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: \( 40.5433512105 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.553885465\) \(a_{3}=-0.512491716\) \(a_{4}=-0.693210892\) \(a_{5}=+0.315765235\)
\(a_{6}=+0.283861712\) \(a_{7}=-0.001465467\) \(a_{8}=+0.937844902\) \(a_{9}=-0.737352241\) \(a_{10}=-0.174897774\)
\(a_{11}=-0.500777247\) \(a_{12}=+0.355264840\) \(a_{13}=-1.296761186\) \(a_{14}=+0.000811701\) \(a_{15}=-0.161827067\)
\(a_{16}=+0.173752233\) \(a_{17}=+0.063001480\) \(a_{18}=+0.408408689\) \(a_{19}=-1.777750202\) \(a_{20}=-0.218891901\)
\(a_{21}=+0.000751040\) \(a_{22}=+0.277373238\) \(a_{23}=-0.388630268\) \(a_{24}=-0.480637743\) \(a_{25}=-0.900292316\)
\(a_{26}=+0.718257172\) \(a_{27}=+0.890378631\) \(a_{28}=+0.001015878\) \(a_{29}=+0.206906504\) \(a_{30}=+0.089633660\)
\(a_{31}=-1.304857208\) \(a_{32}=-1.034083738\) \(a_{33}=+0.256644190\) \(a_{34}=-0.034895604\) \(a_{35}=-0.000462744\)
\(a_{36}=+0.511140605\) \(a_{37}=+1.560441461\) \(a_{38}=+0.984669996\) \(a_{39}=+0.664579365\) \(a_{40}=+0.296138816\)
\(a_{41}=+1.815957027\) \(a_{42}=-0.000415990\) \(a_{43}=+0.731110415\) \(a_{44}=+0.347144242\) \(a_{45}=-0.232830204\)
\(a_{46}=+0.215256657\) \(a_{47}=+1.116620865\) \(a_{48}=-0.089046580\) \(a_{49}=-0.999997852\) \(a_{50}=+0.498658828\)
\(a_{51}=-0.032287736\) \(a_{52}=+0.898928979\) \(a_{53}=-0.349215572\) \(a_{54}=-0.493167782\) \(a_{55}=-0.158128045\)
\(a_{56}=-0.001374381\) \(a_{57}=+0.911082251\) \(a_{58}=-0.114602505\) \(a_{59}=-0.487510608\) \(a_{60}=+0.112180285\)
\(a_{61}=-0.667066283\) \(a_{62}=+0.722741441\) \(a_{63}=+0.001080565\) \(a_{64}=+0.399011718\) \(a_{65}=-0.409472100\)
\(a_{66}=-0.142151490\) \(a_{67}=-0.166871371\) \(a_{68}=-0.043673310\) \(a_{69}=+0.199169793\) \(a_{70}=+0.000256307\)
\(a_{71}=+1.020288321\) \(a_{72}=-0.691522040\) \(a_{73}=-0.393267919\) \(a_{74}=-0.864305844\) \(a_{75}=+0.461392354\)
\(a_{76}=+1.232355803\) \(a_{77}=+0.000733873\) \(a_{78}=-0.368100851\) \(a_{79}=-0.624444704\) \(a_{80}=+0.054864915\)
\(a_{81}=+0.281040569\) \(a_{82}=-1.005832201\) \(a_{83}=+1.422912233\) \(a_{84}=-0.000520629\) \(a_{85}=+0.019893677\)
\(a_{86}=-0.404951432\) \(a_{87}=-0.106037869\) \(a_{88}=-0.469651388\) \(a_{89}=+0.290728220\) \(a_{90}=+0.128961266\)
\(a_{91}=+0.001900361\) \(a_{92}=+0.269402735\) \(a_{93}=+0.668728509\) \(a_{94}=-0.618480066\) \(a_{95}=-0.561351710\)
\(a_{96}=+0.529959349\) \(a_{97}=-1.158456720\) \(a_{98}=+0.553884275\) \(a_{99}=+0.369249225\) \(a_{100}=+0.624092440\)

Showing 100 of 5000 available coefficients

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