929599i
\(635\) −16.4924 28.5657i −0.654482 1.13360i
\(636\) 3.31534 + 7.81855i 0.131462 + 0.310026i
\(637\) 0 0
\(638\) −7.12311 4.71659i −0.282006 0.186732i
\(639\) 10.7852 6.22681i 0.426654 0.246329i
\(640\) −19.1037 + 1.81434i −0.755139 + 0.0717181i
\(641\) 4.75379 8.23380i 0.187763 0.325216i −0.756741 0.653715i \(-0.773210\pi\)
0.944504 + 0.328499i \(0.106543\pi\)
\(642\) −0.490933 + 8.00222i −0.0193756 + 0.315822i
\(643\) −29.6155 −1.16792 −0.583961 0.811782i \(-0.698498\pi\)
−0.583961 + 0.811782i \(0.698498\pi\)
\(644\) 0 0
\(645\) 13.7538 0.541555
\(646\) 0.422568 6.88787i 0.0166257 0.271000i
\(647\) 16.4924 28.5657i 0.648384 1.12303i −0.335125 0.942174i \(-0.608778\pi\)
0.983509 0.180860i \(-0.0578882\pi\)
\(648\) 1.83812 2.14973i 0.0722081 0.0844492i
\(649\) −10.4631 + 6.04090i −0.410714 + 0.237126i
\(650\) −15.1231 10.0138i −0.593177 0.392774i
\(651\) 0 0
\(652\) −21.1771 + 8.97983i −0.829358 + 0.351677i
\(653\) 16.3693 + 28.3525i 0.640581 + 1.10952i 0.985303 + 0.170814i \(0.0546397\pi\)
−0.344722 + 0.938705i \(0.612027\pi\)
\(654\) 5.20157 + 10.4376i 0.203398 + 0.408143i
\(655\) 32.6775 + 18.8664i 1.27682 + 0.737170i
\(656\) 7.50940 30.0233i 0.293193 1.17221i
\(657\) 3.39228i 0.132346i
\(658\) 0 0
\(659\) 38.1045i 1.48434i −0.670210 0.742171i \(-0.733796\pi\)
0.670210 0.742171i \(-0.266204\pi\)
\(660\) 6.16937 8.18069i 0.240142 0.318433i
\(661\) 2.29377 + 1.32431i 0.0892172 + 0.0515096i 0.543945 0.839121i \(-0.316930\pi\)
−0.454728 + 0.890631i \(0.650263\pi\)
\(662\) −6.91130 + 3.44424i −0.268615 + 0.133864i
\(663\) −13.1231 22.7299i −0.509659 0.882756i
\(664\) 17.3693 + 3.22925i 0.674060 + 0.125319i
\(665\) 0 0
\(666\) −5.56155 + 8.39919i −0.215506 + 0.325462i
\(667\) 5.23157 3.02045i 0.202567 0.116952i
\(668\) 4.45873 + 0.549150i 0.172514 + 0.0212472i
\(669\) 9.43845 16.3479i 0.364911 0.632045i
\(670\) 4.95115 + 0.303751i 0.191280 + 0.0117349i
\(671\) −28.4924 −1.09994
\(672\) 0 0
\(673\) 29.8617 1.15109 0.575543 0.817772i \(-0.304791\pi\)
0.575543 + 0.817772i \(0.304791\pi\)
\(674\) 11.6400 + 0.714110i 0.448357 + 0.0275065i
\(675\) −1.06155 + 1.83866i −0.0408592 + 0.0707702i
\(676\) −46.6325 5.74338i −1.79356 0.220899i
\(677\) 28.2708 16.3221i 1.08653 0.627311i 0.153883 0.988089i \(-0.450822\pi\)
0.932652 + 0.360778i \(0.117489\pi\)
\(678\) 9.56155 14.4401i 0.367209 0.554568i
\(679\) 0 0
\(680\) 20.4924 + 3.80989i 0.785849 + 0.146103i
\(681\) 8.24621 + 14.2829i 0.315996 + 0.547320i
