Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 22.5374419869 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.725143115\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.219860395\) \(a_{7}=+1.767650773\) \(a_{8}=+0.353553391\) \(a_{9}=+1.976118766\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.856304491\) \(a_{12}=-0.862571557\) \(a_{13}=+1.577969623\) \(a_{14}=+1.249917849\) \(a_{15}=+0.771507455\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.866003957\) \(a_{18}=+1.397326980\) \(a_{19}=+0.597896770\) \(a_{20}=-0.223606798\)
\(a_{21}=-3.049450560\) \(a_{22}=+0.605498713\) \(a_{23}=-0.210893853\) \(a_{24}=-0.609930197\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.115793021\) \(a_{27}=-1.683944567\) \(a_{28}=+0.883825387\) \(a_{29}=+0.393556592\) \(a_{30}=+0.545538153\)
\(a_{31}=+1.349810620\) \(a_{32}=+0.176776695\) \(a_{33}=-1.477247797\) \(a_{34}=+0.612357270\) \(a_{35}=-0.790517458\)
\(a_{36}=+0.988059383\) \(a_{37}=-1.200143133\) \(a_{38}=+0.422776860\) \(a_{39}=-2.722223429\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.774236886\) \(a_{42}=-2.156287170\) \(a_{43}=+0.237204880\) \(a_{44}=+0.428152246\) \(a_{45}=-0.883747178\)
\(a_{46}=-0.149124473\) \(a_{47}=-0.695481853\) \(a_{48}=-0.431285779\) \(a_{49}=+2.124589256\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.493980763\) \(a_{52}=+0.788984811\) \(a_{53}=+1.234603462\) \(a_{54}=-1.190728623\) \(a_{55}=-0.382951010\)
\(a_{56}=+0.624958924\) \(a_{57}=-1.031457495\) \(a_{58}=+0.278286535\) \(a_{59}=-1.027911287\) \(a_{60}=+0.385753727\)
\(a_{61}=+0.243581416\) \(a_{62}=+0.954460242\) \(a_{63}=+3.493087864\) \(a_{64}=+0.125000000\) \(a_{65}=-0.705689469\)
\(a_{66}=-1.044571935\) \(a_{67}=-0.287435881\) \(a_{68}=+0.433001978\) \(a_{69}=+0.363822078\) \(a_{70}=-0.558980255\)
\(a_{71}=+1.270778922\) \(a_{72}=+0.698663490\) \(a_{73}=+1.267644201\) \(a_{74}=-0.848629348\) \(a_{75}=-0.345028623\)
\(a_{76}=+0.298948385\) \(a_{77}=+1.513647296\) \(a_{78}=-1.924902647\) \(a_{79}=+0.280217712\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.928926610\) \(a_{82}=-0.547468152\) \(a_{83}=-1.121584023\) \(a_{84}=-1.524725280\) \(a_{85}=-0.387288743\)
\(a_{86}=+0.167729179\) \(a_{87}=-0.678941444\) \(a_{88}=+0.302749356\) \(a_{89}=-0.052452080\) \(a_{90}=-0.624903623\)
\(a_{91}=+2.789299224\) \(a_{92}=-0.105446926\) \(a_{93}=-2.328616496\) \(a_{94}=-0.491779934\) \(a_{95}=-0.267387564\)
\(a_{96}=-0.304965099\) \(a_{97}=-1.016542960\) \(a_{98}=+1.502311470\) \(a_{99}=+1.692159374\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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