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: \( 16.3341323969 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.976292983\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.118891665\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.690343389\)
\(a_{11}=-0.768715749\) \(a_{12}=+0.288675135\) \(a_{13}=-0.002131033\) \(a_{14}=+0.084069103\) \(a_{15}=-0.563663017\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.241263296\) \(a_{18}=+0.235702260\) \(a_{19}=-1.611856558\) \(a_{20}=-0.488146492\)
\(a_{21}=+0.068642135\) \(a_{22}=-0.543564119\) \(a_{23}=+1.602196524\) \(a_{24}=+0.204124145\) \(a_{25}=-0.046852011\)
\(a_{26}=-0.001506868\) \(a_{27}=+0.192450090\) \(a_{28}=+0.059445833\) \(a_{29}=-0.272360232\) \(a_{30}=-0.398569941\)
\(a_{31}=-0.719291271\) \(a_{32}=+0.176776695\) \(a_{33}=-0.443818245\) \(a_{34}=-0.877705694\) \(a_{35}=-0.116073099\)
\(a_{36}=+0.166666667\) \(a_{37}=-1.929570969\) \(a_{38}=-1.139754702\) \(a_{39}=-0.001230353\) \(a_{40}=-0.345171694\)
\(a_{41}=+0.037998583\) \(a_{42}=+0.048537319\) \(a_{43}=+0.127474709\) \(a_{44}=-0.384357875\) \(a_{45}=-0.325430994\)
\(a_{46}=+1.132924027\) \(a_{47}=-1.941062880\) \(a_{48}=+0.144337567\) \(a_{49}=-0.985864772\) \(a_{50}=-0.033129375\)
\(a_{51}=-0.716643698\) \(a_{52}=-0.001065517\) \(a_{53}=+1.737529299\) \(a_{54}=+0.136082763\) \(a_{55}=+0.750491792\)
\(a_{56}=+0.042034551\) \(a_{57}=-0.930605818\) \(a_{58}=-0.192587767\) \(a_{59}=-0.837815548\) \(a_{60}=-0.281831508\)
\(a_{61}=+0.829112501\) \(a_{62}=-0.508615735\) \(a_{63}=+0.039630555\) \(a_{64}=+0.125000000\) \(a_{65}=+0.002080513\)
\(a_{66}=-0.313826890\) \(a_{67}=+0.386930850\) \(a_{68}=-0.620631648\) \(a_{69}=+0.925028594\) \(a_{70}=-0.082076075\)
\(a_{71}=+0.564480130\) \(a_{72}=+0.117851130\) \(a_{73}=+0.926272900\) \(a_{74}=-1.364412717\) \(a_{75}=-0.027050021\)
\(a_{76}=-0.805928279\) \(a_{77}=-0.091393896\) \(a_{78}=-0.000869991\) \(a_{79}=+0.574286997\) \(a_{80}=-0.244073246\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.026869056\) \(a_{83}=-0.959890001\) \(a_{84}=+0.034321068\) \(a_{85}=+1.211836646\)
\(a_{86}=+0.090138231\) \(a_{87}=-0.157247253\) \(a_{88}=-0.271782059\) \(a_{89}=+0.789800000\) \(a_{90}=-0.230114463\)
\(a_{91}=-0.000253362\) \(a_{92}=+0.801098262\) \(a_{93}=-0.415283009\) \(a_{94}=-1.372538725\) \(a_{95}=+1.573644247\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.984000206\) \(a_{98}=-0.697111666\) \(a_{99}=-0.256238583\) \(a_{100}=-0.023426005\)

Showing 100 of 108 available coefficients

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