\(682\) 0 0
\(683\) −25.1918 14.5445i −0.963937 0.556529i −0.0665546 0.997783i \(-0.521201\pi\)
−0.897383 + 0.441253i \(0.854534\pi\)
\(684\) −1.35247 + 1.79340i −0.0517131 + 0.0685724i
\(685\) 27.5559i 1.05286i
\(686\) 0 0
\(687\) 18.1227i 0.691424i
\(688\) 7.87030 31.4662i 0.300052 1.19964i
\(689\) −22.2143 12.8255i −0.846299 0.488611i
\(690\) 3.23157 + 6.48455i 0.123024 + 0.246863i
\(691\) 6.00000 + 10.3923i 0.228251 + 0.395342i 0.957290 0.289130i \(-0.0933661\pi\)
−0.729039 + 0.684472i \(0.760033\pi\)
\(692\) −15.6155 + 6.62153i −0.593613 + 0.251713i
\(693\) 0 0
\(694\) −40.9309 27.1025i −1.55371 1.02880i
\(695\) 17.6268 10.1768i 0.668623 0.386030i
\(696\) −3.67624 + 4.29945i −0.139347 + 0.162970i
\(697\) −16.8078 + 29.1119i −0.636639 + 1.10269i
\(698\) −0.358167 + 5.83814i −0.0135568 + 0.220977i
\(699\) −10.4924 −0.396860
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) −0.523133 + 8.52708i −0.0197444 + 0.321834i
\(703\) 4.00000 6.92820i 0.150863 0.261302i
\(704\) −15.1856 18.7956i −0.572330 0.708386i
\(705\) 15.0507 8.68951i 0.566841 0.327266i
\(706\) 7.36932 + 4.87962i 0.277348 + 0.183647i
\(707\) 0 0
\(708\) 3.12311 + 7.36520i 0.117373 + 0.276801i
\(709\) −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) −13.3241 26.7365i −0.500045 1.00340i
\(711\) −4.08469 2.35829i −0.153188 0.0884430i
\(712\) −20.6325 + 7.29338i −0.773236 + 0.273331i
\(713\) 0 0
\(714\) 0 0
\(715\) 30.9481i 1.15740i
\(716\) 3.63561 + 2.74175i 0.135869 + 0.102464i
\(717\) −1.97175 1.13839i −0.0736363 0.0425139i
\(718\) 1.41194 0.703640i 0.0526932 0.0262596i
\(719\) −2.24621 3.89055i −0.0837695 0.145093i 0.821097 0.570789i \(-0.193363\pi\)
−0.904866 + 0.425696i \(0.860029\pi\)
\(720\) −4.87689 4.71659i −0.181751 0.175777i
\(721\) 0 0
\(722\) −13.8499 + 20.9165i −0.515440 + 0.778430i
\(723\) −1.64973 + 0.952473i −0.0613542 + 0.0354228i
\(724\) −1.47687 + 11.9912i −0.0548873 + 0.445649i
\(725\) 2.12311 3.67733i 0.0788502 0.136572i
\(726\) −2.64935 0.162536i −0.0983265 0.00603229i
\(727\) 32.9848 1.22334 0.611670 0.791113i \(-0.290498\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 8.12182 + 0.498270i 0.300602 + 0.0184418i
\(731\) −17.6155 + 30.5110i −0.651534 + 1.12849i
\(732\) −2.30621 + 18.7249i −0.0852398 + 0.692091i
\(733\) −14.4066 + 8.31768i −0.532121 + 0.307220i −0.741880 0.670533i \(-0.766066\pi\)
0.209759 + 0.977753i \(0.432732\pi\)
\(734\) 6.73863 10.1768i 0.248728 0.375634i
