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: \( 10.4363421604 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.358604350\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.960678349\) \(a_{7}=-1.517857988\) \(a_{8}=-0.353553391\) \(a_{9}=+0.845805781\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.422822856\) \(a_{12}=-0.679302175\) \(a_{13}=-1.659263885\) \(a_{14}=+1.073287676\) \(a_{15}=-0.607586336\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.509665516\) \(a_{18}=-0.598075003\) \(a_{19}=-0.212122258\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.062168466\) \(a_{22}=+1.006087690\) \(a_{23}=-0.472358723\) \(a_{24}=+0.480339175\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.173276745\) \(a_{27}=+0.209488937\) \(a_{28}=-0.758928994\) \(a_{29}=+0.987238505\) \(a_{30}=+0.429628419\)
\(a_{31}=-1.130489963\) \(a_{32}=-0.176776695\) \(a_{33}=+1.933053322\) \(a_{34}=+0.360387942\) \(a_{35}=-0.678806728\)
\(a_{36}=+0.422902890\) \(a_{37}=-1.030951848\) \(a_{38}=+0.149993087\) \(a_{39}=+2.254283132\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.405257393\) \(a_{42}=-1.458173306\) \(a_{43}=-0.598466278\) \(a_{44}=-0.711411428\) \(a_{45}=+0.378255844\)
\(a_{46}=+0.334008056\) \(a_{47}=-0.285137600\) \(a_{48}=-0.339651088\) \(a_{49}=+1.303892872\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.692433787\) \(a_{52}=-0.829631942\) \(a_{53}=+0.866780956\) \(a_{54}=-0.148131048\) \(a_{55}=-0.636305725\)
\(a_{56}=+0.536643838\) \(a_{57}=+0.288190223\) \(a_{58}=-0.698083042\) \(a_{59}=+0.141125513\) \(a_{60}=-0.303793168\)
\(a_{61}=+0.770282295\) \(a_{62}=+0.799377119\) \(a_{63}=-1.283813061\) \(a_{64}=+0.125000000\) \(a_{65}=-0.742045368\)
\(a_{66}=-1.366875112\) \(a_{67}=+0.079332639\) \(a_{68}=-0.254832758\) \(a_{69}=+0.641748616\) \(a_{70}=+0.479988841\)
\(a_{71}=+0.165556355\) \(a_{72}=-0.299037502\) \(a_{73}=+1.780711691\) \(a_{74}=+0.728993043\) \(a_{75}=-0.271720870\)
\(a_{76}=-0.106061129\) \(a_{77}=+2.159643034\) \(a_{78}=-1.594018889\) \(a_{79}=-0.442401821\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.130418362\) \(a_{82}=-0.286560251\) \(a_{83}=-1.551860306\) \(a_{84}=+1.031084233\) \(a_{85}=-0.227929348\)
\(a_{86}=+0.423179563\) \(a_{87}=-1.341266549\) \(a_{88}=+0.503043845\) \(a_{89}=-1.255093165\) \(a_{90}=-0.267467273\)
\(a_{91}=+2.518526931\) \(a_{92}=-0.236179362\) \(a_{93}=+1.535888509\) \(a_{94}=+0.201622731\) \(a_{95}=-0.094863958\)
\(a_{96}=+0.240169587\) \(a_{97}=-0.025591087\) \(a_{98}=-0.921991492\) \(a_{99}=-1.203432128\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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