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: \( 11.4177272153 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.935440518\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.661456334\) \(a_{7}=+0.504930466\) \(a_{8}=+0.353553391\) \(a_{9}=-0.124951037\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.302129301\) \(a_{12}=+0.467720259\) \(a_{13}=+0.581158602\) \(a_{14}=+0.357039757\) \(a_{15}=+0.418341718\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.514298998\) \(a_{18}=-0.088353725\) \(a_{19}=-1.159742018\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.472332417\) \(a_{22}=+0.920744459\) \(a_{23}=+0.918436777\) \(a_{24}=+0.330728167\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.410941188\) \(a_{27}=-1.052324781\) \(a_{28}=+0.252465233\) \(a_{29}=+1.401997950\) \(a_{30}=+0.295812265\)
\(a_{31}=+1.190428166\) \(a_{32}=+0.176776695\) \(a_{33}=+1.218064508\) \(a_{34}=-0.363664309\) \(a_{35}=+0.225811769\)
\(a_{36}=-0.062475518\) \(a_{37}=+0.755986385\) \(a_{38}=-0.820061446\) \(a_{39}=+0.543639304\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.477738292\) \(a_{42}=+0.333989455\) \(a_{43}=-1.248819864\) \(a_{44}=+0.651064650\) \(a_{45}=-0.055879802\)
\(a_{46}=+0.649432873\) \(a_{47}=+1.844205084\) \(a_{48}=+0.233860130\) \(a_{49}=-0.745045225\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.481096121\) \(a_{52}=+0.290579301\) \(a_{53}=-0.577654357\) \(a_{54}=-0.744105989\) \(a_{55}=+0.582329926\)
\(a_{56}=+0.178519878\) \(a_{57}=-1.084869675\) \(a_{58}=+0.991362257\) \(a_{59}=-1.166768114\) \(a_{60}=+0.209170859\)
\(a_{61}=+0.139542988\) \(a_{62}=+0.841759829\) \(a_{63}=-0.063091585\) \(a_{64}=+0.125000000\) \(a_{65}=+0.259902028\)
\(a_{66}=+0.861301674\) \(a_{67}=-0.781761486\) \(a_{68}=-0.257149499\) \(a_{69}=+0.859142975\) \(a_{70}=+0.159673033\)
\(a_{71}=-1.898137958\) \(a_{72}=-0.044176863\) \(a_{73}=+0.739473969\) \(a_{74}=+0.534563099\) \(a_{75}=+0.187088104\)
\(a_{76}=-0.579871009\) \(a_{77}=+0.657484755\) \(a_{78}=+0.384411038\) \(a_{79}=-1.366024241\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.859436202\) \(a_{82}=-0.337811986\) \(a_{83}=+0.535031880\) \(a_{84}=+0.236166208\) \(a_{85}=-0.230001504\)
\(a_{86}=-0.883048995\) \(a_{87}=+1.311485692\) \(a_{88}=+0.460372229\) \(a_{89}=-0.790896341\) \(a_{90}=-0.039512987\)
\(a_{91}=+0.293444686\) \(a_{92}=+0.459218388\) \(a_{93}=+1.113574724\) \(a_{94}=+1.304049921\) \(a_{95}=-0.518652398\)
\(a_{96}=+0.165364083\) \(a_{97}=-0.328176228\) \(a_{98}=-0.526826531\) \(a_{99}=-0.162702404\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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