Properties

Label 666.2.x.g.181.2
Level $666$
Weight $2$
Character 666.181
Analytic conductor $5.318$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [666,2,Mod(127,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.x (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 74)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 181.2
Root \(2.14169 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 666.181
Dual form 666.2.x.g.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{5} +(0.773586 - 0.649116i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\) \(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{5} +(0.773586 - 0.649116i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.173648 - 0.300767i) q^{10} +(-2.73237 + 4.73261i) q^{11} +(-5.97892 - 2.17615i) q^{13} +(0.504922 + 0.874551i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.490749 - 0.178618i) q^{17} +(0.869950 + 4.93373i) q^{19} +(0.326352 - 0.118782i) q^{20} +(-4.18624 - 3.51267i) q^{22} +(0.721492 + 1.24966i) q^{23} +(-0.847296 + 4.80526i) q^{25} +(3.18132 - 5.51020i) q^{26} +(-0.948944 + 0.345387i) q^{28} +(-3.16714 + 5.48565i) q^{29} +3.30777 q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.0906868 + 0.514310i) q^{34} +(-0.0609011 + 0.345387i) q^{35} +(-5.88521 - 1.53765i) q^{37} -5.00984 q^{38} +(0.0603074 + 0.342020i) q^{40} +(-1.03412 - 0.376390i) q^{41} -6.27037 q^{43} +(4.18624 - 3.51267i) q^{44} +(-1.35596 + 0.493529i) q^{46} +(-5.71910 - 9.90577i) q^{47} +(-1.03845 + 5.88936i) q^{49} +(-4.58512 - 1.66885i) q^{50} +(4.87406 + 4.08982i) q^{52} +(-0.0706817 - 0.0593090i) q^{53} +(-0.329565 - 1.86905i) q^{55} +(-0.175358 - 0.994503i) q^{56} +(-4.85235 - 4.07160i) q^{58} +(-2.29059 - 1.92203i) q^{59} +(-3.58571 - 1.30509i) q^{61} +(-0.574388 + 3.25751i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(2.07646 - 0.755769i) q^{65} +(-0.892251 + 0.748687i) q^{67} -0.522244 q^{68} +(-0.329565 - 0.119952i) q^{70} +(-0.0543332 - 0.308139i) q^{71} +13.2325 q^{73} +(2.53624 - 5.52879i) q^{74} +(0.869950 - 4.93373i) q^{76} +(0.958285 + 5.43471i) q^{77} +(7.12939 - 5.98227i) q^{79} -0.347296 q^{80} +(0.550245 - 0.953052i) q^{82} +(8.89395 - 3.23713i) q^{83} +(-0.0906868 + 0.157074i) q^{85} +(1.08884 - 6.17511i) q^{86} +(2.73237 + 4.73261i) q^{88} +(12.0788 + 10.1354i) q^{89} +(-6.03778 + 2.19757i) q^{91} +(-0.250571 - 1.42106i) q^{92} +(10.7484 - 3.91209i) q^{94} +(-1.33284 - 1.11839i) q^{95} +(0.464564 + 0.804648i) q^{97} +(-5.61956 - 2.04535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 + 0.984808i −0.122788 + 0.696364i
\(3\) 0 0
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) −0.266044 + 0.223238i −0.118979 + 0.0998350i −0.700336 0.713814i \(-0.746966\pi\)
0.581357 + 0.813649i \(0.302522\pi\)
\(6\) 0 0
\(7\) 0.773586 0.649116i 0.292388 0.245343i −0.484780 0.874636i \(-0.661100\pi\)
0.777168 + 0.629294i \(0.216656\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) 0 0
\(10\) −0.173648 0.300767i −0.0549124 0.0951110i
\(11\) −2.73237 + 4.73261i −0.823842 + 1.42694i 0.0789595 + 0.996878i \(0.474840\pi\)
−0.902801 + 0.430058i \(0.858493\pi\)
\(12\) 0 0
\(13\) −5.97892 2.17615i −1.65825 0.603555i −0.668167 0.744011i \(-0.732921\pi\)
−0.990087 + 0.140456i \(0.955143\pi\)
\(14\) 0.504922 + 0.874551i 0.134946 + 0.233734i
\(15\) 0 0
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 0.490749 0.178618i 0.119024 0.0433212i −0.281821 0.959467i \(-0.590939\pi\)
0.400846 + 0.916146i \(0.368716\pi\)
\(18\) 0 0
\(19\) 0.869950 + 4.93373i 0.199580 + 1.13188i 0.905743 + 0.423827i \(0.139313\pi\)
−0.706163 + 0.708049i \(0.749575\pi\)
\(20\) 0.326352 0.118782i 0.0729745 0.0265605i
\(21\) 0 0
\(22\) −4.18624 3.51267i −0.892509 0.748904i
\(23\) 0.721492 + 1.24966i 0.150441 + 0.260572i 0.931390 0.364023i \(-0.118597\pi\)
−0.780948 + 0.624596i \(0.785264\pi\)
\(24\) 0 0
\(25\) −0.847296 + 4.80526i −0.169459 + 0.961051i
\(26\) 3.18132 5.51020i 0.623908 1.08064i
\(27\) 0 0
\(28\) −0.948944 + 0.345387i −0.179333 + 0.0652720i
\(29\) −3.16714 + 5.48565i −0.588124 + 1.01866i 0.406354 + 0.913716i \(0.366800\pi\)
−0.994478 + 0.104945i \(0.966533\pi\)
\(30\) 0 0
\(31\) 3.30777 0.594092 0.297046 0.954863i \(-0.403998\pi\)
0.297046 + 0.954863i \(0.403998\pi\)
\(32\) −0.766044 + 0.642788i −0.135419 + 0.113630i
\(33\) 0 0
\(34\) 0.0906868 + 0.514310i 0.0155527 + 0.0882035i
\(35\) −0.0609011 + 0.345387i −0.0102942 + 0.0583811i
\(36\) 0 0
\(37\) −5.88521 1.53765i −0.967522 0.252787i
\(38\) −5.00984 −0.812704
\(39\) 0 0
\(40\) 0.0603074 + 0.342020i 0.00953543 + 0.0540781i
\(41\) −1.03412 0.376390i −0.161503 0.0587822i 0.260004 0.965608i \(-0.416276\pi\)
−0.421506 + 0.906825i \(0.638498\pi\)
\(42\) 0 0
\(43\) −6.27037 −0.956222 −0.478111 0.878299i \(-0.658678\pi\)
−0.478111 + 0.878299i \(0.658678\pi\)
\(44\) 4.18624 3.51267i 0.631099 0.529555i
\(45\) 0 0
\(46\) −1.35596 + 0.493529i −0.199926 + 0.0727670i
\(47\) −5.71910 9.90577i −0.834216 1.44491i −0.894667 0.446734i \(-0.852587\pi\)
0.0604506 0.998171i \(-0.480746\pi\)
\(48\) 0 0
\(49\) −1.03845 + 5.88936i −0.148350 + 0.841337i
\(50\) −4.58512 1.66885i −0.648434 0.236011i
\(51\) 0 0
\(52\) 4.87406 + 4.08982i 0.675911 + 0.567156i
\(53\) −0.0706817 0.0593090i −0.00970887 0.00814671i 0.637920 0.770102i \(-0.279795\pi\)
−0.647629 + 0.761956i \(0.724239\pi\)
\(54\) 0 0
\(55\) −0.329565 1.86905i −0.0444385 0.252023i
\(56\) −0.175358 0.994503i −0.0234332 0.132896i
\(57\) 0 0
\(58\) −4.85235 4.07160i −0.637144 0.534628i
\(59\) −2.29059 1.92203i −0.298210 0.250228i 0.481389 0.876507i \(-0.340132\pi\)
−0.779599 + 0.626279i \(0.784577\pi\)
\(60\) 0 0
\(61\) −3.58571 1.30509i −0.459103 0.167100i 0.102107 0.994773i \(-0.467442\pi\)
−0.561210 + 0.827674i \(0.689664\pi\)
\(62\) −0.574388 + 3.25751i −0.0729473 + 0.413705i
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 2.07646 0.755769i 0.257553 0.0937416i
\(66\) 0 0
\(67\) −0.892251 + 0.748687i −0.109006 + 0.0914667i −0.695662 0.718370i \(-0.744889\pi\)
0.586656 + 0.809836i \(0.300444\pi\)
\(68\) −0.522244 −0.0633314
\(69\) 0 0
\(70\) −0.329565 0.119952i −0.0393905 0.0143370i
\(71\) −0.0543332 0.308139i −0.00644816 0.0365693i 0.981414 0.191903i \(-0.0614659\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(72\) 0 0