\(735\) 0 0
\(736\) 16.6847 3.68260i 0.615005 0.135742i
\(737\) 3.12311 + 5.40938i 0.115041 + 0.199257i
\(738\) 9.79312 4.88039i 0.360490 0.179650i
\(739\) −5.09038 2.93893i −0.187253 0.108110i 0.403443 0.915005i \(-0.367813\pi\)
−0.590696 + 0.806894i \(0.701147\pi\)
\(740\) 19.2925 + 14.5492i 0.709206 + 0.534839i
\(741\) 6.78456i 0.249237i
\(742\) 0 0
\(743\) 13.6149i 0.499482i −0.968313 0.249741i \(-0.919654\pi\)
0.968313 0.249741i \(-0.0803455\pi\)
\(744\) 0 0
\(745\) 14.6890 + 8.48071i 0.538164 + 0.310709i
\(746\) −6.30783 12.6575i −0.230946 0.463422i
\(747\) 3.12311 + 5.40938i 0.114268 + 0.197919i
\(748\) 10.2462 + 24.1636i 0.374639 + 0.883508i
\(749\) 0 0
\(750\) 14.2462 + 9.43318i 0.520198 + 0.344451i
\(751\) 26.6607 15.3926i 0.972863 0.561682i 0.0727548 0.997350i \(-0.476821\pi\)
0.900108 + 0.435667i \(0.143488\pi\)
\(752\) −11.2676 39.4056i −0.410887 1.43697i
\(753\) −11.1231 + 19.2658i −0.405349 + 0.702084i
\(754\) 1.04627 17.0542i 0.0381028 0.621076i
\(755\) −13.7538 −0.500552
\(756\) 0 0
\(757\) 30.9848 1.12616 0.563082 0.826401i \(-0.309616\pi\)
0.563082 + 0.826401i \(0.309616\pi\)
\(758\) −1.61968 + 26.4009i −0.0588295 + 0.958922i
\(759\) −4.56155 + 7.90084i −0.165574 + 0.286782i
\(760\) 4.09511 + 3.50151i 0.148545 + 0.127013i
\(761\) 29.2765 16.9028i 1.06127 0.612725i 0.135488 0.990779i \(-0.456740\pi\)
0.925784 + 0.378054i \(0.123407\pi\)
\(762\) −22.9309 15.1838i −0.830698 0.550049i
\(763\) 0 0
\(764\) 16.6847 7.07488i 0.603630 0.255960i
\(765\) 3.68466 + 6.38202i 0.133219 + 0.230742i
\(766\) 16.5557 + 33.2210i 0.598181 + 1.20032i
\(767\) −20.9263 12.0818i −0.755604 0.436248i
\(768\) −13.5814 + 8.45848i −0.490076 + 0.305219i
\(769\) 44.5173i 1.60533i −0.596427 0.802667i \(-0.703414\pi\)
0.596427 0.802667i \(-0.296586\pi\)
\(770\) 0 0
\(771\) 19.8188i 0.713758i
\(772\) −11.2828 + 14.9611i −0.406076 + 0.538463i
\(773\) −1.46890 0.848071i −0.0528327 0.0305030i 0.473351 0.880874i \(-0.343044\pi\)
−0.526184 + 0.850371i \(0.676378\pi\)
\(774\) 10.2638 5.11494i 0.368924 0.183853i
\(775\) 0 0
\(776\) 4.49242 24.1636i 0.161269 0.867422i
\(777\) 0 0
\(778\) 0.192236 0.290319i 0.00689199 0.0104085i
\(779\) −7.52534 + 4.34475i −0.269623 + 0.155667i
\(780\) 20.3387 + 2.50497i 0.728244 + 0.0896925i
\(781\) 18.8078 32.5760i 0.672995 1.16566i
\(782\) −18.5240 1.13644i −0.662419 0.0406391i
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) 7.01515 0.250382
