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: \( 22.9121308668 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.406756056\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.994726746\) \(a_{7}=-1.494252299\) \(a_{8}=+0.353553391\) \(a_{9}=+0.978962600\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.926257167\) \(a_{12}=-0.703378028\) \(a_{13}=-0.979676554\) \(a_{14}=-1.056595933\) \(a_{15}=-0.629120434\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.883178897\) \(a_{18}=+0.692231093\) \(a_{19}=-1.352316746\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.102048470\) \(a_{22}=+0.654962724\) \(a_{23}=+0.483836290\) \(a_{24}=-0.497363373\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.692735935\) \(a_{27}=+0.029594490\) \(a_{28}=-0.747126149\) \(a_{29}=+0.563574328\) \(a_{30}=-0.444855325\)
\(a_{31}=-1.208063225\) \(a_{32}=+0.176776695\) \(a_{33}=-1.303017879\) \(a_{34}=+1.331608569\) \(a_{35}=-0.668249943\)
\(a_{36}=+0.489481300\) \(a_{37}=+0.109694222\) \(a_{38}=-0.956232341\) \(a_{39}=+1.378165925\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.587978595\) \(a_{42}=+1.486372728\) \(a_{43}=-0.051947945\) \(a_{44}=+0.463128584\) \(a_{45}=+0.437805384\)
\(a_{46}=+0.342123922\) \(a_{47}=+0.851538651\) \(a_{48}=-0.351689014\) \(a_{49}=+1.232789933\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.649173318\) \(a_{52}=-0.489838277\) \(a_{53}=+0.361023677\) \(a_{54}=+0.020926465\) \(a_{55}=+0.414234798\)
\(a_{56}=-0.528297967\) \(a_{57}=+1.902379771\) \(a_{58}=+0.398507229\) \(a_{59}=-1.475065344\) \(a_{60}=-0.314560217\)
\(a_{61}=+1.497736714\) \(a_{62}=-0.854229698\) \(a_{63}=-1.462817115\) \(a_{64}=+0.125000000\) \(a_{65}=-0.438124674\)
\(a_{66}=-0.921372778\) \(a_{67}=-0.052470200\) \(a_{68}=+0.941589449\) \(a_{69}=-0.680639631\) \(a_{70}=-0.472524066\)
\(a_{71}=-0.702952933\) \(a_{72}=+0.346115546\) \(a_{73}=-0.164900949\) \(a_{74}=+0.077565528\) \(a_{75}=-0.281351211\)
\(a_{76}=-0.676158373\) \(a_{77}=-1.384061902\) \(a_{78}=+0.974510471\) \(a_{79}=-0.963847604\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.020594828\) \(a_{82}=+1.122870433\) \(a_{83}=+1.346772062\) \(a_{84}=+1.051024235\) \(a_{85}=+0.842183206\)
\(a_{86}=-0.036732744\) \(a_{87}=-0.792811598\) \(a_{88}=+0.327481362\) \(a_{89}=-1.622109778\) \(a_{90}=+0.309575156\)
\(a_{91}=+1.463883943\) \(a_{92}=+0.241918145\) \(a_{93}=+1.699450257\) \(a_{94}=+0.602128755\) \(a_{95}=-0.604774434\)
\(a_{96}=-0.248681687\) \(a_{97}=-1.033850827\) \(a_{98}=+0.871714121\) \(a_{99}=+0.906771125\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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