\(73\) 13.2325 1.54875 0.774376 0.632726i \(-0.218064\pi\)
0.774376 + 0.632726i \(0.218064\pi\)
\(74\) 2.53624 5.52879i 0.294832 0.642708i
\(75\) 0 0
\(76\) 0.869950 4.93373i 0.0997902 0.565938i
\(77\) 0.958285 + 5.43471i 0.109207 + 0.619342i
\(78\) 0 0
\(79\) 7.12939 5.98227i 0.802119 0.673058i −0.146594 0.989197i \(-0.546831\pi\)
0.948713 + 0.316139i \(0.102387\pi\)
\(80\) −0.347296 −0.0388289
\(81\) 0 0
\(82\) 0.550245 0.953052i 0.0607644 0.105247i
\(83\) 8.89395 3.23713i 0.976238 0.355322i 0.195862 0.980632i \(-0.437250\pi\)
0.780377 + 0.625310i \(0.215027\pi\)
\(84\) 0 0
\(85\) −0.0906868 + 0.157074i −0.00983636 + 0.0170371i
\(86\) 1.08884 6.17511i 0.117412 0.665879i
\(87\) 0 0
\(88\) 2.73237 + 4.73261i 0.291272 + 0.504498i
\(89\) 12.0788 + 10.1354i 1.28035 + 1.07435i 0.993195 + 0.116463i \(0.0371555\pi\)
0.287160 + 0.957883i \(0.407289\pi\)
\(90\) 0 0
\(91\) −6.03778 + 2.19757i −0.632931 + 0.230368i
\(92\) −0.250571 1.42106i −0.0261239 0.148156i
\(93\) 0 0
\(94\) 10.7484 3.91209i 1.10861 0.403502i
\(95\) −1.33284 1.11839i −0.136747 0.114744i
\(96\) 0 0
\(97\) 0.464564 + 0.804648i 0.0471693 + 0.0816997i 0.888646 0.458594i \(-0.151647\pi\)
−0.841477 + 0.540293i \(0.818313\pi\)
\(98\) −5.61956 2.04535i −0.567662 0.206612i
\(99\) 0 0
\(100\) 2.43969 4.22567i 0.243969 0.422567i
\(101\) 4.28093 + 7.41479i 0.425969 + 0.737799i 0.996510 0.0834694i \(-0.0266001\pi\)
−0.570542 + 0.821269i \(0.693267\pi\)
\(102\) 0 0
\(103\) −2.47956 + 4.29473i −0.244319 + 0.423172i −0.961940 0.273261i \(-0.911898\pi\)
0.717621 + 0.696434i \(0.245231\pi\)
\(104\) −4.87406 + 4.08982i −0.477941 + 0.401040i
\(105\) 0 0
\(106\) 0.0706817 0.0593090i 0.00686521 0.00576059i
\(107\) −3.35307 1.22042i −0.324153 0.117982i 0.174818 0.984601i \(-0.444066\pi\)
−0.498971 + 0.866619i \(0.666289\pi\)
\(108\) 0 0
\(109\) −0.169947 + 0.963819i −0.0162780 + 0.0923171i −0.991864 0.127299i \(-0.959369\pi\)
0.975586 + 0.219616i \(0.0704804\pi\)
\(110\) 1.89789 0.180956
\(111\) 0 0
\(112\) 1.00984 0.0954213
\(113\) −1.60399 + 9.09669i −0.150891 + 0.855745i 0.811556 + 0.584275i \(0.198621\pi\)
−0.962447 + 0.271470i \(0.912490\pi\)
\(114\) 0 0
\(115\) −0.470920 0.171401i −0.0439136 0.0159832i
\(116\) 4.85235 4.07160i 0.450529 0.378039i
\(117\) 0 0
\(118\) 2.29059 1.92203i 0.210866 0.176938i
\(119\) 0.263693 0.456729i 0.0241727 0.0418683i
\(120\) 0 0
\(121\) −9.43174 16.3362i −0.857430 1.48511i
\(122\) 1.90792 3.30461i 0.172735 0.299185i
\(123\) 0 0
\(124\) −3.10828 1.13132i −0.279132 0.101596i
\(125\) −1.71554 2.97140i −0.153442 0.265770i
\(126\) 0 0
\(127\) 5.18728 + 4.35264i 0.460296 + 0.386235i 0.843240 0.537537i \(-0.180645\pi\)
−0.382944 + 0.923772i \(0.625090\pi\)
\(128\) 0.939693 0.342020i 0.0830579 0.0302306i
\(129\) 0 0
\(130\) 0.383714 + 2.17615i 0.0336539 + 0.190861i
\(131\) −14.2349 + 5.18108i −1.24371 + 0.452673i −0.878271 0.478163i \(-0.841303\pi\)
−0.365438 + 0.930836i \(0.619081\pi\)
\(132\) 0 0
\(133\) 3.87554 + 3.25197i 0.336052 + 0.281981i
\(134\) −0.582375 1.00870i −0.0503096 0.0871387i
\(135\) 0 0
\(136\) 0.0906868 0.514310i 0.00777633 0.0441017i
\(137\) −4.24086 + 7.34539i −0.362321 + 0.627559i −0.988342 0.152247i \(-0.951349\pi\)
0.626021 + 0.779806i \(0.284682\pi\)
\(138\) 0 0
\(139\) 17.2324 6.27209i 1.46164 0.531992i 0.515820 0.856697i \(-0.327487\pi\)
0.945815 + 0.324705i \(0.105265\pi\)
\(140\) 0.175358 0.303728i 0.0148204 0.0256697i
\(141\) 0 0
\(142\) 0.312892 0.0262573
\(143\) 26.6355 22.3499i 2.22737 1.86899i
\(144\) 0 0
\(145\) −0.382004 2.16645i −0.0317237 0.179914i
\(146\) −2.29781 + 13.0315i −0.190168 + 1.07850i
\(147\) 0 0
\(148\) 5.00438 + 3.45777i 0.411357 + 0.284227i
\(149\) −5.45291 −0.446720 −0.223360 0.974736i \(-0.571703\pi\)
−0.223360 + 0.974736i \(0.571703\pi\)
\(150\) 0 0
\(151\) −2.70116 15.3190i −0.219817 1.24665i −0.872349 0.488884i \(-0.837404\pi\)
0.652531 0.757762i \(-0.273707\pi\)
\(152\) 4.70771 + 1.71347i 0.381846 + 0.138981i
\(153\) 0 0
\(154\) −5.51855 −0.444697
\(155\) −0.880013 + 0.738419i −0.0706843 + 0.0593112i
\(156\) 0 0
\(157\) 3.76650 1.37089i 0.300599 0.109409i −0.187317 0.982299i \(-0.559979\pi\)
0.487916 + 0.872890i \(0.337757\pi\)
\(158\) 4.65338 + 8.05989i 0.370203 + 0.641211i
\(159\) 0 0
\(160\) 0.0603074 0.342020i 0.00476772 0.0270391i
\(161\) 1.36931 + 0.498388i 0.107917 + 0.0392785i
\(162\) 0 0
\(163\) 3.59446 + 3.01611i 0.281540 + 0.236240i 0.772611 0.634879i \(-0.218950\pi\)
−0.491072 + 0.871119i \(0.663395\pi\)
\(164\) 0.843024 + 0.707381i 0.0658291 + 0.0552372i
\(165\) 0 0
\(166\) 1.64354 + 9.32096i 0.127563 + 0.723447i
\(167\) 0.134923 + 0.765189i 0.0104407 + 0.0592121i 0.989583 0.143964i \(-0.0459848\pi\)
−0.979142 + 0.203176i \(0.934874\pi\)
\(168\) 0 0
\(169\) 21.0533 + 17.6658i 1.61948 + 1.35891i
\(170\) −0.138940 0.116585i −0.0106562 0.00894164i
\(171\) 0 0
\(172\) 5.89222 + 2.14459i 0.449277 + 0.163524i
\(173\) −1.86383 + 10.5703i −0.141704 + 0.803644i 0.828251 + 0.560358i \(0.189336\pi\)
−0.969955 + 0.243286i \(0.921775\pi\)
\(174\) 0 0
\(175\) 2.46371 + 4.26727i 0.186239 + 0.322575i
\(176\) −5.13518 + 1.86905i −0.387079 + 0.140885i
\(177\) 0 0
\(178\) −12.0788 + 10.1354i −0.905348 + 0.759677i
\(179\) 11.8976 0.889267 0.444633 0.895713i \(-0.353334\pi\)
0.444633 + 0.895713i \(0.353334\pi\)
\(180\) 0 0
\(181\) −4.12213 1.50033i −0.306395 0.111519i 0.184247 0.982880i \(-0.441015\pi\)
−0.490642 + 0.871361i \(0.663238\pi\)
\(182\) −1.11574 6.32766i −0.0827039 0.469037i
\(183\) 0 0
\(184\) 1.44298 0.106378
\(185\) 1.90899 0.904718i 0.140352 0.0665162i
\(186\) 0 0
\(187\) −0.495580 + 2.81058i −0.0362404 + 0.205530i
\(188\) 1.98622 + 11.2644i 0.144860 + 0.821543i
\(189\) 0 0
\(190\) 1.33284 1.11839i 0.0966945 0.0811363i
\(191\) 10.4903 0.759053 0.379527 0.925181i \(-0.376087\pi\)
0.379527 + 0.925181i \(0.376087\pi\)
\(192\) 0 0
\(193\) −4.91474 + 8.51259i −0.353771 + 0.612749i −0.986907 0.161291i \(-0.948434\pi\)
0.633136 + 0.774041i \(0.281767\pi\)
\(194\) −0.873095 + 0.317780i −0.0626845 + 0.0228153i
\(195\) 0 0
\(196\) 2.99011 5.17902i 0.213579 0.369930i
\(197\) 2.09473 11.8798i 0.149244 0.846402i −0.814618 0.579998i \(-0.803053\pi\)
0.963861 0.266404i \(-0.0858356\pi\)
\(198\) 0 0
\(199\) 4.64995 + 8.05395i 0.329626 + 0.570929i 0.982438 0.186591i \(-0.0597439\pi\)