\(786\) 31.4019 + 1.92649i 1.12007 + 0.0687156i
\(787\) 10.4924 18.1734i 0.374014 0.647812i −0.616165 0.787617i \(-0.711314\pi\)
0.990179 + 0.139805i \(0.0446477\pi\)
\(788\) 0.488730 + 0.0601933i 0.0174103 + 0.00214430i
\(789\) −4.26552 + 2.46270i −0.151856 + 0.0876743i
\(790\) −6.24621 + 9.43318i −0.222230 + 0.335617i
\(791\) 0 0
\(792\) 1.56155 8.39919i 0.0554874 0.298452i
\(793\) −28.4924 49.3503i −1.01180 1.75248i
\(794\) −20.5275 + 10.2299i −0.728495 + 0.363045i
\(795\) 6.23726 + 3.60109i 0.221213 + 0.127717i
\(796\) 6.16937 8.18069i 0.218668 0.289957i
\(797\) 34.1316i 1.20900i 0.796604 + 0.604502i \(0.206628\pi\)
−0.796604 + 0.604502i \(0.793372\pi\)
\(798\) 0 0
\(799\) 44.5173i 1.57491i
\(800\) 8.86233 8.10566i 0.313331 0.286578i
\(801\) −6.70047 3.86852i −0.236749 0.136687i
\(802\) −5.20157 10.4376i −0.183674 0.368565i
\(803\) 5.12311 + 8.87348i 0.180790 + 0.313138i
\(804\) 3.80776 1.61463i 0.134289 0.0569435i
\(805\) 0 0
\(806\) 0 0
\(807\) 19.4574 11.2337i 0.684932 0.395446i
\(808\) −15.0338 12.8546i −0.528888 0.452225i
\(809\) 5.24621 9.08670i 0.184447 0.319472i −0.758943 0.651157i \(-0.774284\pi\)
0.943390 + 0.331685i \(0.107617\pi\)
\(810\) 0.146883 2.39420i 0.00516096 0.0841238i
\(811\) 32.4924 1.14096 0.570482 0.821310i \(-0.306757\pi\)
0.570482 + 0.821310i \(0.306757\pi\)
\(812\) 0 0
\(813\) −4.49242 −0.157556
\(814\) −1.86317 + 30.3697i −0.0653039 + 1.06446i
\(815\) −9.75379 + 16.8941i −0.341660 + 0.591773i
\(816\) 16.7093 4.77786i 0.584944 0.167259i
\(817\) −7.88700 + 4.55356i −0.275931 + 0.159309i
\(818\) 32.4924 + 21.5150i 1.13607 + 0.752253i
\(819\) 0 0
\(820\) −10.2462 24.1636i −0.357813 0.843829i
\(821\) −12.6155 21.8507i −0.440285 0.762596i 0.557425 0.830227i \(-0.311789\pi\)
−0.997710 + 0.0676311i \(0.978456\pi\)
\(822\) −10.2478 20.5636i −0.357434 0.717237i
\(823\) 39.0559 + 22.5490i 1.36140 + 0.786007i 0.989811 0.142388i \(-0.0454782\pi\)
0.371594 + 0.928396i \(0.378811\pi\)
\(824\) 7.54127 + 21.3338i 0.262713 + 0.743197i
\(825\) 6.41273i 0.223263i
\(826\) 0 0
\(827\) 30.9939i 1.07776i 0.842381 + 0.538882i \(0.181153\pi\)
−0.842381 + 0.538882i \(0.818847\pi\)
\(828\) 4.82312 + 3.63730i 0.167615 + 0.126405i
\(829\) −27.4459 15.8459i −0.953236 0.550351i −0.0591514 0.998249i \(-0.518839\pi\)
−0.894085 + 0.447898i \(0.852173\pi\)
\(830\) 13.4099 6.68280i 0.465464 0.231964i
\(831\) −1.56155 2.70469i −0.0541697 0.0938246i
\(832\) 17.3693 45.0979i 0.602173 1.56349i
\(833\) 0 0
