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: \( 12.0150070407 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.505075638\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.064249190\) \(a_{7}=-1.564071733\) \(a_{8}=-0.353553391\) \(a_{9}=+1.265252678\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.242956793\) \(a_{12}=-0.752537819\) \(a_{13}=+0.021811658\) \(a_{14}=+1.105965729\) \(a_{15}=+0.673090288\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.775103937\) \(a_{18}=-0.894668748\) \(a_{19}=+1.549663754\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.354046262\) \(a_{22}=-0.878903177\) \(a_{23}=-0.824733725\) \(a_{24}=+0.532124595\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.015423171\) \(a_{27}=-0.399225343\) \(a_{28}=-0.782035866\) \(a_{29}=-1.405887307\) \(a_{30}=-0.475946707\)
\(a_{31}=+0.532443419\) \(a_{32}=-0.176776695\) \(a_{33}=-1.870743990\) \(a_{34}=-0.548081250\) \(a_{35}=+0.699474143\)
\(a_{36}=+0.632626339\) \(a_{37}=+0.027001262\) \(a_{38}=-1.095777749\) \(a_{39}=-0.032828195\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.391224231\) \(a_{42}=-1.664562075\) \(a_{43}=+0.851446279\) \(a_{44}=+0.621478397\) \(a_{45}=-0.565838199\)
\(a_{46}=+0.583174809\) \(a_{47}=-0.668496874\) \(a_{48}=-0.376268910\) \(a_{49}=+1.446320386\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.166590053\) \(a_{52}=+0.010905829\) \(a_{53}=+1.206791580\) \(a_{54}=+0.282294947\) \(a_{55}=-0.555867177\)
\(a_{56}=+0.552982864\) \(a_{57}=-2.332361164\) \(a_{58}=+0.994112449\) \(a_{59}=+0.902244675\) \(a_{60}=+0.336545144\)
\(a_{61}=-1.001160630\) \(a_{62}=-0.376494352\) \(a_{63}=-1.978945948\) \(a_{64}=+0.125000000\) \(a_{65}=-0.009754470\)
\(a_{66}=+1.322815761\) \(a_{67}=+0.111558910\) \(a_{68}=+0.387551969\) \(a_{69}=+1.241286637\) \(a_{70}=-0.494602910\)
\(a_{71}=+1.902004605\) \(a_{72}=-0.447334374\) \(a_{73}=-0.521703378\) \(a_{74}=-0.019092776\) \(a_{75}=-0.301015128\)
\(a_{76}=+0.774831877\) \(a_{77}=-1.944073584\) \(a_{78}=+0.023213039\) \(a_{79}=-1.679075684\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.664388335\) \(a_{82}=+0.983744088\) \(a_{83}=+0.171954657\) \(a_{84}=+1.177023131\) \(a_{85}=-0.346637019\)
\(a_{86}=-0.602063438\) \(a_{87}=+2.115966729\) \(a_{88}=-0.439451589\) \(a_{89}=+0.144597440\) \(a_{90}=+0.400108028\)
\(a_{91}=-0.034115019\) \(a_{92}=-0.412366862\) \(a_{93}=-0.801367722\) \(a_{94}=+0.472698673\) \(a_{95}=-0.693030699\)
\(a_{96}=+0.266062298\) \(a_{97}=-0.126102379\) \(a_{98}=-1.022702953\) \(a_{99}=+1.572654500\) \(a_{100}=+0.099975586\)

Showing 100 of 148 available coefficients

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