−0.652811 + 0.757520i \(0.726411\pi\)
\(200\) 3.73783 + 3.13641i 0.264304 + 0.221778i
\(201\) 0 0
\(202\) −8.04552 + 2.92833i −0.566081 + 0.206037i
\(203\) 1.11077 + 6.29947i 0.0779605 + 0.442136i
\(204\) 0 0
\(205\) 0.359147 0.130719i 0.0250839 0.00912980i
\(206\) −3.79891 3.18767i −0.264683 0.222095i
\(207\) 0 0
\(208\) −3.18132 5.51020i −0.220585 0.382064i
\(209\) −25.7265 9.36367i −1.77954 0.647699i
\(210\) 0 0
\(211\) 2.20002 3.81054i 0.151455 0.262329i −0.780307 0.625396i \(-0.784937\pi\)
0.931763 + 0.363068i \(0.118271\pi\)
\(212\) 0.0461342 + 0.0799067i 0.00316851 + 0.00548802i
\(213\) 0 0
\(214\) 1.78413 3.09020i 0.121961 0.211242i
\(215\) 1.66820 1.39978i 0.113770 0.0954644i
\(216\) 0 0
\(217\) 2.55884 2.14712i 0.173705 0.145756i
\(218\) −0.919666 0.334731i −0.0622876 0.0226708i
\(219\) 0 0
\(220\) −0.329565 + 1.86905i −0.0222192 + 0.126012i
\(221\) −3.32285 −0.223519
\(222\) 0 0
\(223\) 11.2311 0.752092 0.376046 0.926601i \(-0.377283\pi\)
0.376046 + 0.926601i \(0.377283\pi\)
\(224\) −0.175358 + 0.994503i −0.0117166 + 0.0664480i
\(225\) 0 0
\(226\) −8.67996 3.15925i −0.577382 0.210150i
\(227\) 11.6086 9.74076i 0.770489 0.646517i −0.170345 0.985384i \(-0.554488\pi\)
0.940834 + 0.338868i \(0.110044\pi\)
\(228\) 0 0
\(229\) −11.9210 + 10.0029i −0.787759 + 0.661008i −0.945190 0.326522i \(-0.894123\pi\)
0.157431 + 0.987530i \(0.449679\pi\)
\(230\) 0.250571 0.434003i 0.0165222 0.0286173i
\(231\) 0 0
\(232\) 3.16714 + 5.48565i 0.207933 + 0.360151i
\(233\) 6.79356 11.7668i 0.445061 0.770868i −0.552995 0.833184i \(-0.686515\pi\)
0.998056 + 0.0623159i \(0.0198486\pi\)
\(234\) 0 0
\(235\) 3.73288 + 1.35866i 0.243506 + 0.0886289i
\(236\) 1.49508 + 2.58955i 0.0973213 + 0.168565i
\(237\) 0 0
\(238\) 0.404001 + 0.338997i 0.0261875 + 0.0219739i
\(239\) −18.3188 + 6.66750i −1.18494 + 0.431285i −0.857946 0.513740i \(-0.828260\pi\)
−0.326999 + 0.945025i \(0.606037\pi\)
\(240\) 0 0
\(241\) 0.250684 + 1.42170i 0.0161480 + 0.0915797i 0.991817 0.127671i \(-0.0407500\pi\)
−0.975669 + 0.219250i \(0.929639\pi\)
\(242\) 17.7259 6.45169i 1.13946 0.414730i
\(243\) 0 0
\(244\) 2.92310 + 2.45277i 0.187132 + 0.157022i
\(245\) −1.03845 1.79865i −0.0663443 0.114912i
\(246\) 0 0
\(247\) 5.53518 31.3915i 0.352195 1.99740i
\(248\) 1.65388 2.86461i 0.105022 0.181903i
\(249\) 0 0
\(250\) 3.22416 1.17350i 0.203913 0.0742184i
\(251\) 5.03646 8.72340i 0.317898 0.550616i −0.662151 0.749371i \(-0.730356\pi\)
0.980049 + 0.198754i \(0.0636895\pi\)
\(252\) 0 0
\(253\) −7.88554 −0.495760
\(254\) −5.18728 + 4.35264i −0.325479 + 0.273109i
\(255\) 0 0
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) 1.21293 6.87888i 0.0756607 0.429093i −0.923323 0.384024i \(-0.874538\pi\)
0.998984 0.0450692i \(-0.0143508\pi\)
\(258\) 0 0
\(259\) −5.55082 + 2.63068i −0.344911 + 0.163462i
\(260\) −2.20972 −0.137041
\(261\) 0 0
\(262\) −2.63050 14.9183i −0.162513 0.921657i
\(263\) 2.50225 + 0.910746i 0.154296 + 0.0561590i 0.418013 0.908441i \(-0.362727\pi\)
−0.263718 + 0.964600i \(0.584949\pi\)
\(264\) 0 0
\(265\) 0.0320445 0.00196848
\(266\) −3.87554 + 3.25197i −0.237625 + 0.199391i
\(267\) 0 0
\(268\) 1.09451 0.398368i 0.0668577 0.0243342i
\(269\) 1.20752 + 2.09148i 0.0736236 + 0.127520i 0.900487 0.434883i \(-0.143210\pi\)
−0.826863 + 0.562403i \(0.809877\pi\)
\(270\) 0 0
\(271\) −4.38472 + 24.8670i −0.266353 + 1.51056i 0.498803 + 0.866715i \(0.333773\pi\)
−0.765156 + 0.643845i \(0.777338\pi\)
\(272\) 0.490749 + 0.178618i 0.0297560 + 0.0108303i
\(273\) 0 0
\(274\) −6.49738 5.45195i −0.392521 0.329364i
\(275\) −20.4263 17.1397i −1.23175 1.03356i
\(276\) 0 0
\(277\) −3.07913 17.4626i −0.185007 1.04923i −0.925947 0.377654i \(-0.876731\pi\)
0.740940 0.671571i \(-0.234380\pi\)
\(278\) 3.18442 + 18.0598i 0.190989 + 1.08315i
\(279\) 0 0
\(280\) 0.268664 + 0.225435i 0.0160557 + 0.0134723i
\(281\) −15.1288 12.6946i −0.902511 0.757297i 0.0681682 0.997674i \(-0.478285\pi\)
−0.970680 + 0.240377i \(0.922729\pi\)
\(282\) 0 0
\(283\) −22.8810 8.32799i −1.36013 0.495047i −0.444037 0.896009i \(-0.646454\pi\)
−0.916095 + 0.400961i \(0.868676\pi\)
\(284\) −0.0543332 + 0.308139i −0.00322408 + 0.0182847i
\(285\) 0 0
\(286\) 17.3851 + 30.1119i 1.02800 + 1.78055i
\(287\) −1.04430 + 0.380095i −0.0616432 + 0.0224363i
\(288\) 0 0
\(289\) −12.8138 + 10.7521i −0.753754 + 0.632475i
\(290\) 2.19988 0.129181
\(291\) 0 0
\(292\) −12.4345 4.52580i −0.727675 0.264852i
\(293\) 4.03707 + 22.8954i 0.235848 + 1.33756i 0.840820 + 0.541315i \(0.182073\pi\)
−0.604972 + 0.796247i \(0.706816\pi\)
\(294\) 0 0
\(295\) 1.03847 0.0604621
\(296\) −4.27424 + 4.32791i −0.248435 + 0.251555i
\(297\) 0 0
\(298\) 0.946888 5.37007i 0.0548518 0.311080i
\(299\) −1.59429 9.04170i −0.0922005 0.522895i
\(300\) 0 0
\(301\) −4.85067 + 4.07019i −0.279588 + 0.234602i
\(302\) 15.5554 0.895111
\(303\) 0 0
\(304\) −2.50492 + 4.33865i −0.143667 + 0.248839i
\(305\) 1.24530 0.453253i 0.0713059 0.0259532i
\(306\) 0 0
\(307\) 5.33508 9.24063i 0.304489 0.527391i −0.672658 0.739953i \(-0.734848\pi\)
0.977147 + 0.212563i \(0.0681809\pi\)
\(308\) 0.958285 5.43471i 0.0546034 0.309671i
\(309\) 0 0
\(310\) −0.574388 0.994869i −0.0326230 0.0565047i
\(311\) −13.0382 10.9403i −0.739326 0.620368i 0.193330 0.981134i \(-0.438071\pi\)
−0.932657 + 0.360765i \(0.882516\pi\)
\(312\) 0 0
\(313\) −10.2525 + 3.73159i −0.579503 + 0.210922i −0.615106 0.788444i \(-0.710887\pi\)
0.0356035 + 0.999366i \(0.488665\pi\)
\(314\) 0.696020 + 3.94733i 0.0392787 + 0.222761i
\(315\) 0 0
\(316\) −8.74550 + 3.18310i −0.491973 + 0.179063i
\(317\) 22.0930 + 18.5382i 1.24086 + 1.04121i 0.997456 + 0.0712854i \(0.0227101\pi\)
0.243409 + 0.969924i \(0.421734\pi\)
\(318\) 0 0
\(319\) −17.3076 29.9777i −0.969042 1.67843i
\(320\) 0.326352 + 0.118782i 0.0182436 + 0.00664014i
\(321\) 0 0
\(322\) −0.728595 + 1.26196i −0.0406030 + 0.0703264i
\(323\) 1.30818 + 2.26584i 0.0727892 + 0.126075i
\(324\) 0 0
\(325\) 15.5229 26.8864i 0.861054 1.49139i
\(326\) −3.59446 + 3.01611i −0.199079 + 0.167047i
\(327\) 0 0
\(328\) −0.843024 + 0.707381i −0.0465482 + 0.0390586i
\(329\) −10.8542 3.95061i −0.598412 0.217804i
\(330\) 0 0
\(331\) 0.687569 3.89939i 0.0377922 0.214330i −0.960064 0.279782i \(-0.909738\pi\)
0.997856 + 0.0654519i \(0.0208489\pi\)
\(332\) −9.46475 −0.519446
\(333\) 0 0
\(334\) −0.776993 −0.0425152
