Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 6.62442165748 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.866606352\) \(a_{3}=+0.577350269\) \(a_{4}=-0.248993431\) \(a_{5}=-0.477730785\)
\(a_{6}=-0.500335411\) \(a_{7}=+0.377964473\) \(a_{8}=+1.082385641\) \(a_{9}=+0.333333333\) \(a_{10}=+0.414004533\)
\(a_{11}=+0.289946062\) \(a_{12}=-0.143756424\) \(a_{13}=+0.485311320\) \(a_{14}=-0.327546413\) \(a_{15}=-0.275817998\)
\(a_{16}=-0.689008840\) \(a_{17}=-0.648707707\) \(a_{18}=-0.288868784\) \(a_{19}=-0.453710356\) \(a_{20}=+0.118951827\)
\(a_{21}=+0.218217890\) \(a_{22}=-0.251269099\) \(a_{23}=-0.547184157\) \(a_{24}=+0.624915641\) \(a_{25}=-0.771773297\)
\(a_{26}=-0.420573872\) \(a_{27}=+0.192450090\) \(a_{28}=-0.094110671\) \(a_{29}=-1.713021023\) \(a_{30}=+0.239025629\)
\(a_{31}=-0.362113381\) \(a_{32}=-0.485286203\) \(a_{33}=+0.167400437\) \(a_{34}=+0.562174219\) \(a_{35}=-0.180565265\)
\(a_{36}=-0.082997810\) \(a_{37}=+0.455859336\) \(a_{38}=+0.393188276\) \(a_{39}=+0.280194621\) \(a_{40}=-0.517088942\)
\(a_{41}=+0.693338622\) \(a_{42}=-0.189109010\) \(a_{43}=+0.654026674\) \(a_{44}=-0.072194665\) \(a_{45}=-0.159243595\)
\(a_{46}=+0.474193266\) \(a_{47}=-1.595676531\) \(a_{48}=-0.397799439\) \(a_{49}=+0.142857143\) \(a_{50}=+0.668823641\)
\(a_{51}=-0.374531569\) \(a_{52}=-0.120839331\) \(a_{53}=-1.452935547\) \(a_{54}=-0.166778470\) \(a_{55}=-0.138516160\)
\(a_{56}=+0.409103318\) \(a_{57}=-0.261949796\) \(a_{58}=+1.484514899\) \(a_{59}=-1.926973642\) \(a_{60}=+0.068676870\)
\(a_{61}=+1.360886025\) \(a_{62}=+0.313809756\) \(a_{63}=+0.125988158\) \(a_{64}=+1.109560946\) \(a_{65}=-0.231848158\)
\(a_{66}=-0.145070282\) \(a_{67}=+1.332741208\) \(a_{68}=+0.161523958\) \(a_{69}=-0.315916920\) \(a_{70}=+0.156479005\)
\(a_{71}=+0.217751005\) \(a_{72}=+0.360795214\) \(a_{73}=-1.915470374\) \(a_{74}=-0.395050596\) \(a_{75}=-0.445583521\)
\(a_{76}=+0.112970898\) \(a_{77}=+0.109589311\) \(a_{78}=-0.242818438\) \(a_{79}=-0.239405730\) \(a_{80}=+0.329160735\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.600851654\) \(a_{83}=+0.041268223\) \(a_{84}=-0.054334821\) \(a_{85}=+0.309907642\)
\(a_{86}=-0.566783670\) \(a_{87}=-0.989013149\) \(a_{88}=+0.313833454\) \(a_{89}=+0.166029575\) \(a_{90}=+0.138001511\)
\(a_{91}=+0.183430437\) \(a_{92}=+0.136245261\) \(a_{93}=-0.209066258\) \(a_{94}=+1.382823417\) \(a_{95}=+0.216751405\)
\(a_{96}=-0.280180120\) \(a_{97}=+0.734485542\) \(a_{98}=-0.123800907\) \(a_{99}=+0.096648687\) \(a_{100}=+0.192166481\)

Showing 100 of 262 available coefficients

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