Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 13.3101642835 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.041049637\) \(a_{4}=+0.500000000\) \(a_{5}=+1.041949552\)
\(a_{6}=+0.029026477\) \(a_{7}=-1.370237499\) \(a_{8}=-0.353553391\) \(a_{9}=-0.998314927\) \(a_{10}=-0.736769594\)
\(a_{11}=+0.501563457\) \(a_{12}=-0.020524819\) \(a_{13}=-1.238579805\) \(a_{14}=+0.968904227\) \(a_{15}=-0.042771651\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.042293530\) \(a_{18}=+0.705915255\) \(a_{19}=-0.324962839\) \(a_{20}=+0.520974776\)
\(a_{21}=+0.056247752\) \(a_{22}=-0.354658921\) \(a_{23}=-0.343976494\) \(a_{24}=+0.014513238\) \(a_{25}=+0.085658868\)
\(a_{26}=+0.875808179\) \(a_{27}=+0.082030103\) \(a_{28}=-0.685118749\) \(a_{29}=-0.839578150\) \(a_{30}=+0.030244125\)
\(a_{31}=+1.227276131\) \(a_{32}=-0.176776695\) \(a_{33}=-0.020588998\) \(a_{34}=+0.737012823\) \(a_{35}=-1.427718347\)
\(a_{36}=-0.499157464\) \(a_{37}=+0.819716167\) \(a_{38}=+0.229783427\) \(a_{39}=+0.050843252\) \(a_{40}=-0.368384797\)
\(a_{41}=+0.808449395\) \(a_{42}=-0.039773167\) \(a_{43}=-0.653058363\) \(a_{44}=+0.250781728\) \(a_{45}=-1.040193791\)
\(a_{46}=+0.243228112\) \(a_{47}=+0.558171757\) \(a_{48}=-0.010262409\) \(a_{49}=+0.877550803\) \(a_{50}=-0.060569967\)
\(a_{51}=+0.042785772\) \(a_{52}=-0.619289903\) \(a_{53}=-1.097294437\) \(a_{54}=-0.058004043\) \(a_{55}=+0.522603818\)
\(a_{56}=+0.484452116\) \(a_{57}=+0.013339606\) \(a_{58}=+0.593671403\) \(a_{59}=+0.342652063\) \(a_{60}=-0.021385826\)
\(a_{61}=-1.205530337\) \(a_{62}=-0.867815274\) \(a_{63}=+1.367928549\) \(a_{64}=+0.125000000\) \(a_{65}=-1.290537672\)
\(a_{66}=+0.014558620\) \(a_{67}=+1.499806588\) \(a_{68}=-0.521146765\) \(a_{69}=+0.014120110\) \(a_{70}=+1.009549325\)
\(a_{71}=-0.904174260\) \(a_{72}=+0.352957627\) \(a_{73}=-0.281864809\) \(a_{74}=-0.579626860\) \(a_{75}=-0.003516265\)
\(a_{76}=-0.162481420\) \(a_{77}=-0.687261056\) \(a_{78}=-0.035951608\) \(a_{79}=+1.614428722\) \(a_{80}=+0.260487388\)
\(a_{81}=+0.994947621\) \(a_{82}=-0.571660049\) \(a_{83}=-0.850978080\) \(a_{84}=+0.028123876\) \(a_{85}=-1.086017276\)
\(a_{86}=+0.461781997\) \(a_{87}=+0.034464379\) \(a_{88}=-0.177329461\) \(a_{89}=-0.902015256\) \(a_{90}=+0.735528083\)
\(a_{91}=+1.697148494\) \(a_{92}=-0.171988248\) \(a_{93}=-0.050379241\) \(a_{94}=-0.394687035\) \(a_{95}=-0.338594887\)
\(a_{96}=+0.007256622\) \(a_{97}=+0.549952794\) \(a_{98}=-0.620522128\) \(a_{99}=-0.500718287\) \(a_{100}=+0.042829431\)

Showing 100 of 4999 available coefficients

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