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: \( 44.0774047617 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.203192929\) \(a_{3}=+1.697140200\) \(a_{4}=-0.958712634\) \(a_{5}=+1.265940239\)
\(a_{6}=+0.344846888\) \(a_{7}=+0.726151231\) \(a_{8}=-0.397996557\) \(a_{9}=+1.880284860\) \(a_{10}=+0.257230105\)
\(a_{11}=+0.527189829\) \(a_{12}=-1.627069751\) \(a_{13}=-0.879618710\) \(a_{14}=+0.147548796\) \(a_{15}=+2.148478070\)
\(a_{16}=+0.877842547\) \(a_{17}=+0.954567664\) \(a_{18}=+0.382060588\) \(a_{19}=+0.318106018\) \(a_{20}=-1.213672903\)
\(a_{21}=+1.232380475\) \(a_{22}=+0.107121245\) \(a_{23}=+0.185975051\) \(a_{24}=-0.675455957\) \(a_{25}=+0.602604688\)
\(a_{26}=-0.178732302\) \(a_{27}=+1.493966823\) \(a_{28}=-0.696170359\) \(a_{29}=-1.035323838\) \(a_{30}=+0.436555552\)
\(a_{31}=-0.657733379\) \(a_{32}=+0.576367956\) \(a_{33}=+0.894715052\) \(a_{34}=+0.193961400\) \(a_{35}=+0.919264062\)
\(a_{36}=-1.802652850\) \(a_{37}=-0.099287939\) \(a_{38}=+0.064636894\) \(a_{39}=-1.492836274\) \(a_{40}=-0.503839857\)
\(a_{41}=+0.829448034\) \(a_{42}=+0.250410992\) \(a_{43}=+1.237331053\) \(a_{44}=-0.505423549\) \(a_{45}=+2.380328264\)
\(a_{46}=+0.037788815\) \(a_{47}=+1.251592075\) \(a_{48}=+1.489821877\) \(a_{49}=-0.472704390\) \(a_{50}=+0.122445012\)
\(a_{51}=+1.620035157\) \(a_{52}=+0.843301570\) \(a_{53}=-1.088994385\) \(a_{54}=+0.303563495\) \(a_{55}=+0.667390818\)
\(a_{56}=-0.289005690\) \(a_{57}=+0.539870511\) \(a_{58}=-0.210370483\) \(a_{59}=+0.978517073\) \(a_{60}=-2.059773069\)
\(a_{61}=+1.078773478\) \(a_{62}=-0.133646772\) \(a_{63}=+1.365371165\) \(a_{64}=-0.760728653\) \(a_{65}=-1.113544721\)
\(a_{66}=+0.181799772\) \(a_{67}=+1.273510759\) \(a_{68}=-0.915156088\) \(a_{69}=+0.315625739\) \(a_{70}=+0.186787957\)
\(a_{71}=+0.161671137\) \(a_{72}=-0.748346901\) \(a_{73}=-0.133224980\) \(a_{74}=-0.020174607\) \(a_{75}=+1.022704640\)
\(a_{76}=-0.304972258\) \(a_{77}=+0.382819543\) \(a_{78}=-0.303333775\) \(a_{79}=-1.727710298\) \(a_{80}=+1.111296204\)
\(a_{81}=+0.655186294\) \(a_{82}=+0.168537975\) \(a_{83}=-0.083361210\) \(a_{84}=-1.181498702\) \(a_{85}=+1.208425616\)
\(a_{86}=+0.251416921\) \(a_{87}=-1.757089706\) \(a_{88}=-0.209819737\) \(a_{89}=+1.835521597\) \(a_{90}=+0.483665872\)
\(a_{91}=-0.638736209\) \(a_{92}=-0.178296631\) \(a_{93}=-1.116265758\) \(a_{94}=+0.254314660\) \(a_{95}=+0.402703208\)
\(a_{96}=+0.978177228\) \(a_{97}=-0.942153153\) \(a_{98}=-0.096050190\) \(a_{99}=+0.991267054\) \(a_{100}=-0.577724727\)

Showing 100 of 5000 available coefficients

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