\(335\) 0.0702431 0.398368i 0.00383779 0.0217652i
\(336\) 0 0
\(337\) 4.01886 + 1.46274i 0.218921 + 0.0796807i 0.449152 0.893455i \(-0.351726\pi\)
−0.230231 + 0.973136i \(0.573948\pi\)
\(338\) −21.0533 + 17.6658i −1.14515 + 0.960893i
\(339\) 0 0
\(340\) 0.138940 0.116585i 0.00753509 0.00632269i
\(341\) −9.03806 + 15.6544i −0.489438 + 0.847732i
\(342\) 0 0
\(343\) 6.55400 + 11.3519i 0.353883 + 0.612943i
\(344\) −3.13518 + 5.43030i −0.169038 + 0.292782i
\(345\) 0 0
\(346\) −10.0860 3.67102i −0.542229 0.197355i
\(347\) −5.06401 8.77113i −0.271850 0.470859i 0.697485 0.716599i \(-0.254302\pi\)
−0.969336 + 0.245740i \(0.920969\pi\)
\(348\) 0 0
\(349\) −5.50852 4.62220i −0.294864 0.247421i 0.483338 0.875434i \(-0.339424\pi\)
−0.778203 + 0.628013i \(0.783869\pi\)
\(350\) −4.63026 + 1.68528i −0.247498 + 0.0900819i
\(351\) 0 0
\(352\) −0.948944 5.38173i −0.0505789 0.286847i
\(353\) −32.0012 + 11.6475i −1.70325 + 0.619933i −0.996189 0.0872167i \(-0.972203\pi\)
−0.707064 + 0.707150i \(0.749981\pi\)
\(354\) 0 0
\(355\) 0.0832432 + 0.0698494i 0.00441809 + 0.00370722i
\(356\) −7.88391 13.6553i −0.417846 0.723731i
\(357\) 0 0
\(358\) −2.06599 + 11.7168i −0.109191 + 0.619254i
\(359\) 4.93976 8.55592i 0.260711 0.451564i −0.705720 0.708491i \(-0.749376\pi\)
0.966431 + 0.256926i \(0.0827098\pi\)
\(360\) 0 0
\(361\) −5.73076 + 2.08582i −0.301619 + 0.109780i
\(362\) 2.19334 3.79897i 0.115279 0.199670i
\(363\) 0 0
\(364\) 6.42527 0.336776
\(365\) −3.52044 + 2.95400i −0.184268 + 0.154620i
\(366\) 0 0
\(367\) −5.88735 33.3888i −0.307317 1.74288i −0.612391 0.790555i \(-0.709792\pi\)
0.305074 0.952329i \(-0.401319\pi\)
\(368\) −0.250571 + 1.42106i −0.0130619 + 0.0740780i
\(369\) 0 0
\(370\) 0.559481 + 2.03709i 0.0290860 + 0.105903i
\(371\) −0.0931767 −0.00483749
\(372\) 0 0
\(373\) 5.44457 + 30.8777i 0.281909 + 1.59879i 0.716121 + 0.697976i \(0.245916\pi\)
−0.434212 + 0.900811i \(0.642973\pi\)
\(374\) −2.68182 0.976103i −0.138674 0.0504731i
\(375\) 0 0
\(376\) −11.4382 −0.589880
\(377\) 30.8737 25.9061i 1.59008 1.33423i
\(378\) 0 0
\(379\) −10.0119 + 3.64403i −0.514276 + 0.187181i −0.586104 0.810236i \(-0.699339\pi\)
0.0718279 + 0.997417i \(0.477117\pi\)
\(380\) 0.869950 + 1.50680i 0.0446275 + 0.0772971i
\(381\) 0 0
\(382\) −1.82163 + 10.3310i −0.0932025 + 0.528577i
\(383\) 18.2315 + 6.63571i 0.931585 + 0.339069i 0.762838 0.646590i \(-0.223806\pi\)
0.168747 + 0.985659i \(0.446028\pi\)
\(384\) 0 0
\(385\) −1.46818 1.23195i −0.0748253 0.0627859i
\(386\) −7.52982 6.31827i −0.383258 0.321592i
\(387\) 0 0
\(388\) −0.161341 0.915012i −0.00819087 0.0464527i
\(389\) −3.24705 18.4149i −0.164632 0.933674i −0.949443 0.313939i \(-0.898351\pi\)
0.784811 0.619735i \(-0.212760\pi\)
\(390\) 0 0
\(391\) 0.577283 + 0.484398i 0.0291945 + 0.0244971i
\(392\) 4.58111 + 3.84401i 0.231381 + 0.194152i
\(393\) 0 0
\(394\) 11.3356 + 4.12582i 0.571079 + 0.207856i
\(395\) −0.561266 + 3.18310i −0.0282404 + 0.160159i
\(396\) 0 0
\(397\) 11.9316 + 20.6661i 0.598829 + 1.03720i 0.992994 + 0.118163i \(0.0377005\pi\)
−0.394165 + 0.919040i \(0.628966\pi\)
\(398\) −8.73905 + 3.18075i −0.438049 + 0.159437i
\(399\) 0 0
\(400\) −3.73783 + 3.13641i −0.186891 + 0.156820i
\(401\) −17.8350 −0.890638 −0.445319 0.895372i \(-0.646910\pi\)
−0.445319 + 0.895372i \(0.646910\pi\)
\(402\) 0 0
\(403\) −19.7769 7.19819i −0.985156 0.358568i
\(404\) −1.48675 8.43179i −0.0739687 0.419497i
\(405\) 0 0
\(406\) −6.39665 −0.317460
\(407\) 23.3577 23.6510i 1.15780 1.17233i
\(408\) 0 0
\(409\) −1.73417 + 9.83496i −0.0857492 + 0.486308i 0.911443 + 0.411426i \(0.134969\pi\)
−0.997192 + 0.0748818i \(0.976142\pi\)
\(410\) 0.0663677 + 0.376390i 0.00327767 + 0.0185886i
\(411\) 0 0
\(412\) 3.79891 3.18767i 0.187159 0.157045i
\(413\) −3.01959 −0.148584
\(414\) 0 0
\(415\) −1.64354 + 2.84669i −0.0806780 + 0.139738i
\(416\) 5.97892 2.17615i 0.293141 0.106694i
\(417\) 0 0
\(418\) 13.6888 23.7096i 0.669540 1.15968i
\(419\) −6.25638 + 35.4817i −0.305644 + 1.73340i 0.314812 + 0.949154i \(0.398059\pi\)
−0.620456 + 0.784241i \(0.713052\pi\)
\(420\) 0 0
\(421\) −11.1668 19.3414i −0.544235 0.942643i −0.998655 0.0518555i \(-0.983486\pi\)
0.454419 0.890788i \(-0.349847\pi\)
\(422\) 3.37062 + 2.82829i 0.164079 + 0.137679i
\(423\) 0 0
\(424\) −0.0867039 + 0.0315576i −0.00421071 + 0.00153257i
\(425\) 0.442496 + 2.50952i 0.0214642 + 0.121729i
\(426\) 0 0
\(427\) −3.62101 + 1.31794i −0.175233 + 0.0637796i
\(428\) 2.73344 + 2.29363i 0.132126 + 0.110867i
\(429\) 0 0
\(430\) 1.08884 + 1.88592i 0.0525084 + 0.0909472i
\(431\) 29.3710 + 10.6902i 1.41475 + 0.514928i 0.932521 0.361116i \(-0.117604\pi\)
0.482231 + 0.876044i \(0.339827\pi\)
\(432\) 0 0
\(433\) −2.71093 + 4.69547i −0.130279 + 0.225650i −0.923784 0.382914i \(-0.874921\pi\)
0.793505 + 0.608564i \(0.208254\pi\)
\(434\) 1.67017 + 2.89281i 0.0801705 + 0.138859i
\(435\) 0 0
\(436\) 0.489344 0.847568i 0.0234353 0.0405912i
\(437\) −5.53783 + 4.64679i −0.264910 + 0.222286i
\(438\) 0 0
\(439\) −11.8195 + 9.91772i −0.564113 + 0.473347i −0.879687 0.475554i \(-0.842248\pi\)
0.315573 + 0.948901i \(0.397803\pi\)
\(440\) −1.78343 0.649116i −0.0850217 0.0309454i
\(441\) 0 0
\(442\) 0.577007 3.27237i 0.0274454 0.155651i
\(443\) 8.45523 0.401720 0.200860 0.979620i \(-0.435626\pi\)
0.200860 + 0.979620i \(0.435626\pi\)
\(444\) 0 0
\(445\) −5.47610 −0.259592
\(446\) −1.95027 + 11.0605i −0.0923478 + 0.523730i
\(447\) 0 0
\(448\) −0.948944 0.345387i −0.0448334 0.0163180i
\(449\) −27.8798 + 23.3939i −1.31573 + 1.10403i −0.328538 + 0.944491i \(0.606556\pi\)
−0.987192 + 0.159538i \(0.949000\pi\)
\(450\) 0 0
\(451\) 4.60691 3.86566i 0.216931 0.182027i
\(452\) 4.61851 7.99950i 0.217236 0.376265i
\(453\) 0 0
\(454\) 7.57697 + 13.1237i 0.355605 + 0.615925i
\(455\) 1.11574 1.93251i 0.0523066 0.0905976i
\(456\) 0 0
\(457\) −12.2550 4.46044i −0.573263 0.208651i 0.0390893 0.999236i \(-0.487554\pi\)
−0.612352 + 0.790585i \(0.709777\pi\)
\(458\) −7.78085 13.4768i −0.363575 0.629731i
\(459\) 0 0
\(460\) 0.383898 + 0.322128i 0.0178993 + 0.0150193i
\(461\) 16.5840 6.03608i 0.772393 0.281128i 0.0743962 0.997229i \(-0.476297\pi\)
0.697997 + 0.716101i \(0.254075\pi\)
\(462\) 0 0
\(463\) 4.60063 + 26.0915i 0.213809 + 1.21257i 0.882961 + 0.469447i \(0.155547\pi\)
−0.669151 + 0.743126i \(0.733342\pi\)
