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: \( 6.67376039246 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.288826447\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.911337920\) \(a_{7}=+1.198128217\) \(a_{8}=+0.353553391\) \(a_{9}=+0.661073610\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.178577678\) \(a_{12}=+0.644413223\) \(a_{13}=+1.223833478\) \(a_{14}=+0.847204587\) \(a_{15}=-0.576380709\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.638928339\) \(a_{18}=+0.467449633\) \(a_{19}=+0.303324089\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.544179332\) \(a_{22}=+0.126273487\) \(a_{23}=-1.891271380\) \(a_{24}=+0.455668960\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.865380952\) \(a_{27}=-0.436817295\) \(a_{28}=+0.599064108\) \(a_{29}=+0.396206980\) \(a_{30}=-0.407562708\)
\(a_{31}=-1.119329096\) \(a_{32}=+0.176776695\) \(a_{33}=+0.230155634\) \(a_{34}=-1.158897342\) \(a_{35}=-0.535819228\)
\(a_{36}=+0.330536805\) \(a_{37}=+0.677443778\) \(a_{38}=+0.214482520\) \(a_{39}=+1.577308954\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.175219012\) \(a_{42}=+1.091899677\) \(a_{43}=-1.174580737\) \(a_{44}=+0.089288839\) \(a_{45}=-0.295641106\)
\(a_{46}=-1.337330818\) \(a_{47}=+0.530510713\) \(a_{48}=+0.322206612\) \(a_{49}=+0.435511224\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.112294188\) \(a_{52}=+0.611916739\) \(a_{53}=-0.040819091\) \(a_{54}=-0.308876471\) \(a_{55}=-0.079862365\)
\(a_{56}=+0.423602293\) \(a_{57}=+0.390932108\) \(a_{58}=+0.280160642\) \(a_{59}=+1.744273206\) \(a_{60}=-0.288190355\)
\(a_{61}=-0.084819501\) \(a_{62}=-0.791485194\) \(a_{63}=+0.792050946\) \(a_{64}=+0.125000000\) \(a_{65}=-0.547314970\)
\(a_{66}=+0.162744609\) \(a_{67}=+1.399580625\) \(a_{68}=-0.819464170\) \(a_{69}=-2.437520573\) \(a_{70}=-0.378881409\)
\(a_{71}=-0.450207317\) \(a_{72}=+0.233724816\) \(a_{73}=+0.021212320\) \(a_{74}=+0.479025089\) \(a_{75}=+0.257765289\)
\(a_{76}=+0.151662045\) \(a_{77}=+0.213958954\) \(a_{78}=+1.115325857\) \(a_{79}=+0.291414880\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.224055292\) \(a_{82}=-0.123898552\) \(a_{83}=-0.226413900\) \(a_{84}=+0.772089666\) \(a_{85}=+0.732951035\)
\(a_{86}=-0.830554004\) \(a_{87}=+0.510642034\) \(a_{88}=+0.063136743\) \(a_{89}=+0.138121000\) \(a_{90}=-0.209049831\)
\(a_{91}=+1.466309423\) \(a_{92}=-0.945635690\) \(a_{93}=-1.442620941\) \(a_{94}=+0.375127723\) \(a_{95}=-0.135650656\)
\(a_{96}=+0.227834480\) \(a_{97}=+1.136899948\) \(a_{98}=+0.307952939\) \(a_{99}=+0.118052990\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

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