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: \( 23.3561291756 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.825387800\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.290744091\) \(a_{7}=-1.062178660\) \(a_{8}=-0.353553391\) \(a_{9}=+2.332040619\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.114816868\) \(a_{12}=+0.912693900\) \(a_{13}=+1.366139368\) \(a_{14}=+0.751073733\) \(a_{15}=+0.816338241\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.082587517\) \(a_{18}=-1.649001736\) \(a_{19}=-0.882625424\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.938887967\) \(a_{22}=-0.788294567\) \(a_{23}=+0.953598440\) \(a_{24}=-0.645372046\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.966006411\) \(a_{27}=+2.431490695\) \(a_{28}=-0.531089330\) \(a_{29}=+0.169897483\) \(a_{30}=-0.577238306\)
\(a_{31}=-1.520339692\) \(a_{32}=-0.176776695\) \(a_{33}=+2.034973109\) \(a_{34}=-0.765504975\) \(a_{35}=-0.475020737\)
\(a_{36}=+1.166020310\) \(a_{37}=-0.766948320\) \(a_{38}=+0.624110423\) \(a_{39}=+2.493734135\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.304873156\) \(a_{42}=+1.371000829\) \(a_{43}=+0.955047071\) \(a_{44}=+0.557408434\) \(a_{45}=+1.042920270\)
\(a_{46}=-0.674295923\) \(a_{47}=+0.831933369\) \(a_{48}=+0.456346950\) \(a_{49}=+0.128223505\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.976142046\) \(a_{52}=+0.683069684\) \(a_{53}=+1.337200236\) \(a_{54}=-1.719323559\) \(a_{55}=+0.498561260\)
\(a_{56}=+0.375536867\) \(a_{57}=-1.611133681\) \(a_{58}=-0.120135662\) \(a_{59}=-0.189366510\) \(a_{60}=+0.408169121\)
\(a_{61}=-1.586710465\) \(a_{62}=+1.075042506\) \(a_{63}=-2.477043779\) \(a_{64}=+0.125000000\) \(a_{65}=+0.610956099\)
\(a_{66}=-1.438943285\) \(a_{67}=-1.369532425\) \(a_{68}=+0.541293759\) \(a_{69}=+1.740686958\) \(a_{70}=+0.335890385\)
\(a_{71}=+0.644999357\) \(a_{72}=-0.824500868\) \(a_{73}=-0.448936249\) \(a_{74}=+0.542314358\) \(a_{75}=+0.365077560\)
\(a_{76}=-0.441312712\) \(a_{77}=-1.184134687\) \(a_{78}=-1.763336317\) \(a_{79}=+1.859669162\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.106372831\) \(a_{82}=+0.215577876\) \(a_{83}=-0.223388909\) \(a_{84}=-0.969443983\) \(a_{85}=+0.484147856\)
\(a_{86}=-0.675320260\) \(a_{87}=+0.310128792\) \(a_{88}=-0.394147284\) \(a_{89}=+0.255985082\) \(a_{90}=-0.737455995\)
\(a_{91}=-1.451084083\) \(a_{92}=+0.476799220\) \(a_{93}=-2.775209524\) \(a_{94}=-0.588265727\) \(a_{95}=-0.394722089\)
\(a_{96}=-0.322686023\) \(a_{97}=+0.794571274\) \(a_{98}=-0.090667710\) \(a_{99}=+2.599798219\) \(a_{100}=+0.099975586\)

Showing 100 of 217 available coefficients

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