\(464\) −5.95228 + 2.16645i −0.276328 + 0.100575i
\(465\) 0 0
\(466\) 10.4083 + 8.73363i 0.482157 + 0.404578i
\(467\) −9.54875 16.5389i −0.441864 0.765330i 0.555964 0.831206i \(-0.312349\pi\)
−0.997828 + 0.0658760i \(0.979016\pi\)
\(468\) 0 0
\(469\) −0.204248 + 1.15835i −0.00943129 + 0.0534875i
\(470\) −1.98622 + 3.44024i −0.0916176 + 0.158686i
\(471\) 0 0
\(472\) −2.80983 + 1.02269i −0.129333 + 0.0470733i
\(473\) 17.1330 29.6752i 0.787776 1.36447i
\(474\) 0 0
\(475\) −24.4450 −1.12161
\(476\) −0.404001 + 0.338997i −0.0185173 + 0.0155379i
\(477\) 0 0
\(478\) −3.38518 19.1983i −0.154834 0.878110i
\(479\) −3.33101 + 18.8911i −0.152198 + 0.863156i 0.809106 + 0.587663i \(0.199952\pi\)
−0.961303 + 0.275492i \(0.911159\pi\)
\(480\) 0 0
\(481\) 31.8410 + 22.0006i 1.45183 + 1.00314i
\(482\) −1.44363 −0.0657556
\(483\) 0 0
\(484\) 3.27561 + 18.5769i 0.148891 + 0.844404i
\(485\) −0.303223 0.110364i −0.0137686 0.00501137i
\(486\) 0 0
\(487\) −35.7577 −1.62034 −0.810168 0.586197i \(-0.800624\pi\)
−0.810168 + 0.586197i \(0.800624\pi\)
\(488\) −2.92310 + 2.45277i −0.132322 + 0.111032i
\(489\) 0 0
\(490\) 1.95165 0.710344i 0.0881667 0.0320901i
\(491\) 14.8866 + 25.7843i 0.671822 + 1.16363i 0.977387 + 0.211459i \(0.0678214\pi\)
−0.305565 + 0.952171i \(0.598845\pi\)
\(492\) 0 0
\(493\) −0.574436 + 3.25779i −0.0258713 + 0.146723i
\(494\) 29.9535 + 10.9022i 1.34767 + 0.490512i
\(495\) 0 0
\(496\) 2.53390 + 2.12619i 0.113775 + 0.0954688i
\(497\) −0.242049 0.203103i −0.0108574 0.00911043i
\(498\) 0 0
\(499\) 4.30958 + 24.4409i 0.192923 + 1.09412i 0.915345 + 0.402670i \(0.131918\pi\)
−0.722422 + 0.691453i \(0.756971\pi\)
\(500\) 0.595800 + 3.37895i 0.0266450 + 0.151111i
\(501\) 0 0
\(502\) 7.71630 + 6.47475i 0.344395 + 0.288982i
\(503\) −10.4375 8.75811i −0.465386 0.390505i 0.379722 0.925100i \(-0.376019\pi\)
−0.845108 + 0.534596i \(0.820464\pi\)
\(504\) 0 0
\(505\) −2.79418 1.01700i −0.124339 0.0452558i
\(506\) 1.36931 7.76574i 0.0608733 0.345229i
\(507\) 0 0
\(508\) −3.38575 5.86430i −0.150219 0.260186i
\(509\) 19.8285 7.21697i 0.878881 0.319886i 0.137123 0.990554i \(-0.456215\pi\)
0.741758 + 0.670668i \(0.233992\pi\)
\(510\) 0 0
\(511\) 10.2365 8.58945i 0.452836 0.379975i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.56375 + 2.38901i 0.289515 + 0.105375i
\(515\) −0.299072 1.69612i −0.0131787 0.0747400i
\(516\) 0 0
\(517\) 62.5069 2.74905
\(518\) −1.62682 5.92330i −0.0714784 0.260255i
\(519\) 0 0
\(520\) 0.383714 2.17615i 0.0168270 0.0954305i
\(521\) −0.510798 2.89688i −0.0223784 0.126914i 0.971572 0.236745i \(-0.0760804\pi\)
−0.993950 + 0.109830i \(0.964969\pi\)
\(522\) 0 0
\(523\) 8.30708 6.97047i 0.363243 0.304797i −0.442839 0.896601i \(-0.646029\pi\)
0.806082 + 0.591804i \(0.201584\pi\)
\(524\) 15.1485 0.661764
\(525\) 0 0
\(526\) −1.33142 + 2.30609i −0.0580527 + 0.100550i
\(527\) 1.62328 0.590827i 0.0707113 0.0257368i
\(528\) 0 0
\(529\) 10.4589 18.1153i 0.454735 0.787624i
\(530\) −0.00556446 + 0.0315576i −0.000241705 + 0.00137078i
\(531\) 0 0
\(532\) −2.52958 4.38137i −0.109671 0.189956i
\(533\) 5.36386 + 4.50081i 0.232334 + 0.194952i
\(534\) 0 0
\(535\) 1.16451 0.423846i 0.0503461 0.0183245i
\(536\) 0.202257 + 1.14706i 0.00873616 + 0.0495452i
\(537\) 0 0
\(538\) −2.26939 + 0.825991i −0.0978404 + 0.0356110i
\(539\) −25.0346 21.0065i −1.07832 0.904815i
\(540\) 0 0
\(541\) −4.43868 7.68801i −0.190834 0.330534i 0.754693 0.656078i \(-0.227786\pi\)
−0.945527 + 0.325544i \(0.894452\pi\)
\(542\) −23.7278 8.63621i −1.01920 0.370957i
\(543\) 0 0
\(544\) −0.261122 + 0.452277i −0.0111955 + 0.0193912i
\(545\) −0.169947 0.294357i −0.00727974 0.0126089i
\(546\) 0 0
\(547\) 18.2649 31.6358i 0.780952 1.35265i −0.150436 0.988620i \(-0.548068\pi\)
0.931388 0.364028i \(-0.118599\pi\)
\(548\) 6.49738 5.45195i 0.277554 0.232896i
\(549\) 0 0
\(550\) 20.4263 17.1397i 0.870979 0.730838i
\(551\) −29.8200 10.8536i −1.27038 0.462379i
\(552\) 0 0
\(553\) 1.63201 9.25560i 0.0694002 0.393588i
\(554\) 17.7320 0.753360
\(555\) 0 0
\(556\) −18.3384 −0.777720
\(557\) −6.37699 + 36.1657i −0.270202 + 1.53239i 0.483601 + 0.875288i \(0.339329\pi\)
−0.753803 + 0.657101i \(0.771783\pi\)
\(558\) 0 0
\(559\) 37.4900 + 13.6453i 1.58566 + 0.577133i
\(560\) −0.268664 + 0.225435i −0.0113531 + 0.00952639i
\(561\) 0 0
\(562\) 15.1288 12.6946i 0.638172 0.535490i
\(563\) 0.238456 0.413018i 0.0100497 0.0174066i −0.860957 0.508678i \(-0.830134\pi\)
0.871007 + 0.491271i \(0.163468\pi\)
\(564\) 0 0
\(565\) −1.60399 2.77820i −0.0674805 0.116880i
\(566\) 12.1747 21.0872i 0.511741 0.886361i
\(567\) 0 0
\(568\) −0.294023 0.107015i −0.0123369 0.00449027i
\(569\) 4.54906 + 7.87920i 0.190706 + 0.330313i 0.945485 0.325667i \(-0.105589\pi\)
−0.754778 + 0.655980i \(0.772255\pi\)
\(570\) 0 0
\(571\) 19.6081 + 16.4532i 0.820574 + 0.688543i 0.953106 0.302635i \(-0.0978664\pi\)
−0.132532 + 0.991179i \(0.542311\pi\)
\(572\) −32.6733 + 11.8921i −1.36614 + 0.497234i
\(573\) 0 0
\(574\) −0.192979 1.09444i −0.00805480 0.0456811i
\(575\) −6.61626 + 2.40812i −0.275917 + 0.100426i
\(576\) 0 0
\(577\) 11.8194 + 9.91764i 0.492048 + 0.412877i 0.854759 0.519024i \(-0.173705\pi\)
−0.362712 + 0.931901i \(0.618149\pi\)
\(578\) −8.36363 14.4862i −0.347881 0.602548i
\(579\) 0 0
\(580\) −0.382004 + 2.16645i −0.0158619 + 0.0899571i
\(581\) 4.77896 8.27741i 0.198265 0.343405i
\(582\) 0 0
\(583\) 0.473815 0.172455i 0.0196234 0.00714234i
\(584\) 6.61627 11.4597i 0.273783 0.474207i
\(585\) 0 0
\(586\) −23.2486 −0.960390
\(587\) −12.4394 + 10.4379i −0.513430 + 0.430819i −0.862334 0.506340i \(-0.830998\pi\)
0.348904 + 0.937158i \(0.386554\pi\)
\(588\) 0 0
\(589\) 2.87759 + 16.3196i 0.118569 + 0.672439i
\(590\) −0.180328 + 1.02269i −0.00742400 + 0.0421036i
\(591\) 0 0
\(592\) −3.51995 4.96084i −0.144669 0.203889i
\(593\) 27.0626 1.11133 0.555663 0.831407i \(-0.312464\pi\)
0.555663 + 0.831407i \(0.312464\pi\)
\(594\) 0 0
\(595\) 0.0318052 + 0.180376i 0.00130389 + 0.00739472i
\(596\) 5.12406 + 1.86501i 0.209890 + 0.0763936i
\(597\) 0 0
\(598\) 9.18118 0.375446
\(599\) 30.5258 25.6142i 1.24725 1.04657i 0.250328 0.968161i \(-0.419461\pi\)
0.996922 0.0784059i \(-0.0249830\pi\)
\(600\) 0 0
\(601\) −33.5222 + 12.2011i −1.36740 + 0.497692i −0.918334 0.395807i \(-0.870465\pi\)
−0.449065 + 0.893499i \(0.648243\pi\)
