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: \( 25.8262437127 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.258066189\) \(a_{3}=+1.333741473\) \(a_{4}=-0.933401842\) \(a_{5}=+1.276361097\)
\(a_{6}=+0.344193579\) \(a_{7}=+0.743563621\) \(a_{8}=-0.498945645\) \(a_{9}=+0.778866316\) \(a_{10}=+0.329385644\)
\(a_{11}=-0.419019345\) \(a_{12}=-1.244916747\) \(a_{13}=+0.842324634\) \(a_{14}=+0.191888628\) \(a_{15}=+1.702335751\)
\(a_{16}=+0.804640841\) \(a_{17}=+0.711055464\) \(a_{18}=+0.200999062\) \(a_{19}=+1.212121647\) \(a_{20}=-1.191357799\)
\(a_{21}=+0.991721638\) \(a_{22}=-0.108134725\) \(a_{23}=+0.115444271\) \(a_{24}=-0.665464500\) \(a_{25}=+0.629097649\)
\(a_{26}=+0.217375508\) \(a_{27}=-0.294935166\) \(a_{28}=-0.694043653\) \(a_{29}=+0.825729426\) \(a_{30}=+0.439315294\)
\(a_{31}=-1.116882189\) \(a_{32}=+0.706596241\) \(a_{33}=-0.558863478\) \(a_{34}=+0.183499374\) \(a_{35}=+0.949055678\)
\(a_{36}=-0.726995254\) \(a_{37}=-0.742363201\) \(a_{38}=+0.312807614\) \(a_{39}=+1.123443298\) \(a_{40}=-0.636834811\)
\(a_{41}=-0.229326130\) \(a_{42}=+0.255929824\) \(a_{43}=-0.792193142\) \(a_{44}=+0.391113428\) \(a_{45}=+0.994114665\)
\(a_{46}=+0.029792263\) \(a_{47}=-1.729251902\) \(a_{48}=+1.073182860\) \(a_{49}=-0.447113142\) \(a_{50}=+0.162348833\)
\(a_{51}=+0.948364162\) \(a_{52}=-0.786227365\) \(a_{53}=+0.108367329\) \(a_{54}=-0.076112795\) \(a_{55}=-0.534819990\)
\(a_{56}=-0.370997830\) \(a_{57}=+1.616656909\) \(a_{58}=+0.213092848\) \(a_{59}=-0.521396653\) \(a_{60}=-1.588963305\)
\(a_{61}=+1.155963998\) \(a_{62}=-0.288229550\) \(a_{63}=+0.579136684\) \(a_{64}=-0.622292242\) \(a_{65}=+1.075110393\)
\(a_{66}=-0.144223768\) \(a_{67}=-0.663218646\) \(a_{68}=-0.663700480\) \(a_{69}=+0.153972812\) \(a_{70}=+0.244919182\)
\(a_{71}=+1.219907029\) \(a_{72}=-0.388611956\) \(a_{73}=-0.521766135\) \(a_{74}=-0.191578842\) \(a_{75}=+0.839053625\)
\(a_{76}=-1.131396578\) \(a_{77}=-0.311567541\) \(a_{78}=+0.289922730\) \(a_{79}=+0.867425076\) \(a_{80}=+1.027012266\)
\(a_{81}=-1.172233578\) \(a_{82}=-0.059181320\) \(a_{83}=-0.311805849\) \(a_{84}=-0.925674804\) \(a_{85}=+0.907563532\)
\(a_{86}=-0.204438265\) \(a_{87}=+1.101309580\) \(a_{88}=+0.209067877\) \(a_{89}=-1.229331956\) \(a_{90}=+0.256547383\)
\(a_{91}=+0.626321955\) \(a_{92}=-0.107755895\) \(a_{93}=-1.489632095\) \(a_{94}=-0.446261449\) \(a_{95}=+1.547104914\)
\(a_{96}=+0.942416711\) \(a_{97}=-0.411516297\) \(a_{98}=-0.115384785\) \(a_{99}=-0.326360053\) \(a_{100}=-0.587200903\)

Showing 100 of 5000 available coefficients

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