Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 13.1778468571 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.470443478\)
\(a_{6}=-0.408248290\) \(a_{7}=+0.926637007\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.332653773\)
\(a_{11}=-1.466235919\) \(a_{12}=-0.288675135\) \(a_{13}=+0.267936828\) \(a_{14}=+0.655231311\) \(a_{15}=+0.271610669\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.457720836\) \(a_{18}=+0.235702260\) \(a_{19}=+0.392797446\) \(a_{20}=-0.235221739\)
\(a_{21}=-0.534994125\) \(a_{22}=-1.036785361\) \(a_{23}=-1.399559169\) \(a_{24}=-0.204124145\) \(a_{25}=-0.778682934\)
\(a_{26}=+0.189459948\) \(a_{27}=-0.192450090\) \(a_{28}=+0.463318504\) \(a_{29}=-1.109616249\) \(a_{30}=+0.192057745\)
\(a_{31}=-1.119446646\) \(a_{32}=+0.176776696\) \(a_{33}=+0.846531701\) \(a_{34}=-1.030764287\) \(a_{35}=-0.435930336\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.135735546\) \(a_{38}=+0.277749738\) \(a_{39}=-0.154693400\) \(a_{40}=-0.166326887\)
\(a_{41}=+1.535407184\) \(a_{42}=-0.378297974\) \(a_{43}=-0.603214265\) \(a_{44}=-0.733117960\) \(a_{45}=-0.156814493\)
\(a_{46}=-0.989637779\) \(a_{47}=+1.511497212\) \(a_{48}=-0.144337567\) \(a_{49}=-0.141343857\) \(a_{50}=-0.550611983\)
\(a_{51}=+0.841615517\) \(a_{52}=+0.133968414\) \(a_{53}=+0.255532315\) \(a_{54}=-0.136082763\) \(a_{55}=+0.689781125\)
\(a_{56}=+0.327615656\) \(a_{57}=-0.226781711\) \(a_{58}=-0.784617174\) \(a_{59}=-1.721024749\) \(a_{60}=+0.135805334\)
\(a_{61}=+0.949050719\) \(a_{62}=-0.791568314\) \(a_{63}=+0.308879002\) \(a_{64}=+0.125000000\) \(a_{65}=-0.126049133\)
\(a_{66}=+0.598588307\) \(a_{67}=+1.633723197\) \(a_{68}=-0.728860418\) \(a_{69}=+0.808035863\) \(a_{70}=-0.308249297\)
\(a_{71}=-0.610196196\) \(a_{72}=+0.117851130\) \(a_{73}=-1.296549765\) \(a_{74}=+0.095979528\) \(a_{75}=+0.449572801\)
\(a_{76}=+0.196398717\) \(a_{77}=-1.358668458\) \(a_{78}=-0.109384753\) \(a_{79}=+0.778236877\) \(a_{80}=-0.117610869\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.085696832\) \(a_{83}=-0.409014698\) \(a_{84}=-0.267497063\) \(a_{85}=+0.685775260\)
\(a_{86}=-0.426536897\) \(a_{87}=+0.640637240\) \(a_{88}=-0.518392681\) \(a_{89}=-0.050585874\) \(a_{90}=-0.110884591\)
\(a_{91}=+0.248280180\) \(a_{92}=-0.699779584\) \(a_{93}=+0.646312822\) \(a_{94}=+1.068789929\) \(a_{95}=-0.184788997\)
\(a_{96}=-0.102062073\) \(a_{97}=-1.759227322\) \(a_{98}=-0.099945200\) \(a_{99}=-0.488745306\) \(a_{100}=-0.389341467\)

Showing 100 of 1000 available coefficients

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