\(834\) 9.36932 14.1498i 0.324433 0.489966i
\(835\) 3.29946 1.90495i 0.114183 0.0659234i
\(836\) −0.829339 + 6.73368i −0.0286833 + 0.232889i
\(837\) 0 0
\(838\) 23.2800 + 1.42822i 0.804196 + 0.0493371i
\(839\) −6.73863 −0.232643 −0.116322 0.993212i \(-0.537110\pi\)
−0.116322 + 0.993212i \(0.537110\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −26.9934 1.65603i −0.930254 0.0570707i
\(843\) 0.123106 0.213225i 0.00423998 0.00734387i
\(844\) −0.971292 + 7.88625i −0.0334333 + 0.271456i
\(845\) −34.5080 + 19.9232i −1.18711 + 0.685380i
\(846\) 8.00000 12.0818i 0.275046 0.415381i
\(847\) 0 0
\(848\) 11.8078 12.2091i 0.405480 0.419262i
\(849\) 8.56155 + 14.8290i 0.293832 + 0.508931i
\(850\) −11.6757 + 5.81858i −0.400474 + 0.199576i
\(851\) −18.6325 10.7575i −0.638714 0.368762i
\(852\) −19.8862 14.9970i −0.681291 0.513788i
\(853\) 37.4067i 1.28078i −0.768050 0.640390i \(-0.778773\pi\)
0.768050 0.640390i \(-0.221227\pi\)
\(854\) 0 0
\(855\) 1.90495i 0.0651478i
\(856\) 15.1178 5.34399i 0.516716 0.182654i
\(857\) −17.5253 10.1182i −0.598652 0.345632i 0.169859 0.985468i \(-0.445669\pi\)
−0.768511 + 0.639837i \(0.779002\pi\)
\(858\) 11.5094 + 23.0951i 0.392925 + 0.788453i
\(859\) 15.9309 + 27.5931i 0.543554 + 0.941464i 0.998696 + 0.0510448i \(0.0162551\pi\)
−0.455142 + 0.890419i \(0.650412\pi\)
\(860\) −10.7386 25.3249i −0.366184 0.863571i
\(861\) 0 0
\(862\) −17.8078 11.7915i −0.606535 0.401619i
\(863\) −18.9545 + 10.9434i −0.645220 + 0.372518i −0.786622 0.617434i \(-0.788172\pi\)
0.141403 + 0.989952i \(0.454839\pi\)
\(864\) −5.39345 1.70607i −0.183489 0.0580418i
\(865\) −7.19224 + 12.4573i −0.244543 + 0.423562i
\(866\) −0.587534 + 9.57682i −0.0199652 + 0.325433i
\(867\) −1.87689 −0.0637427
\(868\) 0 0
\(869\) −14.2462 −0.483270
\(870\) −0.293767 + 4.78841i −0.00995963 + 0.162342i
\(871\) −6.24621 + 10.8188i −0.211645 + 0.366580i
\(872\) 15.1575 17.7271i 0.513298 0.600315i
\(873\) 7.52534 4.34475i 0.254694 0.147048i
\(874\) −4.00000 2.64861i −0.135302 0.0895907i
\(875\) 0 0
\(876\) 6.24621 2.64861i 0.211040 0.0894884i
\(877\) −9.87689 17.1073i −0.333519 0.577672i 0.649680 0.760208i \(-0.274903\pi\)
−0.983199 + 0.182536i \(0.941569\pi\)
\(878\) 19.7872 + 39.7056i 0.667787 + 1.34000i
\(879\) 6.05643 + 3.49668i 0.204278 + 0.117940i
\(880\) −19.8800 4.97238i −0.670155 0.167619i
\(881\) 39.1028i 1.31741i −0.752403 0.658703i \(-0.771105\pi\)
0.752403 0.658703i \(-0.228895\pi\)
\(882\) 0 0