\(602\) −3.16605 5.48376i −0.129038 0.223501i
\(603\) 0 0
\(604\) −2.70116 + 15.3190i −0.109909 + 0.623323i
\(605\) 6.15613 + 2.24065i 0.250282 + 0.0910953i
\(606\) 0 0
\(607\) −9.76538 8.19413i −0.396365 0.332589i 0.422722 0.906259i \(-0.361075\pi\)
−0.819086 + 0.573670i \(0.805519\pi\)
\(608\) −3.83776 3.22027i −0.155642 0.130599i
\(609\) 0 0
\(610\) 0.230123 + 1.30509i 0.00931740 + 0.0528416i
\(611\) 12.6376 + 71.6714i 0.511263 + 2.89952i
\(612\) 0 0
\(613\) −3.13519 2.63074i −0.126629 0.106255i 0.577274 0.816551i \(-0.304117\pi\)
−0.703903 + 0.710296i \(0.748561\pi\)
\(614\) 8.17382 + 6.85865i 0.329868 + 0.276792i
\(615\) 0 0
\(616\) 5.18574 + 1.88745i 0.208939 + 0.0760477i
\(617\) −8.20856 + 46.5531i −0.330464 + 1.87416i 0.137640 + 0.990482i \(0.456048\pi\)
−0.468104 + 0.883673i \(0.655063\pi\)
\(618\) 0 0
\(619\) 10.5169 + 18.2157i 0.422708 + 0.732152i 0.996203 0.0870571i \(-0.0277463\pi\)
−0.573495 + 0.819209i \(0.694413\pi\)
\(620\) 1.07950 0.392904i 0.0433536 0.0157794i
\(621\) 0 0
\(622\) 13.0382 10.9403i 0.522783 0.438667i
\(623\) 15.9230 0.637943
\(624\) 0 0
\(625\) −21.8059 7.93669i −0.872235 0.317468i
\(626\) −1.89458 10.7447i −0.0757225 0.429444i
\(627\) 0 0
\(628\) −4.00822 −0.159945
\(629\) −3.16281 + 0.296606i −0.126110 + 0.0118264i
\(630\) 0 0
\(631\) −5.68830 + 32.2599i −0.226448 + 1.28425i 0.633451 + 0.773783i \(0.281638\pi\)
−0.859898 + 0.510465i \(0.829473\pi\)
\(632\) −1.61610 9.16537i −0.0642851 0.364579i
\(633\) 0 0
\(634\) −22.0930 + 18.5382i −0.877424 + 0.736246i
\(635\) −2.35172 −0.0933252
\(636\) 0 0
\(637\) 19.0250 32.9522i 0.753796 1.30561i
\(638\) 32.5277 11.8391i 1.28779 0.468716i
\(639\) 0 0
\(640\) −0.173648 + 0.300767i −0.00686405 + 0.0118889i
\(641\) −3.47857 + 19.7280i −0.137395 + 0.779208i 0.835766 + 0.549085i \(0.185024\pi\)
−0.973162 + 0.230123i \(0.926087\pi\)
\(642\) 0 0
\(643\) 6.69618 + 11.5981i 0.264071 + 0.457385i 0.967320 0.253559i \(-0.0816012\pi\)
−0.703249 + 0.710944i \(0.748268\pi\)
\(644\) −1.11627 0.936663i −0.0439873 0.0369097i
\(645\) 0 0
\(646\) −2.45858 + 0.894849i −0.0967314 + 0.0352074i
\(647\) −2.56647 14.5551i −0.100898 0.572222i −0.992780 0.119953i \(-0.961726\pi\)
0.891881 0.452269i \(-0.149385\pi\)
\(648\) 0 0
\(649\) 15.3550 5.58876i 0.602736 0.219378i
\(650\) 23.7824 + 19.9558i 0.932823 + 0.782732i
\(651\) 0 0
\(652\) −2.34612 4.06359i −0.0918810 0.159143i
\(653\) −25.4991 9.28092i −0.997857 0.363190i −0.209099 0.977894i \(-0.567053\pi\)
−0.788758 + 0.614704i \(0.789275\pi\)
\(654\) 0 0
\(655\) 2.63050 4.55617i 0.102782 0.178024i
\(656\) −0.550245 0.953052i −0.0214835 0.0372104i
\(657\) 0 0
\(658\) 5.77540 10.0033i 0.225149 0.389969i
\(659\) −24.2414 + 20.3409i −0.944311 + 0.792371i −0.978330 0.207050i \(-0.933614\pi\)
0.0340197 + 0.999421i \(0.489169\pi\)
\(660\) 0 0
\(661\) 26.0376 21.8481i 1.01274 0.849793i 0.0240454 0.999711i \(-0.492345\pi\)
0.988698 + 0.149918i \(0.0479009\pi\)
\(662\) 3.72076 + 1.35425i 0.144611 + 0.0526343i
\(663\) 0 0
\(664\) 1.64354 9.32096i 0.0637816 0.361723i
\(665\) −1.75703 −0.0681347
\(666\) 0 0
\(667\) −9.14028 −0.353913
\(668\) 0.134923 0.765189i 0.00522035 0.0296060i
\(669\) 0 0
\(670\) 0.380118 + 0.138352i 0.0146853 + 0.00534500i
\(671\) 15.9740 13.4038i 0.616669 0.517447i
\(672\) 0 0
\(673\) 30.3717 25.4849i 1.17074 0.982372i 0.170749 0.985315i \(-0.445381\pi\)
0.999996 + 0.00294292i \(0.000936763\pi\)
\(674\) −2.13839 + 3.70380i −0.0823676 + 0.142665i
\(675\) 0 0
\(676\) −13.7416 23.8011i −0.528522 0.915426i
\(677\) 9.65303 16.7195i 0.370996 0.642584i −0.618723 0.785609i \(-0.712350\pi\)
0.989719 + 0.143025i \(0.0456830\pi\)
\(678\) 0 0
\(679\) 0.881690 + 0.320909i 0.0338362 + 0.0123154i
\(680\) 0.0906868 + 0.157074i 0.00347768 + 0.00602352i
\(681\) 0 0
\(682\) −13.8471 11.6191i −0.530233 0.444918i
\(683\) 1.90109 0.691940i 0.0727432 0.0264764i −0.305392 0.952227i \(-0.598788\pi\)
0.378135 + 0.925750i \(0.376565\pi\)
\(684\) 0 0
\(685\) −0.511511 2.90092i −0.0195438 0.110838i
\(686\) −12.3175 + 4.48320i −0.470284 + 0.171169i
\(687\) 0 0
\(688\) −4.80338 4.03051i −0.183127 0.153662i
\(689\) 0.293535 + 0.508417i 0.0111828 + 0.0193692i
\(690\) 0 0
\(691\) −0.242292 + 1.37410i −0.00921721 + 0.0522734i −0.989069 0.147450i \(-0.952893\pi\)
0.979852 + 0.199724i \(0.0640045\pi\)
\(692\) 5.36667 9.29535i 0.204010 0.353356i
\(693\) 0 0
\(694\) 9.51723 3.46399i 0.361269 0.131491i
\(695\) −3.18442 + 5.51559i −0.120792 + 0.209218i
\(696\) 0 0
\(697\) −0.574725 −0.0217692
\(698\) 5.50852 4.62220i 0.208501 0.174953i
\(699\) 0 0
\(700\) −0.855638 4.85256i −0.0323401 0.183410i
\(701\) 7.84895 44.5136i 0.296451 1.68126i −0.364797 0.931087i \(-0.618862\pi\)
0.661247 0.750168i \(-0.270027\pi\)
\(702\) 0 0
\(703\) 2.46650 30.3737i 0.0930258 1.14557i
\(704\) 5.46475 0.205960
\(705\) 0 0
\(706\) −5.91359 33.5376i −0.222561 1.26220i
\(707\) 8.12472 + 2.95716i 0.305562 + 0.111215i
\(708\) 0 0
\(709\) −28.5445 −1.07201 −0.536005 0.844215i \(-0.680067\pi\)
−0.536005 + 0.844215i \(0.680067\pi\)
\(710\) −0.0832432 + 0.0698494i −0.00312406 + 0.00262140i
\(711\) 0 0
\(712\) 14.8169 5.39291i 0.555287 0.202108i
\(713\) 2.38653 + 4.13359i 0.0893761 + 0.154804i
\(714\) 0 0
\(715\) −2.09690 + 11.8921i −0.0784196 + 0.444740i
\(716\) −11.1801 4.06921i −0.417819 0.152074i
\(717\) 0 0
\(718\) 7.56816 + 6.35044i 0.282441 + 0.236996i
\(719\) 13.6923 + 11.4892i 0.510637 + 0.428475i 0.861353 0.508007i \(-0.169617\pi\)
−0.350717 + 0.936482i \(0.614062\pi\)
\(720\) 0 0
\(721\) 0.869621 + 4.93187i 0.0323864 + 0.183672i
\(722\) −1.05900 6.00589i −0.0394119 0.223516i
\(723\) 0 0
\(724\) 3.36039 + 2.81970i 0.124888 + 0.104793i
\(725\) −23.6765 19.8669i −0.879322 0.737839i
\(726\) 0 0
\(727\) 16.3955 + 5.96747i 0.608075 + 0.221321i 0.627661 0.778487i \(-0.284013\pi\)
−0.0195860 + 0.999808i \(0.506235\pi\)
\(728\) −1.11574 + 6.32766i −0.0413520 + 0.234519i
\(729\) 0 0
\(730\) −2.29781 3.97992i −0.0850457 0.147303i
\(731\) −3.07718 + 1.12000i −0.113813 + 0.0414247i
\(732\) 0 0
\(733\) −33.6087 + 28.2011i −1.24137 + 1.04163i −0.243950 + 0.969788i \(0.578443\pi\)
−0.997416 + 0.0718424i \(0.977112\pi\)
\(734\) 33.9039 1.25142
\(735\) 0 0
\(736\) −1.35596 0.493529i −0.0499814 0.0181917i
\(737\) −1.10528 6.26837i −0.0407136 0.230898i
\(738\) 0 0
