Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 30.0849560775 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.396524106\) \(a_{3}=-0.577350269\) \(a_{4}=-0.842768633\) \(a_{5}=-1.406757522\)
\(a_{6}=+0.228933300\) \(a_{7}=-1.951890605\) \(a_{8}=+0.730702185\) \(a_{9}=+0.333333333\) \(a_{10}=+0.557813269\)
\(a_{11}=+0.124153439\) \(a_{12}=+0.486572697\) \(a_{13}=+0.716864467\) \(a_{14}=+0.773971678\) \(a_{15}=+0.812191834\)
\(a_{16}=+0.553027602\) \(a_{17}=+0.271432873\) \(a_{18}=-0.132174702\) \(a_{19}=-0.109731708\) \(a_{20}=+1.185571114\)
\(a_{21}=+1.126924566\) \(a_{22}=-0.049229832\) \(a_{23}=-0.450989438\) \(a_{24}=-0.421871103\) \(a_{25}=+0.978966725\)
\(a_{26}=-0.284254042\) \(a_{27}=-0.192450090\) \(a_{28}=+1.644992178\) \(a_{29}=-1.278421850\) \(a_{30}=-0.322053641\)
\(a_{31}=+1.584301411\) \(a_{32}=-0.949990961\) \(a_{33}=-0.071680022\) \(a_{34}=-0.107629677\) \(a_{35}=+2.745836791\)
\(a_{36}=-0.280922878\) \(a_{37}=-0.188314960\) \(a_{38}=+0.043511267\) \(a_{39}=-0.413881893\) \(a_{40}=-1.027920795\)
\(a_{41}=+0.697354365\) \(a_{42}=-0.446852757\) \(a_{43}=-0.147496897\) \(a_{44}=-0.104632624\) \(a_{45}=-0.468919174\)
\(a_{46}=+0.178828184\) \(a_{47}=+0.766130386\) \(a_{48}=-0.319290635\) \(a_{49}=+2.809876936\) \(a_{50}=-0.388183906\)
\(a_{51}=-0.156711842\) \(a_{52}=-0.604150887\) \(a_{53}=+1.018746851\) \(a_{54}=+0.076311100\) \(a_{55}=-0.174653784\)
\(a_{56}=-1.426250731\) \(a_{57}=+0.063353631\) \(a_{58}=+0.506925081\) \(a_{59}=-0.357026204\) \(a_{60}=-0.684489802\)
\(a_{61}=-1.755124351\) \(a_{62}=-0.628213701\) \(a_{63}=-0.650630202\) \(a_{64}=-0.176333285\) \(a_{65}=-1.008454481\)
\(a_{66}=+0.028422856\) \(a_{67}=-0.502010134\) \(a_{68}=-0.228755111\) \(a_{69}=+0.260378874\) \(a_{70}=-1.088790479\)
\(a_{71}=-1.082580885\) \(a_{72}=+0.243567395\) \(a_{73}=-0.641319696\) \(a_{74}=+0.074671421\) \(a_{75}=-0.565206702\)
\(a_{76}=+0.092478441\) \(a_{77}=-0.242333932\) \(a_{78}=+0.164114148\) \(a_{79}=+1.076890842\) \(a_{80}=-0.777975739\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.276517816\) \(a_{83}=-0.374864034\) \(a_{84}=-0.949736677\) \(a_{85}=-0.381840236\)
\(a_{86}=+0.058486075\) \(a_{87}=+0.738097199\) \(a_{88}=+0.090719189\) \(a_{89}=+1.544669648\) \(a_{90}=+0.185937756\)
\(a_{91}=-1.399241018\) \(a_{92}=+0.380079753\) \(a_{93}=-0.914696846\) \(a_{94}=-0.303789167\) \(a_{95}=+0.154365905\)
\(a_{96}=+0.548477537\) \(a_{97}=+0.544741194\) \(a_{98}=-1.114183941\) \(a_{99}=+0.041384480\) \(a_{100}=-0.825042449\)

Showing 100 of 1228 available coefficients

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