Properties

Level $311$
Weight $0$
Character 311.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 311 \)
Weight: \( 0 \)
Character: 311.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.78090506682 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.134243322\) \(a_{3}=+0.363635328\) \(a_{4}=-0.981978726\) \(a_{5}=+0.495202596\)
\(a_{6}=+0.048815600\) \(a_{7}=+1.672241463\) \(a_{8}=-0.266067361\) \(a_{9}=-0.867769321\) \(a_{10}=+0.066477634\)
\(a_{11}=-0.693045847\) \(a_{12}=-0.357082207\) \(a_{13}=-0.348364665\) \(a_{14}=+0.224487207\) \(a_{15}=+0.180073168\)
\(a_{16}=+0.946261033\) \(a_{17}=+1.255322840\) \(a_{18}=-0.116492233\) \(a_{19}=-1.832259732\) \(a_{20}=-0.486278453\)
\(a_{21}=+0.608086115\) \(a_{22}=-0.093036751\) \(a_{23}=-0.091633132\) \(a_{24}=-0.096751505\) \(a_{25}=-0.754774370\)
\(a_{26}=-0.046765591\) \(a_{27}=-0.679186954\) \(a_{28}=-1.642105591\) \(a_{29}=-1.301848025\) \(a_{30}=+0.024173626\)
\(a_{31}=+1.349036129\) \(a_{32}=+0.393096509\) \(a_{33}=-0.252015980\) \(a_{34}=+0.168518656\) \(a_{35}=+0.828098323\)
\(a_{36}=+0.852131061\) \(a_{37}=+0.183605154\) \(a_{38}=-0.245968516\) \(a_{39}=-0.126677716\) \(a_{40}=-0.131757281\)
\(a_{41}=+1.520775451\) \(a_{42}=+0.081631479\) \(a_{43}=+0.652233977\) \(a_{44}=+0.680556290\) \(a_{45}=-0.429721593\)
\(a_{46}=-0.012301190\) \(a_{47}=-1.333522648\) \(a_{48}=+0.344093965\) \(a_{49}=+1.796391531\) \(a_{50}=-0.101323404\)
\(a_{51}=+0.456479793\) \(a_{52}=+0.342086673\) \(a_{53}=+1.444894107\) \(a_{54}=-0.091176331\) \(a_{55}=-0.343198145\)
\(a_{56}=-0.444928845\) \(a_{57}=-0.666274470\) \(a_{58}=-0.174764320\) \(a_{59}=+0.589200069\) \(a_{60}=-0.176828037\)
\(a_{61}=-0.173383274\) \(a_{62}=+0.181099041\) \(a_{63}=-1.451119829\) \(a_{64}=-0.893490467\) \(a_{65}=-0.172511140\)
\(a_{66}=-0.033831413\) \(a_{67}=+1.046118243\) \(a_{68}=-1.232700312\) \(a_{69}=-0.033321040\) \(a_{70}=+0.111166657\)
\(a_{71}=-0.197610664\) \(a_{72}=+0.230885075\) \(a_{73}=+0.138950728\) \(a_{74}=+0.024647742\) \(a_{75}=-0.274462606\)
\(a_{76}=+1.799240096\) \(a_{77}=-1.158940010\) \(a_{78}=-0.017005579\) \(a_{79}=+0.186284617\) \(a_{80}=+0.468590932\)
\(a_{81}=+0.620792951\) \(a_{82}=+0.204153932\) \(a_{83}=+0.943117583\) \(a_{84}=-0.597127606\) \(a_{85}=+0.621639154\)
\(a_{86}=+0.087557968\) \(a_{87}=-0.473398075\) \(a_{88}=+0.184396884\) \(a_{89}=+1.335280319\) \(a_{90}=-0.057687281\)
\(a_{91}=-0.582549812\) \(a_{92}=+0.089981879\) \(a_{93}=+0.490557219\) \(a_{94}=-0.179016504\) \(a_{95}=-0.907339781\)
\(a_{96}=+0.142943844\) \(a_{97}=-0.733569614\) \(a_{98}=+0.241153431\) \(a_{99}=+0.601403926\) \(a_{100}=+0.741172349\)

Showing 100 of 952 available coefficients

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