Properties

Level $68$
Weight $0$
Character 68.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.47522396 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.988811938\) \(a_{4}=+0.000000000\) \(a_{5}=+0.511031662\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.730785634\) \(a_{8}=+0.000000000\) \(a_{9}=-0.022250951\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.734292702\) \(a_{12}=+0.000000000\) \(a_{13}=-0.842083874\) \(a_{14}=+0.000000000\) \(a_{15}=+0.505314208\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-1.982850170\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.722609559\) \(a_{22}=+0.000000000\) \(a_{23}=-0.205508778\) \(a_{24}=+0.000000000\) \(a_{25}=-0.738846640\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.010813944\) \(a_{28}=+0.000000000\) \(a_{29}=+1.002102994\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.664119432\) \(a_{32}=+0.000000000\) \(a_{33}=+0.726077390\) \(a_{34}=+0.000000000\) \(a_{35}=+0.373454597\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.073282460\) \(a_{38}=+0.000000000\) \(a_{39}=-0.832662587\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.759259280\) \(a_{42}=+0.000000000\) \(a_{43}=+1.489820764\) \(a_{44}=+0.000000000\) \(a_{45}=-0.011370941\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.106761780\) \(a_{48}=+0.000000000\) \(a_{49}=-0.465952358\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.239822121\) \(a_{52}=+0.000000000\) \(a_{53}=-1.384072410\) \(a_{54}=+0.000000000\) \(a_{55}=+0.375246820\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.960665919\) \(a_{58}=+0.000000000\) \(a_{59}=+0.815561350\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.282946460\) \(a_{62}=+0.000000000\) \(a_{63}=-0.016260676\) \(a_{64}=+0.000000000\) \(a_{65}=-0.430331521\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.312364956\) \(a_{68}=+0.000000000\) \(a_{69}=-0.203209533\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.289920400\) \(a_{72}=+0.000000000\) \(a_{73}=+0.485066710\) \(a_{74}=+0.000000000\) \(a_{75}=-0.730580378\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.536610557\) \(a_{78}=+0.000000000\) \(a_{79}=-1.614246250\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.977253944\) \(a_{82}=+0.000000000\) \(a_{83}=+1.014087830\) \(a_{84}=+0.000000000\) \(a_{85}=-0.123943384\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.990891404\) \(a_{88}=+0.000000000\) \(a_{89}=-1.254923500\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.615382797\) \(a_{92}=+0.000000000\) \(a_{93}=+1.645501161\) \(a_{94}=+0.000000000\) \(a_{95}=-1.013299218\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.061641300\) \(a_{98}=+0.000000000\) \(a_{99}=-0.016338711\) \(a_{100}=+0.000000000\)

Showing 100 of 310 available coefficients

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