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: \( 22.1946739776 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.596845692\) \(a_{3}=-1.116480464\) \(a_{4}=+1.549916165\) \(a_{5}=-0.638230992\)
\(a_{6}=-1.782847019\) \(a_{7}=-0.995227443\) \(a_{8}=+0.878131258\) \(a_{9}=+0.246528626\) \(a_{10}=-1.019156410\)
\(a_{11}=-0.825934593\) \(a_{12}=-1.730451118\) \(a_{13}=+0.531935412\) \(a_{14}=-1.589224655\) \(a_{15}=+0.712572434\)
\(a_{16}=-0.147676047\) \(a_{17}=-0.588261344\) \(a_{18}=+0.393668174\) \(a_{19}=+0.368540574\) \(a_{20}=-0.989204531\)
\(a_{21}=+1.111151997\) \(a_{22}=-1.318890097\) \(a_{23}=+1.639354617\) \(a_{24}=-0.980416395\) \(a_{25}=-0.592661201\)
\(a_{26}=+0.849418772\) \(a_{27}=+0.841236069\) \(a_{28}=-1.542519101\) \(a_{29}=-0.127551432\) \(a_{30}=+1.137868221\)
\(a_{31}=+0.109380599\) \(a_{32}=-1.113947119\) \(a_{33}=+0.922139837\) \(a_{34}=-0.939362593\) \(a_{35}=+0.635184998\)
\(a_{36}=+0.382098702\) \(a_{37}=-0.651136677\) \(a_{38}=+0.588502428\) \(a_{39}=-0.593895496\) \(a_{40}=-0.560450584\)
\(a_{41}=+0.564530383\) \(a_{42}=+1.774338280\) \(a_{43}=-1.346868756\) \(a_{44}=-1.280129377\) \(a_{45}=-0.157342210\)
\(a_{46}=+2.617796359\) \(a_{47}=-1.379067735\) \(a_{48}=+0.164877422\) \(a_{49}=-0.009522337\) \(a_{50}=-0.946388486\)
\(a_{51}=+0.656782298\) \(a_{52}=+0.824455294\) \(a_{53}=-1.690412382\) \(a_{54}=+1.343324193\) \(a_{55}=+0.527137055\)
\(a_{56}=-0.873940328\) \(a_{57}=-0.411468351\) \(a_{58}=-0.203679948\) \(a_{59}=-0.006191552\) \(a_{60}=+1.104427533\)
\(a_{61}=+0.043956530\) \(a_{62}=+0.174663938\) \(a_{63}=-0.245352054\) \(a_{64}=-1.631125610\) \(a_{65}=-0.339497666\)
\(a_{66}=+1.472515027\) \(a_{67}=+1.732309221\) \(a_{68}=-0.911755766\) \(a_{69}=-1.830307404\) \(a_{70}=+1.014292428\)
\(a_{71}=-0.079566554\) \(a_{72}=+0.216484493\) \(a_{73}=+0.041293918\) \(a_{74}=-1.039764798\) \(a_{75}=+0.661694652\)
\(a_{76}=+0.571206993\) \(a_{77}=+0.821992773\) \(a_{78}=-0.948359464\) \(a_{79}=-0.443696794\) \(a_{80}=+0.094251430\)
\(a_{81}=-1.185752263\) \(a_{82}=+0.901467910\) \(a_{83}=+0.022710546\) \(a_{84}=+1.722192442\) \(a_{85}=+0.375446621\)
\(a_{86}=-2.150741570\) \(a_{87}=+0.142408682\) \(a_{88}=-0.725278984\) \(a_{89}=+0.869378004\) \(a_{90}=-0.251251229\)
\(a_{91}=-0.529396720\) \(a_{92}=+2.540862221\) \(a_{93}=-0.122121301\) \(a_{94}=-2.202158371\) \(a_{95}=-0.235214016\)
\(a_{96}=+1.243700194\) \(a_{97}=-0.072600048\) \(a_{98}=-0.015205704\) \(a_{99}=-0.203616518\) \(a_{100}=-0.918575179\)

Showing 100 of 4999 available coefficients

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