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: \( 6.75741527775 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.507020616\) \(a_{3}=+0.577350269\) \(a_{4}=+1.271111137\) \(a_{5}=-0.876487111\)
\(a_{6}=+0.870078768\) \(a_{7}=-0.498718588\) \(a_{8}=+0.408570354\) \(a_{9}=+0.333331754\) \(a_{10}=-1.320875167\)
\(a_{11}=+0.531066033\) \(a_{12}=+0.734167204\) \(a_{13}=+0.287451061\) \(a_{14}=-0.751579116\) \(a_{15}=-0.506040069\)
\(a_{16}=-0.655387614\) \(a_{17}=+1.596522303\) \(a_{18}=+0.502340205\) \(a_{19}=-0.242512029\) \(a_{20}=-1.114112526\)
\(a_{21}=-0.287935281\) \(a_{22}=+0.800404498\) \(a_{23}=-0.260757601\) \(a_{24}=+0.235888042\) \(a_{25}=-0.231770347\)
\(a_{26}=+0.435693656\) \(a_{27}=+0.192450090\) \(a_{28}=-0.633926686\) \(a_{29}=+1.050474666\) \(a_{30}=-0.762612816\)
\(a_{31}=-0.453862859\) \(a_{32}=-1.396252719\) \(a_{33}=+0.306640631\) \(a_{34}=+2.405992025\) \(a_{35}=+0.437120369\)
\(a_{36}=+0.423703712\) \(a_{37}=-1.974968869\) \(a_{38}=-0.365470629\) \(a_{39}=+0.166917325\) \(a_{40}=-0.358106404\)
\(a_{41}=+0.003249259\) \(a_{42}=-0.433924399\) \(a_{43}=+1.425858140\) \(a_{44}=+0.675108933\) \(a_{45}=-0.292162386\)
\(a_{46}=-0.392967056\) \(a_{47}=+0.334133041\) \(a_{48}=-0.378388241\) \(a_{49}=-0.751279823\) \(a_{50}=-0.349282761\)
\(a_{51}=+0.921752774\) \(a_{52}=+0.367489964\) \(a_{53}=-0.794891743\) \(a_{54}=+0.290026022\) \(a_{55}=-0.465517307\)
\(a_{56}=-0.203760497\) \(a_{57}=-0.140015147\) \(a_{58}=+1.583086787\) \(a_{59}=+0.969422078\) \(a_{60}=-0.643233178\)
\(a_{61}=+0.003591959\) \(a_{62}=-0.683980670\) \(a_{63}=-0.166239503\) \(a_{64}=-1.448794038\) \(a_{65}=-0.253400587\)
\(a_{66}=+0.462113768\) \(a_{67}=-0.718711007\) \(a_{68}=+2.029357281\) \(a_{69}=-0.150548543\) \(a_{70}=+0.658749366\)
\(a_{71}=+0.592013082\) \(a_{72}=+0.136190141\) \(a_{73}=+0.992696902\) \(a_{74}=-2.976319022\) \(a_{75}=-0.133812695\)
\(a_{76}=-0.308259430\) \(a_{77}=-0.264877756\) \(a_{78}=+0.251547481\) \(a_{79}=+0.572760004\) \(a_{80}=+0.574439088\)
\(a_{81}=+0.111112047\) \(a_{82}=+0.004896774\) \(a_{83}=-0.201420556\) \(a_{84}=-0.365998612\) \(a_{85}=-1.399329544\)
\(a_{86}=+2.148799917\) \(a_{87}=+0.606490619\) \(a_{88}=+0.216994377\) \(a_{89}=-0.600039302\) \(a_{90}=-0.440288857\)
\(a_{91}=-0.144180048\) \(a_{92}=-0.331458524\) \(a_{93}=-0.262047677\) \(a_{94}=+0.503550124\) \(a_{95}=+0.212575966\)
\(a_{96}=-0.806123898\) \(a_{97}=+0.216577716\) \(a_{98}=-1.132212630\) \(a_{99}=+0.177067538\) \(a_{100}=-0.294605805\)

Showing 100 of 5000 available coefficients

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