Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.65240704243 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.269701471\)
\(a_{6}=+0.408248290\) \(a_{7}=-1.797953354\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.897814520\)
\(a_{11}=+1.163449386\) \(a_{12}=-0.288675135\) \(a_{13}=-0.232986482\) \(a_{14}=+1.271345009\) \(a_{15}=+0.733062486\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.333820917\) \(a_{18}=-0.235702260\) \(a_{19}=+0.079802332\) \(a_{20}=-0.634850736\)
\(a_{21}=+1.038048853\) \(a_{22}=-0.822682950\) \(a_{23}=+0.310662340\) \(a_{24}=+0.204124145\) \(a_{25}=+0.612141826\)
\(a_{26}=+0.164746321\) \(a_{27}=-0.192450090\) \(a_{28}=-0.898976678\) \(a_{29}=+0.695233234\) \(a_{30}=-0.518353455\)
\(a_{31}=+0.077729272\) \(a_{32}=-0.176776695\) \(a_{33}=-0.671717816\) \(a_{34}=-0.236047034\) \(a_{35}=+2.282864018\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.999231734\) \(a_{38}=-0.056428770\) \(a_{39}=+0.134514808\) \(a_{40}=+0.448907260\)
\(a_{41}=+0.281524140\) \(a_{42}=-0.734011383\) \(a_{43}=-1.719544629\) \(a_{44}=+0.581724693\) \(a_{45}=-0.423233824\)
\(a_{46}=-0.219671448\) \(a_{47}=+1.227296100\) \(a_{48}=-0.144337567\) \(a_{49}=+2.232636262\) \(a_{50}=-0.432849636\)
\(a_{51}=-0.192731596\) \(a_{52}=-0.116493241\) \(a_{53}=-0.797365958\) \(a_{54}=+0.136082763\) \(a_{55}=-1.477233397\)
\(a_{56}=+0.635672504\) \(a_{57}=-0.046073898\) \(a_{58}=-0.491604135\) \(a_{59}=+0.758827078\) \(a_{60}=+0.366531243\)
\(a_{61}=-0.280167373\) \(a_{62}=-0.054962895\) \(a_{63}=-0.599317784\) \(a_{64}=+0.125000000\) \(a_{65}=+0.295823279\)
\(a_{66}=+0.474976223\) \(a_{67}=+1.313613571\) \(a_{68}=+0.166910456\) \(a_{69}=-0.179360980\) \(a_{70}=-1.614228630\)
\(a_{71}=-0.514588536\) \(a_{72}=-0.117851134\) \(a_{73}=+1.353483122\) \(a_{74}=+0.706563535\) \(a_{75}=-0.353420248\)
\(a_{76}=+0.039901166\) \(a_{77}=-2.091827725\) \(a_{78}=-0.095116333\) \(a_{79}=+0.170279120\) \(a_{80}=-0.317425368\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.199067628\) \(a_{83}=+1.610818984\) \(a_{84}=+0.519024426\) \(a_{85}=-0.423852909\)
\(a_{86}=+1.215901668\) \(a_{87}=-0.401393095\) \(a_{88}=-0.411341475\) \(a_{89}=-0.306743950\) \(a_{90}=+0.299271507\)
\(a_{91}=+0.418898826\) \(a_{92}=+0.155331170\) \(a_{93}=-0.044877016\) \(a_{94}=-0.867829395\) \(a_{95}=-0.101325139\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.655839387\) \(a_{98}=-1.578712241\) \(a_{99}=+0.387816462\) \(a_{100}=+0.306070913\)

Showing 100 of 1000 available coefficients

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