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: \( 24.5476372745 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.949202860\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.671187779\) \(a_{7}=-1.927448864\) \(a_{8}=+0.353553391\) \(a_{9}=-0.099013930\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.066689473\) \(a_{12}=-0.474601430\) \(a_{13}=+1.616760056\) \(a_{14}=-1.362912162\) \(a_{15}=-0.424496424\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.871708397\) \(a_{18}=-0.070013421\) \(a_{19}=+1.604203703\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.829539975\) \(a_{22}=-0.047156579\) \(a_{23}=+0.344538103\) \(a_{24}=-0.335593890\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.143221999\) \(a_{27}=+1.043187166\) \(a_{28}=-0.963724432\) \(a_{29}=+0.889978156\) \(a_{30}=-0.300164300\)
\(a_{31}=-1.569447546\) \(a_{32}=+0.176776695\) \(a_{33}=+0.063301838\) \(a_{34}=-0.616390919\) \(a_{35}=-0.861981337\)
\(a_{36}=-0.049506965\) \(a_{37}=+0.317753478\) \(a_{38}=+1.134343317\) \(a_{39}=-1.534633269\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.407356019\) \(a_{42}=+1.293680123\) \(a_{43}=+0.646194066\) \(a_{44}=-0.033344736\) \(a_{45}=-0.044280376\)
\(a_{46}=+0.243625229\) \(a_{47}=-1.068969176\) \(a_{48}=-0.237300715\) \(a_{49}=+2.715059124\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.827428104\) \(a_{52}=+0.808380028\) \(a_{53}=+0.845422053\) \(a_{54}=+0.737644719\) \(a_{55}=-0.029824439\)
\(a_{56}=-0.681456081\) \(a_{57}=-1.522714743\) \(a_{58}=+0.629309589\) \(a_{59}=+0.806137428\) \(a_{60}=-0.212248212\)
\(a_{61}=-1.123951690\) \(a_{62}=-1.109767003\) \(a_{63}=+0.190844287\) \(a_{64}=+0.125000000\) \(a_{65}=+0.723037078\)
\(a_{66}=+0.044761159\) \(a_{67}=+0.085553433\) \(a_{68}=-0.435854199\) \(a_{69}=-0.327036552\) \(a_{70}=-0.609512848\)
\(a_{71}=+0.348270964\) \(a_{72}=-0.035006711\) \(a_{73}=-0.465356761\) \(a_{74}=+0.224685639\) \(a_{75}=-0.189840572\)
\(a_{76}=+0.802101851\) \(a_{77}=+0.128540549\) \(a_{78}=-1.085149591\) \(a_{79}=-0.820375759\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.891182312\) \(a_{82}=-0.995150984\) \(a_{83}=-0.133260437\) \(a_{84}=+0.914769987\) \(a_{85}=-0.389839847\)
\(a_{86}=+0.456928206\) \(a_{87}=-0.844769811\) \(a_{88}=-0.023578289\) \(a_{89}=+0.366243406\) \(a_{90}=-0.031310954\)
\(a_{91}=-3.116222333\) \(a_{92}=+0.172269051\) \(a_{93}=+1.489724100\) \(a_{94}=-0.755875353\) \(a_{95}=+0.717421706\)
\(a_{96}=-0.167796945\) \(a_{97}=-0.489852752\) \(a_{98}=+1.919836718\) \(a_{99}=+0.006603187\) \(a_{100}=+0.099975586\)

Showing 100 of 223 available coefficients

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