Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 46.65331836 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.202804106\) \(a_{3}=-0.951164203\) \(a_{4}=+0.446737716\) \(a_{5}=-1.762522315\)
\(a_{6}=-1.144064209\) \(a_{7}=-0.099652767\) \(a_{8}=-0.665466146\) \(a_{9}=-0.095286658\) \(a_{10}=-2.119969077\)
\(a_{11}=-1.055116586\) \(a_{12}=-0.424920924\) \(a_{13}=+0.438287698\) \(a_{14}=-0.119862757\) \(a_{15}=+1.676448134\)
\(a_{16}=-1.247163129\) \(a_{17}=-1.415978067\) \(a_{18}=-0.114611184\) \(a_{19}=+0.209863764\) \(a_{20}=-0.787385194\)
\(a_{21}=+0.094786147\) \(a_{22}=-1.269098586\) \(a_{23}=-0.247499702\) \(a_{24}=+0.632967577\) \(a_{25}=+2.106484911\)
\(a_{26}=+0.527174243\) \(a_{27}=+1.041797462\) \(a_{28}=-0.044518649\) \(a_{29}=-0.033365762\) \(a_{30}=+2.016438698\)
\(a_{31}=-0.014256062\) \(a_{32}=-0.834626786\) \(a_{33}=+1.003589127\) \(a_{34}=-1.703144233\) \(a_{35}=+0.175640225\)
\(a_{36}=-0.042568144\) \(a_{37}=+1.481061061\) \(a_{38}=+0.252424997\) \(a_{39}=-0.416883569\) \(a_{40}=+1.172898933\)
\(a_{41}=-1.426074411\) \(a_{42}=+0.114009164\) \(a_{43}=-1.492547841\) \(a_{44}=-0.471360374\) \(a_{45}=+0.167944861\)
\(a_{46}=-0.297693657\) \(a_{47}=+0.439469780\) \(a_{48}=+1.186256924\) \(a_{49}=-0.990069326\) \(a_{50}=+2.533688699\)
\(a_{51}=+1.346827650\) \(a_{52}=+0.195799645\) \(a_{53}=-0.121442151\) \(a_{54}=+1.253078264\) \(a_{55}=+1.859666527\)
\(a_{56}=+0.066315543\) \(a_{57}=-0.199614900\) \(a_{58}=-0.040132475\) \(a_{59}=+0.818835740\) \(a_{60}=+0.748932611\)
\(a_{61}=-0.194557890\) \(a_{62}=-0.017147250\) \(a_{63}=+0.009495580\) \(a_{64}=+0.243270603\) \(a_{65}=-0.772491847\)
\(a_{66}=+1.207121125\) \(a_{67}=+0.013124518\) \(a_{68}=-0.632570780\) \(a_{69}=+0.235412840\) \(a_{70}=+0.211260700\)
\(a_{71}=-0.647464952\) \(a_{72}=+0.063410045\) \(a_{73}=+0.209835803\) \(a_{74}=+1.781426325\) \(a_{75}=-2.003613042\)
\(a_{76}=+0.093754059\) \(a_{77}=+0.105145287\) \(a_{78}=-0.501429269\) \(a_{79}=+0.242111264\) \(a_{80}=+2.198152846\)
\(a_{81}=-0.895633795\) \(a_{82}=-1.715288157\) \(a_{83}=-0.055621977\) \(a_{84}=+0.042344546\) \(a_{85}=+2.495692941\)
\(a_{86}=-1.795242671\) \(a_{87}=+0.031736318\) \(a_{88}=+0.702144368\) \(a_{89}=-0.826398135\) \(a_{90}=+0.202004768\)
\(a_{91}=-0.043676582\) \(a_{92}=-0.110567451\) \(a_{93}=+0.013559856\) \(a_{94}=+0.528596056\) \(a_{95}=-0.369889567\)
\(a_{96}=+0.793867122\) \(a_{97}=-0.272516700\) \(a_{98}=-1.190859450\) \(a_{99}=+0.100538533\) \(a_{100}=+0.941046258\)

Showing 100 of 5000 available coefficients

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