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: \( 16.6442592019 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.540227826\) \(a_{3}=+0.977492591\) \(a_{4}=+1.372301755\) \(a_{5}=-0.105242363\)
\(a_{6}=-1.505561289\) \(a_{7}=-0.692640859\) \(a_{8}=-0.573429523\) \(a_{9}=-0.044508234\) \(a_{10}=+0.162097215\)
\(a_{11}=-0.760201275\) \(a_{12}=+1.341414799\) \(a_{13}=-1.570437062\) \(a_{14}=+1.066824724\) \(a_{15}=-0.102873630\)
\(a_{16}=-0.489089648\) \(a_{17}=+0.281889823\) \(a_{18}=+0.068552820\) \(a_{19}=+0.104046091\) \(a_{20}=-0.144424279\)
\(a_{21}=-0.677051308\) \(a_{22}=+1.170883158\) \(a_{23}=-0.143879471\) \(a_{24}=-0.560523110\) \(a_{25}=-0.988924045\)
\(a_{26}=+2.418830862\) \(a_{27}=-1.020999060\) \(a_{28}=-0.950512267\) \(a_{29}=+0.791244081\) \(a_{30}=+0.158448827\)
\(a_{31}=-0.757175514\) \(a_{32}=+1.326739008\) \(a_{33}=-0.743091115\) \(a_{34}=-0.434174549\) \(a_{35}=+0.072895160\)
\(a_{36}=-0.061078727\) \(a_{37}=+1.272559864\) \(a_{38}=-0.160254684\) \(a_{39}=-1.535090594\) \(a_{40}=+0.060349078\)
\(a_{41}=+0.547489986\) \(a_{42}=+1.042813264\) \(a_{43}=-0.235422983\) \(a_{44}=-1.043225545\) \(a_{45}=+0.004684152\)
\(a_{46}=+0.221607164\) \(a_{47}=+0.565743802\) \(a_{48}=-0.478081507\) \(a_{49}=-0.520248640\) \(a_{50}=+1.523168332\)
\(a_{51}=+0.275545214\) \(a_{52}=-2.155113537\) \(a_{53}=-0.359753173\) \(a_{54}=+1.572571159\) \(a_{55}=+0.080005379\)
\(a_{56}=+0.397180728\) \(a_{57}=+0.101704271\) \(a_{58}=-1.218696156\) \(a_{59}=-0.245573087\) \(a_{60}=-0.141173663\)
\(a_{61}=+0.569302051\) \(a_{62}=+1.166222795\) \(a_{63}=+0.030828221\) \(a_{64}=-1.554390689\) \(a_{65}=+0.165276507\)
\(a_{66}=+1.144529613\) \(a_{67}=-1.271630541\) \(a_{68}=+0.386837898\) \(a_{69}=-0.140641117\) \(a_{70}=-0.112275155\)
\(a_{71}=+0.875542455\) \(a_{72}=+0.025522335\) \(a_{73}=+1.101292952\) \(a_{74}=-1.960032113\) \(a_{75}=-0.966665928\)
\(a_{76}=+0.142782633\) \(a_{77}=+0.526546465\) \(a_{78}=+2.364389247\) \(a_{79}=-1.027156574\) \(a_{80}=+0.051472950\)
\(a_{81}=-0.953510784\) \(a_{82}=-0.843259311\) \(a_{83}=+1.506895398\) \(a_{84}=-0.929118699\) \(a_{85}=-0.029666751\)
\(a_{86}=+0.362605029\) \(a_{87}=+0.773435228\) \(a_{88}=+0.435921855\) \(a_{89}=-1.462386027\) \(a_{90}=-0.007214660\)
\(a_{91}=+1.087748876\) \(a_{92}=-0.197446051\) \(a_{93}=-0.740133455\) \(a_{94}=-0.871374346\) \(a_{95}=-0.010950053\)
\(a_{96}=+1.296877547\) \(a_{97}=+0.439786611\) \(a_{98}=+0.801301440\) \(a_{99}=+0.033835216\) \(a_{100}=-1.357102210\)

Showing 100 of 5000 available coefficients

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