Properties

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

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.66395307858 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.384726482\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.725994601\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.979149485\)
\(a_{11}=-1.605484184\) \(a_{12}=-0.288675135\) \(a_{13}=+0.419872862\) \(a_{14}=+0.513355705\) \(a_{15}=-0.799472207\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.491349159\) \(a_{18}=-0.235702260\) \(a_{19}=-0.834648435\) \(a_{20}=+0.692363241\)
\(a_{21}=+0.419153178\) \(a_{22}=+1.135248754\) \(a_{23}=-1.713097524\) \(a_{24}=+0.204124145\) \(a_{25}=+0.917467429\)
\(a_{26}=-0.296894948\) \(a_{27}=-0.192450090\) \(a_{28}=-0.362997296\) \(a_{29}=-1.043879907\) \(a_{30}=+0.565312219\)
\(a_{31}=+0.494593857\) \(a_{32}=-0.176776695\) \(a_{33}=+0.926926726\) \(a_{34}=+0.347436322\) \(a_{35}=-1.005303949\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.156307650\) \(a_{38}=+0.590185568\) \(a_{39}=-0.242413710\) \(a_{40}=-0.489574743\)
\(a_{41}=-1.106994503\) \(a_{42}=-0.296386055\) \(a_{43}=+0.624164613\) \(a_{44}=-0.802742092\) \(a_{45}=+0.461575494\)
\(a_{46}=+1.211342876\) \(a_{47}=+1.365484230\) \(a_{48}=-0.144337567\) \(a_{49}=-0.472931840\) \(a_{50}=-0.648747440\)
\(a_{51}=+0.283680569\) \(a_{52}=+0.209936431\) \(a_{53}=-0.663190386\) \(a_{54}=+0.136082764\) \(a_{55}=-2.223156465\)
\(a_{56}=+0.256677853\) \(a_{57}=+0.481884499\) \(a_{58}=+0.738134561\) \(a_{59}=+0.717288403\) \(a_{60}=-0.399736103\)
\(a_{61}=+0.802087525\) \(a_{62}=-0.349730670\) \(a_{63}=-0.241998200\) \(a_{64}=+0.125000000\) \(a_{65}=+0.581409070\)
\(a_{66}=-0.655436173\) \(a_{67}=+0.088348047\) \(a_{68}=-0.245674579\) \(a_{69}=+0.989057320\) \(a_{70}=+0.710857241\)
\(a_{71}=-1.804034843\) \(a_{72}=-0.117851131\) \(a_{73}=-0.041368113\) \(a_{74}=-0.110526199\) \(a_{75}=-0.529700067\)
\(a_{76}=-0.417324217\) \(a_{77}=+1.165572849\) \(a_{78}=+0.171412378\) \(a_{79}=-1.159100128\) \(a_{80}=+0.346181620\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.782763320\) \(a_{83}=+0.827402880\) \(a_{84}=+0.209576589\) \(a_{85}=-0.680384191\)
\(a_{86}=-0.441351030\) \(a_{87}=+0.602684345\) \(a_{88}=+0.567624377\) \(a_{89}=+0.609180926\) \(a_{90}=-0.326383162\)
\(a_{91}=-0.304825430\) \(a_{92}=-0.856548762\) \(a_{93}=-0.285553897\) \(a_{94}=-0.965543159\) \(a_{95}=-1.155759791\)
\(a_{96}=+0.102062072\) \(a_{97}=+1.232706457\) \(a_{98}=+0.334413310\) \(a_{99}=-0.535161394\) \(a_{100}=+0.458733715\)

Showing 100 of 1000 available coefficients

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