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: \( 21.0684479685 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.074511105\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.759794088\) \(a_{7}=+1.337939998\) \(a_{8}=-0.353553391\) \(a_{9}=+0.154574114\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.123047404\) \(a_{12}=+0.537255552\) \(a_{13}=-0.821838971\) \(a_{14}=-0.946066446\) \(a_{15}=-0.480535974\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.136449536\) \(a_{18}=-0.109300404\) \(a_{19}=-0.664394327\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.437631385\) \(a_{22}=+0.087007654\) \(a_{23}=-0.019333744\) \(a_{24}=-0.379897044\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.581127909\) \(a_{27}=-0.908419503\) \(a_{28}=+0.668969999\) \(a_{29}=-0.984025536\) \(a_{30}=+0.339790246\)
\(a_{31}=-0.526000488\) \(a_{32}=-0.176776695\) \(a_{33}=-0.132215802\) \(a_{34}=-0.803591174\) \(a_{35}=-0.598344957\)
\(a_{36}=+0.077287057\) \(a_{37}=-1.852337874\) \(a_{38}=+0.469797734\) \(a_{39}=-0.883075101\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.083764353\) \(a_{42}=-1.016558901\) \(a_{43}=+1.299307531\) \(a_{44}=-0.061523702\) \(a_{45}=-0.069127645\)
\(a_{46}=+0.013671022\) \(a_{47}=+1.748274337\) \(a_{48}=+0.268627776\) \(a_{49}=+0.790083439\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.221127646\) \(a_{52}=-0.410919486\) \(a_{53}=-0.673310265\) \(a_{54}=+0.642349591\) \(a_{55}=+0.055028472\)
\(a_{56}=-0.473033223\) \(a_{57}=-0.713899082\) \(a_{58}=+0.695811129\) \(a_{59}=-0.438120327\) \(a_{60}=-0.240267987\)
\(a_{61}=+0.162151615\) \(a_{62}=+0.371938512\) \(a_{63}=+0.206810890\) \(a_{64}=+0.125000000\) \(a_{65}=+0.367537561\)
\(a_{66}=+0.093490690\) \(a_{67}=-0.497297589\) \(a_{68}=+0.568224768\) \(a_{69}=-0.020774323\) \(a_{70}=+0.423093777\)
\(a_{71}=-0.533658070\) \(a_{72}=-0.054650202\) \(a_{73}=+1.219113628\) \(a_{74}=+1.309800672\) \(a_{75}=+0.214902221\)
\(a_{76}=-0.332197163\) \(a_{77}=-0.164630043\) \(a_{78}=+0.624428392\) \(a_{79}=+0.326991505\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.130680957\) \(a_{82}=+0.766337123\) \(a_{83}=+1.486325392\) \(a_{84}=+0.718815693\) \(a_{85}=-0.508235683\)
\(a_{86}=-0.918749166\) \(a_{87}=-1.057346365\) \(a_{88}=+0.043503827\) \(a_{89}=-1.278577329\) \(a_{90}=+0.048880627\)
\(a_{91}=-1.099571232\) \(a_{92}=-0.009666872\) \(a_{93}=-0.565193365\) \(a_{94}=-1.236216639\) \(a_{95}=+0.297126176\)
\(a_{96}=-0.189948522\) \(a_{97}=+1.673035292\) \(a_{98}=-0.558673358\) \(a_{99}=-0.019019943\) \(a_{100}=+0.099975586\)

Showing 100 of 206 available coefficients

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