\(883\) 26.9752i 0.907789i −0.891056 0.453894i \(-0.850034\pi\)
0.891056 0.453894i \(-0.149966\pi\)
\(884\) −31.6063 + 41.9105i −1.06304 + 1.40960i
\(885\) 5.87560 + 3.39228i 0.197506 + 0.114030i
\(886\) −45.4068 + 22.6284i −1.52547 + 0.760217i
\(887\) 11.3693 + 19.6922i 0.381744 + 0.661201i 0.991312 0.131534i \(-0.0419902\pi\)
−0.609567 + 0.792734i \(0.708657\pi\)
\(888\) 19.8078 + 3.68260i 0.664705 + 0.123580i
\(889\) 0 0
\(890\) −10.2462 + 15.4741i −0.343454 + 0.518692i
\(891\) 2.61578 1.51022i 0.0876321 0.0505944i
\(892\) −37.4707 4.61499i −1.25461 0.154521i
\(893\) −5.75379 + 9.96585i −0.192543 + 0.333495i
\(894\) 14.1156 + 0.865986i 0.472096 + 0.0289629i
\(895\) 3.86174 0.129084
\(896\) 0 0
\(897\) −18.2462 −0.609223
\(898\) −39.8712 2.44608i −1.33052 0.0816268i
\(899\) 0 0
\(900\) 4.21437 + 0.519053i 0.140479 + 0.0173018i
\(901\) −15.9771 + 9.22437i −0.532274 + 0.307308i
\(902\) 18.2462 27.5559i 0.607532 0.917510i
\(903\) 0 0
\(904\) −34.0540 6.33122i −1.13262 0.210573i
\(905\) 5.12311 + 8.87348i 0.170298 + 0.294964i
\(906\) −10.2638 + 5.11494i −0.340991 + 0.169933i
\(907\) 10.3220 + 5.95938i 0.342735 + 0.197878i 0.661481 0.749962i \(-0.269928\pi\)
−0.318746 + 0.947840i \(0.603262\pi\)
\(908\) 19.8606 26.3355i 0.659097 0.873973i
\(909\) 6.99337i 0.231955i
\(910\) 0 0
\(911\) 6.41273i 0.212463i −0.994341 0.106232i \(-0.966122\pi\)
0.994341 0.106232i \(-0.0338785\pi\)
\(912\) 4.35817 + 1.09006i 0.144313 + 0.0360956i
\(913\) 16.3387 + 9.43318i 0.540733 + 0.312193i
\(914\) −10.2478 20.5636i −0.338968 0.680183i
\(915\) 8.00000 + 13.8564i 0.264472 + 0.458079i
\(916\) −33.3693 + 14.1498i −1.10255 + 0.467521i
\(917\) 0 0
\(918\) 5.12311 + 3.39228i 0.169088 + 0.111962i
\(919\) 7.02249 4.05444i 0.231651 0.133743i −0.379683 0.925117i \(-0.623967\pi\)
0.611333 + 0.791373i \(0.290634\pi\)
\(920\) 9.41687 11.0133i 0.310465 0.363097i
\(921\) −10.8078 + 18.7196i −0.356128 + 0.616832i
\(922\) −1.48692 + 24.2368i −0.0489690 + 0.798196i
\(923\) 75.2311 2.47626
\(924\) 0 0
\(925\) −15.1231 −0.497245
\(926\) 3.41845 55.7208i 0.112337 1.83110i
\(927\) −4.00000 + 6.92820i −0.131377 + 0.227552i
\(928\) 10.7869 + 3.41214i 0.354097 + 0.112009i
\(929\) −43.9655 + 25.3835i −1.44246 + 0.832805i −0.998014 0.0629997i \(-0.979933\pi\)
−0.444447 + 0.895805i \(0.646600\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 8.19224 + 19.3197i 0.268346 + 0.632838i
\(933\) 4.00000 + 6.92820i 0.130954 + 0.226819i
