Properties

Level $293$
Weight $0$
Character 293.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 293 \)
Weight: \( 0 \)
Character: 293.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.697875073894 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.459853617\) \(a_{3}=-0.643262538\) \(a_{4}=-0.788534631\) \(a_{5}=-0.063811247\)
\(a_{6}=-0.295806610\) \(a_{7}=+1.778651544\) \(a_{8}=-0.822464125\) \(a_{9}=-0.586213299\) \(a_{10}=-0.029343835\)
\(a_{11}=-1.491082020\) \(a_{12}=+0.507234794\) \(a_{13}=-1.112816608\) \(a_{14}=+0.817919349\) \(a_{15}=+0.041047377\)
\(a_{16}=+0.410321546\) \(a_{17}=-1.218694370\) \(a_{18}=-0.269572313\) \(a_{19}=-0.777476915\) \(a_{20}=+0.050317362\)
\(a_{21}=-1.144139918\) \(a_{22}=-0.685679460\) \(a_{23}=+1.164664840\) \(a_{24}=+0.529060361\) \(a_{25}=-0.995928105\)
\(a_{26}=-0.511732735\) \(a_{27}=+1.020351591\) \(a_{28}=-1.402528377\) \(a_{29}=-1.002602605\) \(a_{30}=+0.018875796\)
\(a_{31}=-0.178187729\) \(a_{32}=+1.011151956\) \(a_{33}=+0.959157198\) \(a_{34}=-0.560421008\) \(a_{35}=-0.113497943\)
\(a_{36}=+0.462249490\) \(a_{37}=+1.801337735\) \(a_{38}=-0.357525567\) \(a_{39}=+0.715833239\) \(a_{40}=+0.052482448\)
\(a_{41}=-0.357503142\) \(a_{42}=-0.526136875\) \(a_{43}=+0.805446135\) \(a_{44}=+1.175769853\) \(a_{45}=+0.037406992\)
\(a_{46}=+0.535575334\) \(a_{47}=-0.187031595\) \(a_{48}=-0.263944466\) \(a_{49}=+2.163601376\) \(a_{50}=-0.457981131\)
\(a_{51}=+0.783940433\) \(a_{52}=+0.877494444\) \(a_{53}=-0.112465104\) \(a_{54}=+0.469212384\) \(a_{55}=+0.095147773\)
\(a_{56}=-1.462877105\) \(a_{57}=+0.500121789\) \(a_{58}=-0.461050446\) \(a_{59}=-1.801438041\) \(a_{60}=-0.032367272\)
\(a_{61}=-1.039171281\) \(a_{62}=-0.081940263\) \(a_{63}=-1.042669197\) \(a_{64}=+0.054660349\) \(a_{65}=+0.071010195\)
\(a_{66}=+0.441071908\) \(a_{67}=-0.090261235\) \(a_{68}=+0.960982739\) \(a_{69}=-0.749185270\) \(a_{70}=-0.052192427\)
\(a_{71}=+0.046151861\) \(a_{72}=+0.482139404\) \(a_{73}=+0.905823272\) \(a_{74}=+0.828351679\) \(a_{75}=+0.640643238\)
\(a_{76}=+0.613067489\) \(a_{77}=-2.652115372\) \(a_{78}=+0.329178505\) \(a_{79}=+0.088026495\) \(a_{80}=-0.026183112\)
\(a_{81}=-0.070140660\) \(a_{82}=-0.164399109\) \(a_{83}=+0.423912383\) \(a_{84}=+0.902193977\) \(a_{85}=+0.077766393\)
\(a_{86}=+0.370387308\) \(a_{87}=+0.644936671\) \(a_{88}=+1.226361482\) \(a_{89}=-0.196782936\) \(a_{90}=+0.017201747\)
\(a_{91}=-1.979312996\) \(a_{92}=-0.918378578\) \(a_{93}=+0.114621492\) \(a_{94}=-0.086007172\) \(a_{95}=+0.049611793\)
\(a_{96}=-0.650436201\) \(a_{97}=-1.512365528\) \(a_{98}=+0.994939919\) \(a_{99}=+0.874092143\) \(a_{100}=+0.785323835\)

Showing 100 of 970 available coefficients

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