Properties

Level $71$
Weight $0$
Character 71.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 71 \)
Weight: \( 0 \)
Character: 71.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.24260200762 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.320737219\) \(a_{3}=+1.229502519\) \(a_{4}=+0.744346802\) \(a_{5}=+1.198282650\)
\(a_{6}=-1.623849738\) \(a_{7}=-1.687090117\) \(a_{8}=+0.337650694\) \(a_{9}=+0.511676445\) \(a_{10}=-1.582616495\)
\(a_{11}=-0.566213878\) \(a_{12}=+0.915176268\) \(a_{13}=-0.693108184\) \(a_{14}=+2.228202710\) \(a_{15}=+1.473291537\)
\(a_{16}=-1.190294640\) \(a_{17}=+1.045596186\) \(a_{18}=-0.675790125\) \(a_{19}=-1.457509948\) \(a_{20}=+0.891937859\)
\(a_{21}=-2.074281549\) \(a_{22}=+0.747819742\) \(a_{23}=-1.793974731\) \(a_{24}=+0.415142379\) \(a_{25}=+0.435881309\)
\(a_{26}=+0.915413776\) \(a_{27}=-0.600395041\) \(a_{28}=-1.255780134\) \(a_{29}=+1.767979068\) \(a_{30}=-1.945830968\)
\(a_{31}=-1.323479191\) \(a_{32}=+1.234415740\) \(a_{33}=-0.696161389\) \(a_{34}=-1.380957798\) \(a_{35}=-2.021610816\)
\(a_{36}=+0.380864726\) \(a_{37}=+0.562266566\) \(a_{38}=+1.924987636\) \(a_{39}=-0.852178259\) \(a_{40}=+0.404600968\)
\(a_{41}=-0.300697956\) \(a_{42}=+2.739580845\) \(a_{43}=+0.280550540\) \(a_{44}=-0.421459489\) \(a_{45}=+0.613133007\)
\(a_{46}=+2.369369197\) \(a_{47}=-0.873013423\) \(a_{48}=-1.463470259\) \(a_{49}=+1.846273063\) \(a_{50}=-0.575684668\)
\(a_{51}=+1.285563144\) \(a_{52}=-0.515912861\) \(a_{53}=-0.896339417\) \(a_{54}=+0.792964077\) \(a_{55}=-0.678484266\)
\(a_{56}=-0.569647148\) \(a_{57}=-1.792012154\) \(a_{58}=-2.335035758\) \(a_{59}=-0.093144107\) \(a_{60}=+1.096639844\)
\(a_{61}=+0.473859060\) \(a_{62}=+1.747968226\) \(a_{63}=-0.863244274\) \(a_{64}=-0.440044171\) \(a_{65}=-0.830539512\)
\(a_{66}=+0.919446257\) \(a_{67}=-0.304295125\) \(a_{68}=+0.778286177\) \(a_{69}=-2.205696451\) \(a_{70}=+2.670016648\)
\(a_{71}=+0.118678166\) \(a_{72}=+0.172767907\) \(a_{73}=-0.362614151\) \(a_{74}=-0.742606380\) \(a_{75}=+0.535917168\)
\(a_{76}=-1.084892869\) \(a_{77}=+0.955253837\) \(a_{78}=+1.125503544\) \(a_{79}=-0.024567055\) \(a_{80}=-1.426309416\)
\(a_{81}=-1.249863661\) \(a_{82}=+0.397142982\) \(a_{83}=+0.904576726\) \(a_{84}=-1.543984838\) \(a_{85}=+1.252919768\)
\(a_{86}=-0.370533540\) \(a_{87}=+2.173734718\) \(a_{88}=-0.191182509\) \(a_{89}=+0.502327210\) \(a_{90}=-0.809787582\)
\(a_{91}=+1.169335968\) \(a_{92}=-1.335339354\) \(a_{93}=-1.627221000\) \(a_{94}=+1.153021320\) \(a_{95}=-1.746508883\)
\(a_{96}=+1.517717262\) \(a_{97}=+0.675351219\) \(a_{98}=-2.438441551\) \(a_{99}=-0.289718304\) \(a_{100}=+0.324446859\)

Showing 100 of 546 available coefficients

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