\(739\) 39.5017 1.45309 0.726546 0.687118i \(-0.241124\pi\)
0.726546 + 0.687118i \(0.241124\pi\)
\(740\) −2.10329 + 0.197245i −0.0773186 + 0.00725087i
\(741\) 0 0
\(742\) 0.0161800 0.0917611i 0.000593985 0.00336866i
\(743\) −3.45404 19.5888i −0.126716 0.718644i −0.980274 0.197645i \(-0.936671\pi\)
0.853557 0.520999i \(-0.174440\pi\)
\(744\) 0 0
\(745\) 1.45072 1.21730i 0.0531502 0.0445983i
\(746\) −31.3540 −1.14795
\(747\) 0 0
\(748\) 1.42697 2.47158i 0.0521751 0.0903699i
\(749\) −3.38608 + 1.23243i −0.123725 + 0.0450320i
\(750\) 0 0
\(751\) 16.6184 28.7839i 0.606413 1.05034i −0.385413 0.922744i \(-0.625941\pi\)
0.991826 0.127594i \(-0.0407255\pi\)
\(752\) 1.98622 11.2644i 0.0724301 0.410771i
\(753\) 0 0
\(754\) 20.1514 + 34.9032i 0.733870 + 1.27110i
\(755\) 4.13842 + 3.47255i 0.150612 + 0.126379i
\(756\) 0 0
\(757\) −40.7915 + 14.8469i −1.48259 + 0.539620i −0.951488 0.307686i \(-0.900445\pi\)
−0.531105 + 0.847306i \(0.678223\pi\)
\(758\) −1.85012 10.4926i −0.0671994 0.381107i
\(759\) 0 0
\(760\) −1.63497 + 0.595081i −0.0593067 + 0.0215859i
\(761\) −19.3702 16.2536i −0.702171 0.589191i 0.220220 0.975450i \(-0.429323\pi\)
−0.922390 + 0.386259i \(0.873767\pi\)
\(762\) 0 0
\(763\) 0.494161 + 0.855912i 0.0178898 + 0.0309861i
\(764\) −9.85768 3.58790i −0.356638 0.129806i
\(765\) 0 0
\(766\) −9.70076 + 16.8022i −0.350503 + 0.607089i
\(767\) 9.51263 + 16.4764i 0.343481 + 0.594927i
\(768\) 0 0
\(769\) −13.8992 + 24.0740i −0.501216 + 0.868132i 0.498783 + 0.866727i \(0.333781\pi\)
−0.999999 + 0.00140492i \(0.999553\pi\)
\(770\) 1.46818 1.23195i 0.0529095 0.0443963i
\(771\) 0 0
\(772\) 7.52982 6.31827i 0.271004 0.227400i
\(773\) −0.927201 0.337474i −0.0333491 0.0121381i 0.325292 0.945614i \(-0.394537\pi\)
−0.358641 + 0.933476i \(0.616760\pi\)
\(774\) 0 0
\(775\) −2.80266 + 15.8947i −0.100674 + 0.570953i
\(776\) 0.929128 0.0333538
\(777\) 0 0
\(778\) 18.6990 0.670392
\(779\) 0.957372 5.42952i 0.0343014 0.194533i
\(780\) 0 0
\(781\) 1.60676 + 0.584812i 0.0574944 + 0.0209262i
\(782\) −0.577283 + 0.484398i −0.0206436 + 0.0173220i
\(783\) 0 0
\(784\) −4.58111 + 3.84401i −0.163611 + 0.137286i
\(785\) −0.696020 + 1.20554i −0.0248420 + 0.0430277i
\(786\) 0 0
\(787\) −12.8990 22.3417i −0.459799 0.796394i 0.539151 0.842209i \(-0.318745\pi\)
−0.998950 + 0.0458144i \(0.985412\pi\)
\(788\) −6.03154 + 10.4469i −0.214865 + 0.372157i
\(789\) 0 0
\(790\) −3.03728 1.10548i −0.108062 0.0393312i
\(791\) 4.66398 + 8.07825i 0.165832 + 0.287229i
\(792\) 0 0
\(793\) 18.5986 + 15.6061i 0.660455 + 0.554188i
\(794\) −22.4240 + 8.16169i −0.795800 + 0.289647i
\(795\) 0 0
\(796\) −1.61491 9.15861i −0.0572390 0.324618i
\(797\) 14.1958 5.16684i 0.502841 0.183019i −0.0781306 0.996943i \(-0.524895\pi\)
0.580971 + 0.813924i \(0.302673\pi\)
\(798\) 0 0
\(799\) −4.57599 3.83971i −0.161887 0.135839i
\(800\) −2.43969 4.22567i −0.0862562 0.149400i
\(801\) 0 0
\(802\) 3.09702 17.5641i 0.109359 0.620208i
\(803\) −36.1563 + 62.6245i −1.27593 + 2.20997i
\(804\) 0 0
\(805\) −0.475556 + 0.173088i −0.0167612 + 0.00610056i
\(806\) 10.5231 18.2265i 0.370659 0.642000i
\(807\) 0 0
\(808\) 8.56186 0.301205
\(809\) 32.7023 27.4405i 1.14975 0.964757i 0.150039 0.988680i \(-0.452060\pi\)
0.999714 + 0.0239226i \(0.00761551\pi\)
\(810\) 0 0
\(811\) 3.54555 + 20.1078i 0.124501 + 0.706081i 0.981603 + 0.190934i \(0.0611517\pi\)
−0.857102 + 0.515147i \(0.827737\pi\)
\(812\) 1.11077 6.29947i 0.0389802 0.221068i
\(813\) 0 0
\(814\) 19.2356 + 27.1098i 0.674209 + 0.950196i
\(815\) −1.62960 −0.0570822
\(816\) 0 0
\(817\) −5.45491 30.9363i −0.190843 1.08232i
\(818\) −9.38441 3.41565i −0.328118 0.119425i
\(819\) 0 0
\(820\) −0.382196 −0.0133469
\(821\) −10.3004 + 8.64304i −0.359485 + 0.301644i −0.804586 0.593837i \(-0.797613\pi\)
0.445100 + 0.895481i \(0.353168\pi\)
\(822\) 0 0
\(823\) 38.3237 13.9487i 1.33588 0.486221i 0.427368 0.904078i \(-0.359441\pi\)
0.908513 + 0.417857i \(0.137219\pi\)
\(824\) 2.47956 + 4.29473i 0.0863797 + 0.149614i
\(825\) 0 0
\(826\) 0.524347 2.97372i 0.0182444 0.103469i
\(827\) −38.0037 13.8322i −1.32152 0.480993i −0.417574 0.908643i \(-0.637120\pi\)
−0.903945 + 0.427650i \(0.859342\pi\)
\(828\) 0 0
\(829\) 2.03399 + 1.70672i 0.0706435 + 0.0592770i 0.677426 0.735591i \(-0.263096\pi\)
−0.606782 + 0.794868i \(0.707540\pi\)
\(830\) −2.51804 2.11289i −0.0874026 0.0733395i
\(831\) 0 0
\(832\) 1.10486 + 6.26597i 0.0383041 + 0.217234i
\(833\) 0.542326 + 3.07569i 0.0187905 + 0.106566i
\(834\) 0 0
\(835\) −0.206715 0.173454i −0.00715366 0.00600263i
\(836\) 20.9724 + 17.5979i 0.725346 + 0.608638i
\(837\) 0 0
\(838\) −33.8563 12.3227i −1.16955 0.425680i
\(839\) 7.48912 42.4729i 0.258553 1.46633i −0.528231 0.849101i \(-0.677145\pi\)
0.786785 0.617228i \(-0.211744\pi\)
\(840\) 0 0
\(841\) −5.56161 9.63298i −0.191780 0.332172i
\(842\) 20.9867 7.63853i 0.723249 0.263241i
\(843\) 0 0
\(844\) −3.37062 + 2.82829i −0.116022 + 0.0973537i
\(845\) −9.54479 −0.328351
\(846\) 0 0
\(847\) −17.9004 6.51520i −0.615064 0.223865i
\(848\) −0.0160222 0.0908666i −0.000550206 0.00312037i
\(849\) 0 0
\(850\) −2.54823 −0.0874036
\(851\) −2.32459 8.46391i −0.0796860 0.290139i
\(852\) 0 0
\(853\) −7.79993 + 44.2356i −0.267064 + 1.51460i 0.496027 + 0.868307i \(0.334792\pi\)
−0.763092 + 0.646290i \(0.776319\pi\)
\(854\) −0.669135 3.79485i −0.0228973 0.129857i
\(855\) 0 0
\(856\) −2.73344 + 2.29363i −0.0934272 + 0.0783947i
\(857\) 1.14287 0.0390395 0.0195198 0.999809i \(-0.493786\pi\)
0.0195198 + 0.999809i \(0.493786\pi\)
\(858\) 0 0
\(859\) −10.3483 + 17.9238i −0.353080 + 0.611552i −0.986787 0.162020i \(-0.948199\pi\)
0.633708 + 0.773573i \(0.281532\pi\)
\(860\) −2.04635 + 0.744809i −0.0697798 + 0.0253978i
\(861\) 0 0
\(862\) −15.6280 + 27.0685i −0.532291 + 0.921956i
\(863\) 1.91838 10.8797i 0.0653023 0.370348i −0.934591 0.355725i \(-0.884234\pi\)
0.999893 0.0146230i \(-0.00465482\pi\)
\(864\) 0 0
\(865\) −1.86383 3.22824i −0.0633720 0.109764i
\(866\) −4.15339 3.48511i −0.141138 0.118429i
\(867\) 0 0
\(868\) −3.13888 + 1.14246i −0.106541 + 0.0387776i
\(869\) 8.83159 + 50.0864i 0.299591 + 1.69907i
\(870\) 0 0
\(871\) 6.96395 2.53467i 0.235965 0.0858841i
\(872\) 0.749718 + 0.629088i 0.0253887 + 0.0213036i
\(873\) 0 0
\(874\) −3.61456 6.26061i −0.122264 0.211768i
\(875\) −3.25590 1.18505i −0.110069 0.0400620i
