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: \( 24.3141784195 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.596250460\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.128719525\) \(a_{7}=+0.699720582\) \(a_{8}=-0.353553391\) \(a_{9}=+1.548015532\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.264423576\) \(a_{12}=+0.798125230\) \(a_{13}=-1.082894265\) \(a_{14}=-0.494777168\) \(a_{15}=-0.713864908\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.166795987\) \(a_{18}=-1.094612280\) \(a_{19}=-1.171799302\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.116929300\) \(a_{22}=-0.186975704\) \(a_{23}=+1.316965551\) \(a_{24}=-0.564359762\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.765721878\) \(a_{27}=+0.874770045\) \(a_{28}=+0.349860291\) \(a_{29}=-1.801030376\) \(a_{30}=+0.504778717\)
\(a_{31}=+0.794379223\) \(a_{32}=-0.176776695\) \(a_{33}=+0.422086255\) \(a_{34}=+0.117942573\) \(a_{35}=-0.312924557\)
\(a_{36}=+0.774007766\) \(a_{37}=-0.293564268\) \(a_{38}=+0.828587232\) \(a_{39}=-1.728570469\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.474135268\) \(a_{42}=-0.789788282\) \(a_{43}=-1.574611446\) \(a_{44}=+0.132211788\) \(a_{45}=-0.692293592\)
\(a_{46}=-0.931235272\) \(a_{47}=-1.399877685\) \(a_{48}=+0.399062615\) \(a_{49}=-0.510391108\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.266248171\) \(a_{52}=-0.541447132\) \(a_{53}=-0.169778281\) \(a_{54}=-0.618555831\) \(a_{55}=-0.118253818\)
\(a_{56}=-0.247388584\) \(a_{57}=-1.870485175\) \(a_{58}=+1.273520792\) \(a_{59}=-0.673130904\) \(a_{60}=-0.356932454\)
\(a_{61}=+0.253754580\) \(a_{62}=-0.561710935\) \(a_{63}=+1.083178328\) \(a_{64}=+0.125000000\) \(a_{65}=+0.484285038\)
\(a_{66}=-0.298460053\) \(a_{67}=+1.876530793\) \(a_{68}=-0.083397993\) \(a_{69}=+2.102206867\) \(a_{70}=+0.221271076\)
\(a_{71}=+0.642069648\) \(a_{72}=-0.547306140\) \(a_{73}=-1.834187215\) \(a_{74}=+0.207581284\) \(a_{75}=+0.319250092\)
\(a_{76}=-0.585899651\) \(a_{77}=+0.185022618\) \(a_{78}=+1.222283900\) \(a_{79}=+1.523050903\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.151663445\) \(a_{82}=-0.335264263\) \(a_{83}=-1.573849257\) \(a_{84}=+0.558464650\) \(a_{85}=+0.074593433\)
\(a_{86}=+1.113418431\) \(a_{87}=-2.874895567\) \(a_{88}=-0.093487852\) \(a_{89}=-0.827518466\) \(a_{90}=+0.489525493\)
\(a_{91}=-0.757723405\) \(a_{92}=+0.658482775\) \(a_{93}=+1.268028200\) \(a_{94}=+0.989863004\) \(a_{95}=+0.524044579\)
\(a_{96}=-0.282179881\) \(a_{97}=+1.432933078\) \(a_{98}=+0.360901013\) \(a_{99}=+0.409331803\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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