\(934\) −11.1988 22.4718i −0.366436 0.735299i
\(935\) 19.2765 + 11.1293i 0.630410 + 0.363968i
\(936\) 16.1094 5.69450i 0.526551 0.186131i
\(937\) 56.5991i 1.84901i 0.381169 + 0.924505i \(0.375522\pi\)
−0.381169 + 0.924505i \(0.624478\pi\)
\(938\) 0 0
\(939\) 25.6509i 0.837086i
\(940\) −27.7512 20.9282i −0.905145 0.682604i
\(941\) 11.5704 + 6.68016i 0.377184 + 0.217767i 0.676592 0.736358i \(-0.263456\pi\)
−0.299409 + 0.954125i \(0.596789\pi\)
\(942\) 5.23506 2.60889i 0.170568 0.0850022i
\(943\) 11.6847 + 20.2384i 0.380505 + 0.659054i
\(944\) 11.1231 11.5012i 0.362026 0.374331i
\(945\) 0 0
\(946\) 19.1231 28.8802i 0.621746 0.938975i
\(947\) 36.5813 21.1202i 1.18873 0.686316i 0.230715 0.973021i \(-0.425893\pi\)
0.958019 + 0.286705i \(0.0925601\pi\)
\(948\) −1.15310 + 9.36244i −0.0374510 + 0.304078i
\(949\) −10.2462 + 17.7470i −0.332606 + 0.576091i
\(950\) −3.36582 0.206492i −0.109202 0.00669948i
\(951\) 18.4924 0.599658
\(952\) 0 0
\(953\) 61.2311 1.98347 0.991734 0.128309i \(-0.0409549\pi\)
0.991734 + 0.128309i \(0.0409549\pi\)
\(954\) 5.99378 + 0.367716i 0.194056 + 0.0119052i
\(955\) 7.68466 13.3102i 0.248670 0.430709i
\(956\) −0.556623 + 4.51941i −0.0180025 + 0.146168i
\(957\) −5.23157 + 3.02045i −0.169113 + 0.0976372i
\(958\) 16.0000 24.1636i 0.516937 0.780690i
\(959\) 0 0
\(960\) −4.87689 + 12.6624i −0.157401 + 0.408678i
\(961\) 15.5000 + 26.8468i 0.500000 + 0.866025i
\(962\) −54.4650 + 27.1426i −1.75602 + 0.875111i
\(963\) 4.90955 + 2.83453i 0.158208 + 0.0913415i
\(964\) 3.04186 + 2.29398i 0.0979717 + 0.0738842i
\(965\) 15.8917i 0.511571i
\(966\) 0 0
\(967\) 40.9620i 1.31725i 0.752472 + 0.658624i \(0.228861\pi\)
−0.752472 + 0.658624i \(0.771139\pi\)
\(968\) 1.76927 + 5.00515i 0.0568665 + 0.160872i
\(969\) −4.22587 2.43981i −0.135755 0.0783780i
\(970\) −9.29688 18.6554i −0.298505 0.598988i
\(971\) −6.00000 10.3923i −0.192549 0.333505i 0.753545 0.657396i \(-0.228342\pi\)
−0.946094 + 0.323891i \(0.895009\pi\)
\(972\) −0.780776 1.84130i −0.0250434 0.0590597i
\(973\) 0 0
\(974\) 38.0540 + 25.1976i 1.21933 + 0.807382i
\(975\) −11.1072 + 6.41273i −0.355714 + 0.205372i
\(976\) 36.2787 10.3735i 1.16125 0.332048i
\(977\) 30.3693 52.6012i 0.971601 1.68286i 0.280875 0.959744i \(-0.409375\pi\)
0.690725 0.723117i \(-0.257291\pi\)
\(978\) −0.995984 + 16.2346i −0.0318480 + 0.519124i
\(979\) −23.3693 −0.746887
\(980\) 0 0
\(981\) 8.24621 0.263281
\(982\) 1.01407 16.5293i 0.0323601 0.527471i
