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: \( 25.8102408383 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.172669766\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.829202744\) \(a_{7}=+0.024281501\) \(a_{8}=+0.353553391\) \(a_{9}=+0.375154380\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.709341650\) \(a_{12}=+0.586334883\) \(a_{13}=-0.239292134\) \(a_{14}=+0.017169614\) \(a_{15}=+0.524433862\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.882893704\) \(a_{18}=+0.265274206\) \(a_{19}=+0.534993775\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.028474182\) \(a_{22}=-0.501580291\) \(a_{23}=-1.325233530\) \(a_{24}=+0.414601372\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.169205091\) \(a_{27}=-0.732737567\) \(a_{28}=+0.012140750\) \(a_{29}=-0.347731088\) \(a_{30}=+0.370830740\)
\(a_{31}=-0.734200820\) \(a_{32}=+0.176776695\) \(a_{33}=-0.831823506\) \(a_{34}=-1.331406906\) \(a_{35}=+0.010859017\)
\(a_{36}=+0.187577190\) \(a_{37}=+0.355331801\) \(a_{38}=+0.378297726\) \(a_{39}=-0.280610651\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.505021374\) \(a_{42}=+0.020134287\) \(a_{43}=+1.246725222\) \(a_{44}=-0.354670825\) \(a_{45}=+0.167774139\)
\(a_{46}=-0.937081616\) \(a_{47}=-1.716560582\) \(a_{48}=+0.293167441\) \(a_{49}=-0.999410409\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.208012519\) \(a_{52}=-0.119646067\) \(a_{53}=+0.219785887\) \(a_{54}=-0.518123703\) \(a_{55}=-0.317227230\)
\(a_{56}=+0.008584807\) \(a_{57}=+0.627371025\) \(a_{58}=-0.245883011\) \(a_{59}=+0.352085884\) \(a_{60}=+0.262216931\)
\(a_{61}=+0.626065177\) \(a_{62}=-0.519158379\) \(a_{63}=+0.009109311\) \(a_{64}=+0.125000000\) \(a_{65}=-0.107014696\)
\(a_{66}=-0.588188042\) \(a_{67}=-0.819391851\) \(a_{68}=-0.941446852\) \(a_{69}=-1.554061294\) \(a_{70}=+0.007678485\)
\(a_{71}=+0.971776482\) \(a_{72}=+0.132637103\) \(a_{73}=-1.123366172\) \(a_{74}=+0.251257526\) \(a_{75}=+0.234533953\)
\(a_{76}=+0.267496888\) \(a_{77}=-0.017223880\) \(a_{78}=-0.198421694\) \(a_{79}=-0.663249673\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.234413571\) \(a_{82}=-0.357104038\) \(a_{83}=+1.308408829\) \(a_{84}=+0.014237091\) \(a_{85}=-0.842055663\)
\(a_{86}=+0.881567859\) \(a_{87}=-0.407773734\) \(a_{88}=-0.250790145\) \(a_{89}=-0.021858396\) \(a_{90}=+0.118634231\)
\(a_{91}=-0.005810372\) \(a_{92}=-0.662616765\) \(a_{93}=-0.860975104\) \(a_{94}=-1.213791628\) \(a_{95}=+0.239256490\)
\(a_{96}=+0.207300686\) \(a_{97}=-0.047115647\) \(a_{98}=-0.706689877\) \(a_{99}=-0.266112627\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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