Properties

Level $1$
Weight $0$
Character 1.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 27.7759207018 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.948350503\) \(a_{3}=-0.192089764\) \(a_{4}=-0.100631323\) \(a_{5}=+0.164082711\)
\(a_{6}=-0.182168425\) \(a_{7}=+1.131591820\) \(a_{8}=-1.043784269\) \(a_{9}=-0.963101522\) \(a_{10}=+0.155607922\)
\(a_{11}=-1.361245748\) \(a_{12}=+0.019330247\) \(a_{13}=+0.305604567\) \(a_{14}=+1.073145672\) \(a_{15}=-0.031518610\)
\(a_{16}=-0.889242014\) \(a_{17}=-0.910915981\) \(a_{18}=-0.913357814\) \(a_{19}=-1.506213383\) \(a_{20}=-0.016511860\)
\(a_{21}=-0.217367206\) \(a_{22}=-1.290938091\) \(a_{23}=+0.723471014\) \(a_{24}=+0.200500274\) \(a_{25}=-0.973076864\)
\(a_{26}=+0.289820245\) \(a_{27}=+0.377091709\) \(a_{28}=-0.113873581\) \(a_{29}=-0.280699259\) \(a_{30}=-0.029890689\)
\(a_{31}=+0.117471785\) \(a_{32}=+0.200471157\) \(a_{33}=+0.261481375\) \(a_{34}=-0.863867629\) \(a_{35}=+0.185674654\)
\(a_{36}=+0.096918180\) \(a_{37}=+1.247379915\) \(a_{38}=-1.428418220\) \(a_{39}=-0.058703509\) \(a_{40}=-0.171266953\)
\(a_{41}=+1.275323870\) \(a_{42}=-0.206140299\) \(a_{43}=-0.834894751\) \(a_{44}=+0.136983960\) \(a_{45}=-0.158028309\)
\(a_{46}=+0.686104100\) \(a_{47}=-0.333412214\) \(a_{48}=+0.170814289\) \(a_{49}=+0.280500048\) \(a_{50}=-0.922817934\)
\(a_{51}=+0.174977636\) \(a_{52}=-0.030753392\) \(a_{53}=+0.649112070\) \(a_{54}=+0.357615112\) \(a_{55}=-0.223356893\)
\(a_{56}=-1.181137741\) \(a_{57}=+0.289328174\) \(a_{58}=-0.266201284\) \(a_{59}=+1.521735372\) \(a_{60}=+0.003171759\)
\(a_{61}=-0.883611722\) \(a_{62}=+0.111404426\) \(a_{63}=-1.089837805\) \(a_{64}=+1.079358937\) \(a_{65}=+0.050144426\)
\(a_{66}=+0.247975994\) \(a_{67}=-0.220649371\) \(a_{68}=+0.091666680\) \(a_{69}=-0.138971377\) \(a_{70}=+0.176084651\)
\(a_{71}=-1.194649766\) \(a_{72}=+1.005270218\) \(a_{73}=-0.671226997\) \(a_{74}=+1.182953371\) \(a_{75}=+0.186918105\)
\(a_{76}=+0.151572245\) \(a_{77}=-1.540374554\) \(a_{78}=-0.055671503\) \(a_{79}=+0.225781167\) \(a_{80}=-0.145909241\)
\(a_{81}=+0.890666065\) \(a_{82}=+1.209454035\) \(a_{83}=-1.425803093\) \(a_{84}=+0.021873949\) \(a_{85}=-0.149465564\)
\(a_{86}=-0.791772857\) \(a_{87}=+0.053919455\) \(a_{88}=+1.420846898\) \(a_{89}=-0.464600064\) \(a_{90}=-0.149866226\)
\(a_{91}=+0.345819629\) \(a_{92}=-0.072803845\) \(a_{93}=-0.022565127\) \(a_{94}=-0.316191641\) \(a_{95}=-0.247143576\)
\(a_{96}=-0.038508458\) \(a_{97}=-0.421102856\) \(a_{98}=+0.266012361\) \(a_{99}=+1.311017852\) \(a_{100}=+0.097922013\)

Showing 100 of 5000 available coefficients

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