Properties

Level $67$
Weight $0$
Character 67.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 67 \)
Weight: \( 0 \)
Character: 67.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.49099435082 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.091675600\) \(a_{3}=-1.446357732\) \(a_{4}=+0.191755615\) \(a_{5}=+1.148799427\)
\(a_{6}=+1.578953445\) \(a_{7}=-0.353799029\) \(a_{8}=+0.882340673\) \(a_{9}=+1.091950689\) \(a_{10}=-1.254116304\)
\(a_{11}=-1.064324000\) \(a_{12}=-0.277347217\) \(a_{13}=+1.506215889\) \(a_{14}=+0.386233767\) \(a_{15}=-1.661574934\)
\(a_{16}=-1.154985399\) \(a_{17}=+0.197273352\) \(a_{18}=-1.192055924\) \(a_{19}=+0.820318672\) \(a_{20}=+0.220288741\)
\(a_{21}=+0.511719961\) \(a_{22}=+1.161896541\) \(a_{23}=-1.182692771\) \(a_{24}=-1.276180255\) \(a_{25}=+0.319740124\)
\(a_{26}=-1.644299134\) \(a_{27}=-0.132993590\) \(a_{28}=-0.067842950\) \(a_{29}=+1.238302416\) \(a_{30}=+1.813900813\)
\(a_{31}=-0.736915366\) \(a_{32}=+0.378528705\) \(a_{33}=+1.539393246\) \(a_{34}=-0.215358505\) \(a_{35}=-0.406444121\)
\(a_{36}=+0.209387676\) \(a_{37}=+0.664560245\) \(a_{38}=-0.895521879\) \(a_{39}=-2.178526997\) \(a_{40}=+1.013632460\)
\(a_{41}=-0.976987176\) \(a_{42}=-0.558632195\) \(a_{43}=-1.179742896\) \(a_{44}=-0.204090104\) \(a_{45}=+1.254432326\)
\(a_{46}=+1.291116840\) \(a_{47}=-0.984507171\) \(a_{48}=+1.670522063\) \(a_{49}=-0.874826247\) \(a_{50}=-0.349052491\)
\(a_{51}=-0.285327838\) \(a_{52}=+0.288825355\) \(a_{53}=-0.389826673\) \(a_{54}=+0.145185857\) \(a_{55}=-1.222694801\)
\(a_{56}=-0.312171273\) \(a_{57}=-1.186474254\) \(a_{58}=-1.351824533\) \(a_{59}=+1.465821809\) \(a_{60}=-0.318616324\)
\(a_{61}=-0.010078108\) \(a_{62}=+0.804472525\) \(a_{63}=-0.386331093\) \(a_{64}=+0.741754848\) \(a_{65}=+1.730339950\)
\(a_{66}=-1.680518046\) \(a_{67}=-0.122169444\) \(a_{68}=+0.037828273\) \(a_{69}=+1.710596834\) \(a_{70}=+0.443705130\)
\(a_{71}=+1.301649662\) \(a_{72}=+0.963472506\) \(a_{73}=-1.921794147\) \(a_{74}=-0.725484204\) \(a_{75}=-0.462458600\)
\(a_{76}=+0.157300712\) \(a_{77}=+0.376556797\) \(a_{78}=+2.378244766\) \(a_{79}=+0.869614267\) \(a_{80}=-1.326846565\)
\(a_{81}=-0.899594382\) \(a_{82}=+1.066553061\) \(a_{83}=-0.986487591\) \(a_{84}=+0.098125176\) \(a_{85}=+0.226627513\)
\(a_{86}=+1.287896534\) \(a_{87}=-1.791028274\) \(a_{88}=-0.939096355\) \(a_{89}=-0.417009799\) \(a_{90}=-1.369433162\)
\(a_{91}=-0.532897718\) \(a_{92}=-0.226787980\) \(a_{93}=+1.065843238\) \(a_{94}=+1.074762456\) \(a_{95}=+0.942381621\)
\(a_{96}=-0.547487920\) \(a_{97}=-0.626143735\) \(a_{98}=+0.955026468\) \(a_{99}=-1.162189325\) \(a_{100}=+0.061311964\)

Showing 100 of 546 available coefficients

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