\(876\) 0 0
\(877\) 6.18401 10.7110i 0.208819 0.361686i −0.742524 0.669820i \(-0.766371\pi\)
0.951343 + 0.308134i \(0.0997046\pi\)
\(878\) −7.71462 13.3621i −0.260356 0.450950i
\(879\) 0 0
\(880\) 0.948944 1.64362i 0.0319889 0.0554064i
\(881\) −13.7758 + 11.5593i −0.464120 + 0.389443i −0.844644 0.535328i \(-0.820188\pi\)
0.380524 + 0.924771i \(0.375744\pi\)
\(882\) 0 0
\(883\) −8.21722 + 6.89507i −0.276532 + 0.232038i −0.770496 0.637444i \(-0.779992\pi\)
0.493965 + 0.869482i \(0.335547\pi\)
\(884\) 3.12246 + 1.13648i 0.105020 + 0.0382240i
\(885\) 0 0
\(886\) −1.46824 + 8.32678i −0.0493263 + 0.279744i
\(887\) 16.7444 0.562222 0.281111 0.959675i \(-0.409297\pi\)
0.281111 + 0.959675i \(0.409297\pi\)
\(888\) 0 0
\(889\) 6.83817 0.229345
\(890\) 0.950915 5.39291i 0.0318748 0.180771i
\(891\) 0 0
\(892\) −10.5538 3.84127i −0.353368 0.128615i
\(893\) 43.8971 36.8340i 1.46896 1.23260i
\(894\) 0 0
\(895\) −3.16528 + 2.65599i −0.105804 + 0.0887799i
\(896\) 0.504922 0.874551i 0.0168683 0.0292167i
\(897\) 0 0
\(898\) −18.1973 31.5186i −0.607250 1.05179i
\(899\) −10.4762 + 18.1453i −0.349400 + 0.605179i
\(900\) 0 0
\(901\) −0.0452806 0.0164808i −0.00150852 0.000549055i
\(902\) 3.00695 + 5.20819i 0.100120 + 0.173414i
\(903\) 0 0
\(904\) 7.07597 + 5.93744i 0.235343 + 0.197476i
\(905\) 1.43160 0.521060i 0.0475880 0.0173206i
\(906\) 0 0
\(907\) 7.53327 + 42.7233i 0.250138 + 1.41860i 0.808251 + 0.588838i \(0.200415\pi\)
−0.558113 + 0.829765i \(0.688474\pi\)
\(908\) −14.2400 + 5.18295i −0.472572 + 0.172002i
\(909\) 0 0
\(910\) 1.70941 + 1.43436i 0.0566663 + 0.0475487i
\(911\) 5.05307 + 8.75217i 0.167416 + 0.289972i 0.937510 0.347957i \(-0.113124\pi\)
−0.770095 + 0.637929i \(0.779791\pi\)
\(912\) 0 0
\(913\) −8.98151 + 50.9367i −0.297245 + 1.68576i
\(914\) 6.52073 11.2942i 0.215687 0.373580i
\(915\) 0 0
\(916\) 14.6232 5.32242i 0.483165 0.175858i
\(917\) −7.64880 + 13.2481i −0.252586 + 0.437491i
\(918\) 0 0
\(919\) 2.82736 0.0932661 0.0466330 0.998912i \(-0.485151\pi\)
0.0466330 + 0.998912i \(0.485151\pi\)
\(920\) −0.383898 + 0.322128i −0.0126567 + 0.0106203i
\(921\) 0 0
\(922\) 3.06460 + 17.3802i 0.100927 + 0.572386i
\(923\) −0.345702 + 1.96057i −0.0113789 + 0.0645331i
\(924\) 0 0
\(925\) 12.3753 26.9771i 0.406897 0.887001i
\(926\) −26.4940 −0.870646
\(927\) 0 0
\(928\) −1.09994 6.23806i −0.0361072 0.204774i
\(929\) 31.4473 + 11.4459i 1.03175 + 0.375528i 0.801748 0.597662i \(-0.203903\pi\)
0.230005 + 0.973189i \(0.426126\pi\)
\(930\) 0 0
\(931\) −29.9599 −0.981897
\(932\) −10.4083 + 8.73363i −0.340937 + 0.286080i
\(933\) 0 0
\(934\) 17.9458 6.53173i 0.587204 0.213725i
\(935\) −0.495580 0.858370i −0.0162072 0.0280717i
\(936\) 0 0
\(937\) 7.99787 45.3582i 0.261279 1.48179i −0.518146 0.855292i \(-0.673378\pi\)
0.779425 0.626495i \(-0.215511\pi\)
\(938\) −1.10528 0.402290i −0.0360888 0.0131352i
\(939\) 0 0
\(940\) −3.04307 2.55344i −0.0992540 0.0832840i
\(941\) 13.4316 + 11.2705i 0.437858 + 0.367406i 0.834907 0.550391i \(-0.185521\pi\)
−0.397049 + 0.917797i \(0.629966\pi\)
\(942\) 0 0
\(943\) −0.275751 1.56386i −0.00897970 0.0509264i
\(944\) −0.519235 2.94473i −0.0168997 0.0958427i
\(945\) 0 0
\(946\) 26.2493 + 22.0257i 0.853437 + 0.716119i
\(947\) −20.0641 16.8357i −0.651994 0.547088i 0.255681 0.966761i \(-0.417700\pi\)
−0.907675 + 0.419673i \(0.862145\pi\)
\(948\) 0 0
\(949\) −79.1163 28.7960i −2.56822 0.934757i
\(950\) 4.24482 24.0736i 0.137720 0.781050i
\(951\) 0 0
\(952\) −0.263693 0.456729i −0.00854633 0.0148027i
\(953\) −24.4034 + 8.88209i −0.790502 + 0.287719i −0.705545 0.708665i \(-0.749298\pi\)
−0.0849574 + 0.996385i \(0.527075\pi\)
\(954\) 0 0
\(955\) −2.79089 + 2.34184i −0.0903112 + 0.0757801i
\(956\) 19.4945 0.630496
\(957\) 0 0
\(958\) −18.0257 6.56080i −0.582383 0.211970i
\(959\) 1.48734 + 8.43510i 0.0480286 + 0.272384i
\(960\) 0 0
\(961\) −20.0587 −0.647054
\(962\) −27.1955 + 27.5369i −0.876817 + 0.887827i
\(963\) 0 0
\(964\) 0.250684 1.42170i 0.00807398 0.0457898i
\(965\) −0.592791 3.36188i −0.0190826 0.108223i
\(966\) 0 0
\(967\) 25.8686 21.7064i 0.831879 0.698029i −0.123843 0.992302i \(-0.539522\pi\)
0.955722 + 0.294273i \(0.0950773\pi\)
\(968\) −18.8635 −0.606295
\(969\) 0 0
\(970\) 0.161341 0.279451i 0.00518036 0.00897265i
\(971\) −12.9625 + 4.71796i −0.415986 + 0.151407i −0.541530 0.840682i \(-0.682155\pi\)
0.125544 + 0.992088i \(0.459932\pi\)
\(972\) 0 0
\(973\) 9.25945 16.0378i 0.296844 0.514150i
\(974\) 6.20926 35.2145i 0.198958 1.12834i
\(975\) 0 0
\(976\) −1.90792 3.30461i −0.0610709 0.105778i
\(977\) 29.8644 + 25.0592i 0.955448 + 0.801716i 0.980207 0.197978i \(-0.0634374\pi\)
−0.0247589 + 0.999693i \(0.507882\pi\)
\(978\) 0 0
\(979\) −80.9706 + 29.4709i −2.58783 + 0.941894i
\(980\) 0.360651 + 2.04535i 0.0115206 + 0.0653364i
\(981\) 0 0
\(982\) −27.9776 + 10.1830i −0.892802 + 0.324953i
\(983\) −9.34290 7.83963i −0.297992 0.250045i 0.481516 0.876437i \(-0.340086\pi\)
−0.779508 + 0.626392i \(0.784531\pi\)
\(984\) 0 0
\(985\) 2.09473 + 3.62818i 0.0667438 + 0.115604i
\(986\) −3.10855 1.13142i −0.0989963 0.0360317i
\(987\) 0 0
\(988\) −15.9379 + 27.6053i −0.507052 + 0.878240i
\(989\) −4.52402 7.83583i −0.143855 0.249165i
\(990\) 0 0
\(991\) −13.2303 + 22.9156i −0.420275 + 0.727937i −0.995966 0.0897299i \(-0.971400\pi\)
0.575691 + 0.817667i \(0.304733\pi\)
\(992\) −2.53390 + 2.12619i −0.0804513 + 0.0675067i
\(993\) 0 0
\(994\) 0.242049 0.203103i 0.00767733 0.00644204i
\(995\) −3.03504 1.10466i −0.0962172 0.0350202i
\(996\) 0 0
\(997\) −2.31702 + 13.1405i −0.0733809 + 0.416164i 0.925883 + 0.377809i \(0.123323\pi\)
−0.999264 + 0.0383540i \(0.987789\pi\)
\(998\) −24.8179 −0.785597
\(999\) 0 0
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 666.2.x.g.181.2 12
3.2 odd 2 74.2.f.b.33.2 yes 12
12.11 even 2 592.2.bc.d.33.1 12
37.9 even 9 inner 666.2.x.g.379.2 12
111.71 odd 18 2738.2.a.t.1.6 6
111.77 odd 18 2738.2.a.q.1.6 6
111.83 odd 18 74.2.f.b.9.2 12
444.83 even 18 592.2.bc.d.305.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.f.b.9.2 12 111.83 odd 18
74.2.f.b.33.2 yes 12 3.2 odd 2
592.2.bc.d.33.1 12 12.11 even 2
592.2.bc.d.305.1 12 444.83 even 18
666.2.x.g.181.2 12 1.1 even 1 trivial
666.2.x.g.379.2 12 37.9 even 9 inner
2738.2.a.q.1.6 6 111.77 odd 18
2738.2.a.t.1.6 6 111.71 odd 18