Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 8.07161868259 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.780952607\) \(a_{3}=+0.261043624\) \(a_{4}=-0.390113025\) \(a_{5}=-1.404882221\)
\(a_{6}=-0.203862699\) \(a_{7}=+0.377964473\) \(a_{8}=+1.085612391\) \(a_{9}=-0.931856226\) \(a_{10}=+1.097146434\)
\(a_{11}=+1.059657438\) \(a_{12}=-0.101836518\) \(a_{13}=+1.345684073\) \(a_{14}=-0.295172341\) \(a_{15}=-0.366735546\)
\(a_{16}=-0.457698802\) \(a_{17}=-0.217306884\) \(a_{18}=+0.727735550\) \(a_{19}=+0.706363097\) \(a_{20}=+0.548062854\)
\(a_{21}=+0.098665216\) \(a_{22}=-0.827542239\) \(a_{23}=-0.809152141\) \(a_{24}=+0.283392193\) \(a_{25}=+0.973694056\)
\(a_{26}=-1.050915486\) \(a_{27}=-0.504298750\) \(a_{28}=-0.147448864\) \(a_{29}=+1.740103489\) \(a_{30}=+0.286403081\)
\(a_{31}=-0.279677966\) \(a_{32}=-0.728171319\) \(a_{33}=+0.276616818\) \(a_{34}=+0.169706377\) \(a_{35}=-0.530995568\)
\(a_{36}=+0.363529252\) \(a_{37}=+0.415266138\) \(a_{38}=-0.551636103\) \(a_{39}=+0.351282247\) \(a_{40}=-1.525157548\)
\(a_{41}=-0.097047869\) \(a_{42}=-0.077052857\) \(a_{43}=+1.059327091\) \(a_{44}=-0.413386169\) \(a_{45}=+1.309148245\)
\(a_{46}=+0.631909474\) \(a_{47}=-0.182646416\) \(a_{48}=-0.119479354\) \(a_{49}=+0.142857143\) \(a_{50}=-0.760408912\)
\(a_{51}=-0.056726576\) \(a_{52}=-0.524968885\) \(a_{53}=-0.094204673\) \(a_{54}=+0.393833424\) \(a_{55}=-1.488693895\)
\(a_{56}=+0.410322915\) \(a_{57}=+0.184391583\) \(a_{58}=-1.358938356\) \(a_{59}=+1.509458435\) \(a_{60}=+0.143068313\)
\(a_{61}=+1.627205862\) \(a_{62}=+0.218415237\) \(a_{63}=-0.352208548\) \(a_{64}=+1.026366092\) \(a_{65}=-1.890527630\)
\(a_{66}=-0.216024625\) \(a_{67}=+0.832843111\) \(a_{68}=+0.084774246\) \(a_{69}=-0.211224007\) \(a_{70}=+0.414682374\)
\(a_{71}=-1.618278351\) \(a_{72}=-1.011634666\) \(a_{73}=+1.041374773\) \(a_{74}=-0.324303173\) \(a_{75}=+0.254176625\)
\(a_{76}=-0.275561445\) \(a_{77}=+0.400512865\) \(a_{78}=-0.274334787\) \(a_{79}=+0.251695345\) \(a_{80}=+0.643012910\)
\(a_{81}=+0.800212253\) \(a_{82}=+0.075789786\) \(a_{83}=-0.849491215\) \(a_{84}=-0.038490586\) \(a_{85}=+0.305290577\)
\(a_{86}=-0.827284253\) \(a_{87}=+0.454242921\) \(a_{88}=+1.150377245\) \(a_{89}=-0.106320995\) \(a_{90}=-1.022382735\)
\(a_{91}=+0.508620772\) \(a_{92}=+0.315660790\) \(a_{93}=-0.073008150\) \(a_{94}=+0.142638195\) \(a_{95}=-0.992356957\)
\(a_{96}=-0.190084480\) \(a_{97}=-0.077287315\) \(a_{98}=-0.111564658\) \(a_{99}=-0.987448381\) \(a_{100}=-0.379850734\)

Showing 100 of 1228 available coefficients

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