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: \( 2.55636946085 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.487312018\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.344581633\) \(a_{7}=+1.517108060\) \(a_{8}=+0.353553391\) \(a_{9}=-0.762526997\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.791899182\) \(a_{12}=-0.243656009\) \(a_{13}=-0.112246479\) \(a_{14}=+1.072757397\) \(a_{15}=+0.217932560\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.408280720\) \(a_{18}=-0.539188010\) \(a_{19}=+0.736844585\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.739304990\) \(a_{22}=-0.559957282\) \(a_{23}=-0.317970899\) \(a_{24}=-0.172290816\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.079370246\) \(a_{27}=+0.858900588\) \(a_{28}=+0.758554030\) \(a_{29}=-1.490060799\) \(a_{30}=+0.154101591\)
\(a_{31}=+0.955018951\) \(a_{32}=+0.176776695\) \(a_{33}=+0.385901989\) \(a_{34}=+0.288698065\) \(a_{35}=-0.678471350\)
\(a_{36}=-0.381263498\) \(a_{37}=-0.419539974\) \(a_{38}=+0.521027803\) \(a_{39}=+0.054699058\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.154836229\) \(a_{42}=-0.522767572\) \(a_{43}=-0.906923136\) \(a_{44}=-0.395949591\) \(a_{45}=+0.341012440\)
\(a_{46}=-0.224839379\) \(a_{47}=+0.492278050\) \(a_{48}=-0.121828005\) \(a_{49}=+1.301616865\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.198960101\) \(a_{52}=-0.056123239\) \(a_{53}=+0.638587800\) \(a_{54}=+0.607334430\) \(a_{55}=+0.354148080\)
\(a_{56}=+0.536378698\) \(a_{57}=-0.359073222\) \(a_{58}=-1.053632095\) \(a_{59}=-0.738583630\) \(a_{60}=+0.108966280\)
\(a_{61}=-1.565414280\) \(a_{62}=+0.675300376\) \(a_{63}=-1.156835853\) \(a_{64}=+0.125000000\) \(a_{65}=+0.050198151\)
\(a_{66}=+0.272873913\) \(a_{67}=+0.413540006\) \(a_{68}=+0.204140360\) \(a_{69}=+0.154951040\) \(a_{70}=-0.479751693\)
\(a_{71}=+0.950606003\) \(a_{72}=-0.269594005\) \(a_{73}=+1.736350060\) \(a_{74}=-0.296659561\) \(a_{75}=-0.097462404\)
\(a_{76}=+0.368422292\) \(a_{77}=-1.201396631\) \(a_{78}=+0.038678075\) \(a_{79}=-0.002670000\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.343974418\) \(a_{82}=+0.109485747\) \(a_{83}=+0.857700348\) \(a_{84}=-0.369652495\) \(a_{85}=-0.182588689\)
\(a_{86}=-0.641291499\) \(a_{87}=+0.726124535\) \(a_{88}=-0.279978641\) \(a_{89}=-1.558200000\) \(a_{90}=+0.241132209\)
\(a_{91}=-0.170290038\) \(a_{92}=-0.158985449\) \(a_{93}=-0.465392212\) \(a_{94}=+0.348093147\) \(a_{95}=-0.329526916\)
\(a_{96}=-0.086145408\) \(a_{97}=+0.308998108\) \(a_{98}=+0.920382112\) \(a_{99}=+0.603844505\) \(a_{100}=+0.099975586\)

Showing 100 of 126 available coefficients

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