\(983\) 27.3693 47.4050i 0.872946 1.51199i 0.0140105 0.999902i \(-0.495540\pi\)
0.858935 0.512084i \(-0.171126\pi\)
\(984\) −16.6325 14.2216i −0.530225 0.453368i
\(985\) 0.361660 0.208805i 0.0115234 0.00665306i
\(986\) −10.2462 6.78456i −0.326306 0.216065i
\(987\) 0 0
\(988\) −12.4924 + 5.29723i −0.397437 + 0.168527i
\(989\) 12.2462 + 21.2111i 0.389407 + 0.674472i
\(990\) −3.23157 6.48455i −0.102706 0.206093i
\(991\) 9.31626 + 5.37874i 0.295941 + 0.170861i 0.640618 0.767860i \(-0.278678\pi\)
−0.344677 + 0.938721i \(0.612012\pi\)
\(992\) 0 0
\(993\) 5.46026i 0.173276i
\(994\) 0 0
\(995\) 8.68951i 0.275476i
\(996\) 7.52184 9.97409i 0.238339 0.316041i
\(997\) −33.6832 19.4470i −1.06676 0.615892i −0.139463 0.990227i \(-0.544538\pi\)
−0.927294 + 0.374335i \(0.877871\pi\)
\(998\) −22.2038 + 11.0652i −0.702848 + 0.350264i
\(999\) 3.56155 + 6.16879i 0.112683 + 0.195172i
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 588.2.o.a.31.1 8
4.3 odd 2 588.2.o.c.31.3 8
7.2 even 3 inner 588.2.o.a.19.3 8
7.3 odd 6 84.2.b.a.55.3 4
7.4 even 3 84.2.b.b.55.3 yes 4
7.5 odd 6 588.2.o.c.19.3 8
7.6 odd 2 588.2.o.c.31.1 8
21.11 odd 6 252.2.b.d.55.2 4
21.17 even 6 252.2.b.e.55.2 4
28.3 even 6 84.2.b.b.55.4 yes 4
28.11 odd 6 84.2.b.a.55.4 yes 4
28.19 even 6 inner 588.2.o.a.19.1 8
28.23 odd 6 588.2.o.c.19.1 8
28.27 even 2 inner 588.2.o.a.31.3 8
56.3 even 6 1344.2.b.e.895.3 4
56.11 odd 6 1344.2.b.f.895.2 4
56.45 odd 6 1344.2.b.f.895.3 4
56.53 even 6 1344.2.b.e.895.2 4
84.11 even 6 252.2.b.e.55.1 4
84.59 odd 6 252.2.b.d.55.1 4
168.11 even 6 4032.2.b.n.3583.3 4
168.53 odd 6 4032.2.b.j.3583.3 4
168.59 odd 6 4032.2.b.j.3583.2 4
168.101 even 6 4032.2.b.n.3583.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.b.a.55.3 4 7.3 odd 6
84.2.b.a.55.4 yes 4 28.11 odd 6
84.2.b.b.55.3 yes 4 7.4 even 3
84.2.b.b.55.4 yes 4 28.3 even 6
252.2.b.d.55.1 4 84.59 odd 6
252.2.b.d.55.2 4 21.11 odd 6
252.2.b.e.55.1 4 84.11 even 6
252.2.b.e.55.2 4 21.17 even 6
588.2.o.a.19.1 8 28.19 even 6 inner
588.2.o.a.19.3 8 7.2 even 3 inner
588.2.o.a.31.1 8 1.1 even 1 trivial
588.2.o.a.31.3 8 28.27 even 2 inner
588.2.o.c.19.1 8 28.23 odd 6
588.2.o.c.19.3 8 7.5 odd 6
588.2.o.c.31.1 8 7.6 odd 2
588.2.o.c.31.3 8 4.3 odd 2
1344.2.b.e.895.2 4 56.53 even 6
1344.2.b.e.895.3 4 56.3 even 6
1344.2.b.f.895.2 4 56.11 odd 6
1344.2.b.f.895.3 4 56.45 odd 6
4032.2.b.j.3583.2 4 168.59 odd 6
4032.2.b.j.3583.3 4 168.53 odd 6
4032.2.b.n.3583.2 4 168.101 even 6
4032.2.b.n.3583.3 4 168.11 even 6