Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 26.6272055083 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.035526118\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.732227540\) \(a_{7}=+0.899601515\) \(a_{8}=-0.353553391\) \(a_{9}=+0.072314340\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.110089754\) \(a_{12}=-0.517763059\) \(a_{13}=-0.299780870\) \(a_{14}=-0.636114332\) \(a_{15}=+0.463101358\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.255886737\) \(a_{18}=-0.051133960\) \(a_{19}=+0.281396969\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.931560864\) \(a_{22}=-0.077845211\) \(a_{23}=+1.256026073\) \(a_{24}=+0.366113770\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.211977086\) \(a_{27}=+0.960642729\) \(a_{28}=+0.449800757\) \(a_{29}=+0.262330894\) \(a_{30}=-0.327462111\)
\(a_{31}=+0.149414119\) \(a_{32}=-0.176776695\) \(a_{33}=-0.114000815\) \(a_{34}=+0.180939247\) \(a_{35}=-0.402314028\)
\(a_{36}=+0.036157170\) \(a_{37}=-1.373861529\) \(a_{38}=-0.198977705\) \(a_{39}=+0.310430921\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.923527222\) \(a_{42}=+0.658713004\) \(a_{43}=+1.612877140\) \(a_{44}=+0.055044877\) \(a_{45}=-0.032339956\)
\(a_{46}=-0.888144553\) \(a_{47}=-0.788420253\) \(a_{48}=-0.258881529\) \(a_{49}=-0.190717114\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.264977399\) \(a_{52}=-0.149890435\) \(a_{53}=-0.932994449\) \(a_{54}=-0.679276988\) \(a_{55}=-0.049233635\)
\(a_{56}=-0.318057166\) \(a_{57}=-0.291393911\) \(a_{58}=-0.185495954\) \(a_{59}=+0.602132170\) \(a_{60}=+0.231550679\)
\(a_{61}=-1.432534532\) \(a_{62}=-0.105651737\) \(a_{63}=+0.065054090\) \(a_{64}=+0.125000000\) \(a_{65}=+0.134066081\)
\(a_{66}=+0.080610749\) \(a_{67}=+0.123822208\) \(a_{68}=-0.127943368\) \(a_{69}=-1.300647803\) \(a_{70}=+0.284478977\)
\(a_{71}=-0.103145266\) \(a_{72}=-0.025566980\) \(a_{73}=-0.223678650\) \(a_{74}=+0.971466804\) \(a_{75}=-0.207105224\)
\(a_{76}=+0.140698485\) \(a_{77}=+0.099036909\) \(a_{78}=-0.219507809\) \(a_{79}=+0.169020999\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.067084977\) \(a_{82}=-1.360139143\) \(a_{83}=+0.023737217\) \(a_{84}=-0.465780432\) \(a_{85}=+0.114436028\)
\(a_{86}=-1.140476363\) \(a_{87}=-0.271650493\) \(a_{88}=-0.038922606\) \(a_{89}=-1.790219921\) \(a_{90}=+0.022867802\)
\(a_{91}=-0.269683325\) \(a_{92}=+0.628013036\) \(a_{93}=-0.154722223\) \(a_{94}=+0.557497307\) \(a_{95}=-0.125844550\)
\(a_{96}=+0.183056885\) \(a_{97}=+0.189593671\) \(a_{98}=+0.134857365\) \(a_{99}=+0.007961068\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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