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: \( 23.742410121 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.994847992\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.703463761\) \(a_{7}=-0.914970427\) \(a_{8}=+0.353553391\) \(a_{9}=-0.010277473\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.294622625\) \(a_{12}=+0.497423996\) \(a_{13}=-1.121537571\) \(a_{14}=-0.646981793\) \(a_{15}=+0.444909547\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.114409380\) \(a_{18}=-0.007267271\) \(a_{19}=+0.624659166\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.910256492\) \(a_{22}=+0.208329656\) \(a_{23}=+0.018884910\) \(a_{24}=+0.351731881\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.793046822\) \(a_{27}=-1.005072515\) \(a_{28}=-0.457485213\) \(a_{29}=-1.030285034\) \(a_{30}=+0.314598558\)
\(a_{31}=+1.085126328\) \(a_{32}=+0.176776695\) \(a_{33}=+0.293104727\) \(a_{34}=-0.080899649\) \(a_{35}=-0.409187214\)
\(a_{36}=-0.005138737\) \(a_{37}=-1.075876546\) \(a_{38}=+0.441700732\) \(a_{39}=-1.115759400\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.025159033\) \(a_{42}=-0.643648538\) \(a_{43}=-1.404292714\) \(a_{44}=+0.147311313\) \(a_{45}=-0.004596226\)
\(a_{46}=+0.013353648\) \(a_{47}=+1.306794657\) \(a_{48}=+0.248711998\) \(a_{49}=-0.162829118\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.113819942\) \(a_{52}=-0.560768785\) \(a_{53}=-1.262467244\) \(a_{54}=-0.710693591\) \(a_{55}=+0.131759244\)
\(a_{56}=-0.323490897\) \(a_{57}=+0.621440917\) \(a_{58}=-0.728521534\) \(a_{59}=-0.400566648\) \(a_{60}=+0.222454774\)
\(a_{61}=-0.934993361\) \(a_{62}=+0.767300185\) \(a_{63}=+0.009403584\) \(a_{64}=+0.125000000\) \(a_{65}=-0.501566850\)
\(a_{66}=+0.207256340\) \(a_{67}=-0.507486724\) \(a_{68}=-0.057204690\) \(a_{69}=+0.018787615\) \(a_{70}=-0.289339054\)
\(a_{71}=+0.077778218\) \(a_{72}=-0.003633635\) \(a_{73}=-1.490018974\) \(a_{74}=-0.760759601\) \(a_{75}=+0.198969598\)
\(a_{76}=+0.312329583\) \(a_{77}=-0.269570989\) \(a_{78}=-0.788961038\) \(a_{79}=+0.102038861\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.989616900\) \(a_{82}=-0.724896904\) \(a_{83}=+1.612012499\) \(a_{84}=-0.455128246\) \(a_{85}=-0.051165430\)
\(a_{86}=-0.992984901\) \(a_{87}=-1.024976997\) \(a_{88}=+0.104164828\) \(a_{89}=+0.541683447\) \(a_{90}=-0.003250022\)
\(a_{91}=+1.026173710\) \(a_{92}=+0.009442455\) \(a_{93}=+1.079535749\) \(a_{94}=+0.924043364\) \(a_{95}=+0.279356072\)
\(a_{96}=+0.175865940\) \(a_{97}=+0.587738659\) \(a_{98}=-0.115137574\) \(a_{99}=-0.003027976\) \(a_{100}=+0.099975586\)

Showing 100 of 219 available coefficients

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