Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.9495532252 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.337118998\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.238379129\) \(a_{7}=+0.668379007\) \(a_{8}=+0.353553391\) \(a_{9}=-0.886350781\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.607042549\) \(a_{12}=+0.168559499\) \(a_{13}=+0.908280515\) \(a_{14}=+0.472615328\) \(a_{15}=-0.150764199\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.309308904\) \(a_{18}=-0.626744648\) \(a_{19}=-1.442551474\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.225323261\) \(a_{22}=+1.136350684\) \(a_{23}=-0.846796355\) \(a_{24}=+0.119189565\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.642251311\) \(a_{27}=-0.635924685\) \(a_{28}=+0.334189503\) \(a_{29}=+0.094267163\) \(a_{30}=-0.106606387\)
\(a_{31}=-1.751210696\) \(a_{32}=+0.176776695\) \(a_{33}=+0.541764573\) \(a_{34}=-0.925821205\) \(a_{35}=-0.298908179\)
\(a_{36}=-0.443175391\) \(a_{37}=+0.993621817\) \(a_{38}=-1.020037930\) \(a_{39}=+0.306198617\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.767219665\) \(a_{42}=+0.159327606\) \(a_{43}=+0.653050755\) \(a_{44}=+0.803521275\) \(a_{45}=+0.396388120\)
\(a_{46}=-0.598775445\) \(a_{47}=-1.500392345\) \(a_{48}=+0.084279749\) \(a_{49}=-0.553269503\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.441392905\) \(a_{52}=+0.454140257\) \(a_{53}=+1.551652346\) \(a_{54}=-0.449666657\) \(a_{55}=-0.718691277\)
\(a_{56}=+0.236307664\) \(a_{57}=-0.486311507\) \(a_{58}=+0.066656950\) \(a_{59}=-0.563187637\) \(a_{60}=-0.075382100\)
\(a_{61}=+1.666990929\) \(a_{62}=-1.238292958\) \(a_{63}=-0.592418255\) \(a_{64}=+0.125000000\) \(a_{65}=-0.406195395\)
\(a_{66}=+0.383085404\) \(a_{67}=+0.318120322\) \(a_{68}=-0.654654452\) \(a_{69}=-0.285471138\) \(a_{70}=-0.211360000\)
\(a_{71}=-0.738333051\) \(a_{72}=-0.313372324\) \(a_{73}=-0.275772194\) \(a_{74}=+0.702596725\) \(a_{75}=+0.067423800\)
\(a_{76}=-0.721275737\) \(a_{77}=+1.074113503\) \(a_{78}=+0.216515118\) \(a_{79}=-1.352404509\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.671968489\) \(a_{82}=+0.542506228\) \(a_{83}=-1.261122922\) \(a_{84}=+0.112661630\) \(a_{85}=+0.585540743\)
\(a_{86}=+0.461776617\) \(a_{87}=+0.031779251\) \(a_{88}=+0.568175342\) \(a_{89}=+1.048001008\) \(a_{90}=+0.280288728\)
\(a_{91}=+0.607075628\) \(a_{92}=-0.423398178\) \(a_{93}=-0.590366394\) \(a_{94}=-1.060937602\) \(a_{95}=+0.645128631\)
\(a_{96}=+0.059594782\) \(a_{97}=-1.844826507\) \(a_{98}=-0.391220618\) \(a_{99}=-1.424403420\) \(a_{100}=+0.099975586\)

Showing 100 of 249 available coefficients

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