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: \( 30.3458704079 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.647468259\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.164935978\) \(a_{7}=+0.225871814\) \(a_{8}=-0.353553391\) \(a_{9}=+1.714151665\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.120503384\) \(a_{12}=-0.823734130\) \(a_{13}=-0.603816667\) \(a_{14}=-0.159715492\) \(a_{15}=-0.736770204\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.545014711\) \(a_{18}=-1.212088266\) \(a_{19}=-0.798889526\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.372116645\) \(a_{22}=-0.085208760\) \(a_{23}=+1.413986269\) \(a_{24}=+0.582467989\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.426962860\) \(a_{27}=-1.176542200\) \(a_{28}=+0.112935907\) \(a_{29}=+0.295981277\) \(a_{30}=+0.520975207\)
\(a_{31}=+0.357093024\) \(a_{32}=-0.176776695\) \(a_{33}=-0.198525500\) \(a_{34}=+0.385383598\) \(a_{35}=+0.101012946\)
\(a_{36}=+0.857075832\) \(a_{37}=-0.015357926\) \(a_{38}=+0.564900201\) \(a_{39}=+0.994768794\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.736846907\) \(a_{42}=+0.263126203\) \(a_{43}=-1.660082438\) \(a_{44}=+0.060251692\) \(a_{45}=+0.766591929\)
\(a_{46}=-0.999839279\) \(a_{47}=+1.771799288\) \(a_{48}=-0.411867065\) \(a_{49}=-0.948981924\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.897894437\) \(a_{52}=-0.301908334\) \(a_{53}=+1.245270962\) \(a_{54}=+0.831940968\) \(a_{55}=+0.053890751\)
\(a_{56}=-0.079857746\) \(a_{57}=+1.316145137\) \(a_{58}=-0.209290368\) \(a_{59}=+0.783304972\) \(a_{60}=-0.368385102\)
\(a_{61}=+1.293480912\) \(a_{62}=-0.252502899\) \(a_{63}=+0.387178546\) \(a_{64}=+0.125000000\) \(a_{65}=-0.270035023\)
\(a_{66}=+0.140378727\) \(a_{67}=-1.668042003\) \(a_{68}=-0.272507356\) \(a_{69}=-2.329497497\) \(a_{70}=-0.071426939\)
\(a_{71}=-1.600384803\) \(a_{72}=-0.606044133\) \(a_{73}=-0.877953162\) \(a_{74}=+0.010859694\) \(a_{75}=-0.329493652\)
\(a_{76}=-0.399444763\) \(a_{77}=+0.027218318\) \(a_{78}=-0.703407760\) \(a_{79}=+1.305981891\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.224164265\) \(a_{82}=-1.228136226\) \(a_{83}=+0.035722372\) \(a_{84}=-0.186058322\) \(a_{85}=-0.243737989\)
\(a_{86}=+1.173855549\) \(a_{87}=-0.487619759\) \(a_{88}=-0.042604380\) \(a_{89}=-0.584483389\) \(a_{90}=-0.542062352\)
\(a_{91}=-0.136385166\) \(a_{92}=+0.706993134\) \(a_{93}=-0.588299422\) \(a_{94}=-1.252851291\) \(a_{95}=-0.357274257\)
\(a_{96}=+0.291233994\) \(a_{97}=-0.247804529\) \(a_{98}=+0.671031553\) \(a_{99}=+0.206561076\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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