Properties

Level $53$
Weight $0$
Character 53.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 53 \)
Weight: \( 0 \)
Character: 53.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.8039894596 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.198396668\) \(a_{3}=+0.569921455\) \(a_{4}=-0.960638762\) \(a_{5}=+1.872312561\)
\(a_{6}=+0.113070518\) \(a_{7}=-0.781149968\) \(a_{8}=-0.388984197\) \(a_{9}=-0.675189535\) \(a_{10}=+0.371460573\)
\(a_{11}=-0.248376761\) \(a_{12}=-0.547488642\) \(a_{13}=-0.552914205\) \(a_{14}=-0.154977551\) \(a_{15}=+1.067071100\)
\(a_{16}=+0.883465594\) \(a_{17}=-0.072909181\) \(a_{18}=-0.133955354\) \(a_{19}=-0.280254190\) \(a_{20}=-1.798616021\)
\(a_{21}=-0.445194127\) \(a_{22}=-0.049277122\) \(a_{23}=+0.497550674\) \(a_{24}=-0.221690440\) \(a_{25}=+2.505554326\)
\(a_{26}=-0.109696336\) \(a_{27}=-0.954726458\) \(a_{28}=+0.750402938\) \(a_{29}=+1.174409712\) \(a_{30}=+0.211703351\)
\(a_{31}=+0.890776468\) \(a_{32}=+0.564260827\) \(a_{33}=-0.141555245\) \(a_{34}=-0.014464938\) \(a_{35}=-1.462556897\)
\(a_{36}=+0.648613239\) \(a_{37}=-0.090005347\) \(a_{38}=-0.055601497\) \(a_{39}=-0.315117669\) \(a_{40}=-0.728299998\)
\(a_{41}=-0.893436325\) \(a_{42}=-0.088325031\) \(a_{43}=-1.011924360\) \(a_{44}=+0.238600345\) \(a_{45}=-1.264165847\)
\(a_{46}=+0.098712396\) \(a_{47}=+1.402639369\) \(a_{48}=+0.503505997\) \(a_{49}=-0.389804728\) \(a_{50}=+0.497093629\)
\(a_{51}=-0.041552506\) \(a_{52}=+0.531150818\) \(a_{53}=+0.137360564\) \(a_{54}=-0.189414548\) \(a_{55}=-0.465038930\)
\(a_{56}=+0.303854993\) \(a_{57}=-0.159722876\) \(a_{58}=+0.232998973\) \(a_{59}=-0.081428245\) \(a_{60}=-1.025069861\)
\(a_{61}=-1.011243660\) \(a_{62}=+0.176727083\) \(a_{63}=+0.527424283\) \(a_{64}=-0.771518126\) \(a_{65}=-1.035228211\)
\(a_{66}=-0.028084089\) \(a_{67}=+0.443731128\) \(a_{68}=+0.070039385\) \(a_{69}=+0.283564804\) \(a_{70}=-0.290166415\)
\(a_{71}=-0.223081663\) \(a_{72}=+0.262638059\) \(a_{73}=+0.736715984\) \(a_{74}=-0.017856761\) \(a_{75}=+1.427969168\)
\(a_{76}=+0.269223038\) \(a_{77}=+0.194019499\) \(a_{78}=-0.062518295\) \(a_{79}=+0.465631941\) \(a_{80}=+1.654123728\)
\(a_{81}=+0.131070442\) \(a_{82}=-0.177254790\) \(a_{83}=+0.640085546\) \(a_{84}=+0.427670735\) \(a_{85}=-0.136508775\)
\(a_{86}=-0.200762421\) \(a_{87}=+0.669321292\) \(a_{88}=+0.096614635\) \(a_{89}=-1.607455504\) \(a_{90}=-0.250806292\)
\(a_{91}=+0.431908914\) \(a_{92}=-0.477966464\) \(a_{93}=+0.507672621\) \(a_{94}=+0.278278977\) \(a_{95}=-0.524723440\)
\(a_{96}=+0.321584352\) \(a_{97}=+0.925139131\) \(a_{98}=-0.077335959\) \(a_{99}=+0.167701390\) \(a_{100}=-2.406932606\)

Showing 100 of 546 available coefficients

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