Properties

Level $49$
Weight $0$
Character 49.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 49 = 7^{2} \)
Weight: \( 0 \)
Character: 49.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 1.50418661999 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.260688906\) \(a_{3}=-0.804858100\) \(a_{4}=-0.932041294\) \(a_{5}=-0.454220740\)
\(a_{6}=+0.209817578\) \(a_{7}=+0.000000000\) \(a_{8}=+0.503661731\) \(a_{9}=-0.352203439\) \(a_{10}=+0.118410308\)
\(a_{11}=+0.740623100\) \(a_{12}=+0.750160985\) \(a_{13}=-1.198138300\) \(a_{14}=+0.000000000\) \(a_{15}=+0.365583242\)
\(a_{16}=+0.800742269\) \(a_{17}=+0.243410006\) \(a_{18}=+0.091815529\) \(a_{19}=-0.641487000\) \(a_{20}=+0.423352486\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.193072226\) \(a_{23}=-0.949197000\) \(a_{24}=-0.405376224\) \(a_{25}=-0.793683519\)
\(a_{26}=+0.312341363\) \(a_{27}=+1.088331891\) \(a_{28}=+0.000000000\) \(a_{29}=-0.767708000\) \(a_{30}=-0.095303495\)
\(a_{31}=-0.411640000\) \(a_{32}=-0.712406357\) \(a_{33}=-0.596096501\) \(a_{34}=-0.063454287\) \(a_{35}=+0.000000000\)
\(a_{36}=+0.328268149\) \(a_{37}=+1.089497998\) \(a_{38}=+0.167228544\) \(a_{39}=+0.964331316\) \(a_{40}=-0.228773604\)
\(a_{41}=-0.620020002\) \(a_{42}=+0.000000000\) \(a_{43}=+0.388529986\) \(a_{44}=-0.690291313\) \(a_{45}=+0.159978107\)
\(a_{46}=+0.247445128\) \(a_{47}=+1.605029941\) \(a_{48}=-0.644483901\) \(a_{49}=+0.000000000\) \(a_{50}=+0.206904488\)
\(a_{51}=-0.195910510\) \(a_{52}=+1.116714372\) \(a_{53}=+0.839500427\) \(a_{54}=-0.283716050\) \(a_{55}=-0.336406373\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.516306008\) \(a_{58}=+0.200132959\) \(a_{59}=-0.670400023\) \(a_{60}=-0.340738678\)
\(a_{61}=-0.872500002\) \(a_{62}=+0.107309981\) \(a_{63}=+0.000000000\) \(a_{64}=-0.615025835\) \(a_{65}=+0.544219265\)
\(a_{66}=+0.155395745\) \(a_{67}=-0.860000610\) \(a_{68}=-0.226868171\) \(a_{69}=+0.763968894\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.544399977\) \(a_{72}=-0.177391394\) \(a_{73}=-1.017999649\) \(a_{74}=-0.284020042\) \(a_{75}=+0.638802609\)
\(a_{76}=+0.597892374\) \(a_{77}=+0.000000000\) \(a_{78}=-0.251390476\) \(a_{79}=-0.765999794\) \(a_{80}=-0.363713746\)
\(a_{81}=-0.523749299\) \(a_{82}=+0.161632335\) \(a_{83}=+0.900390625\) \(a_{84}=+0.000000000\) \(a_{85}=-0.110561870\)
\(a_{86}=-0.101285461\) \(a_{87}=+0.617896002\) \(a_{88}=+0.373023513\) \(a_{89}=-1.426000000\) \(a_{90}=-0.041704518\)
\(a_{91}=+0.000000000\) \(a_{92}=+0.884690800\) \(a_{93}=+0.331311788\) \(a_{94}=-0.418413515\) \(a_{95}=+0.291376700\)
\(a_{96}=+0.573386027\) \(a_{97}=-1.430000000\) \(a_{98}=+0.000000000\) \(a_{99}=-0.260850003\) \(a_{100}=+0.739745815\)

Showing 100 of 106 available coefficients

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