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: \( 0.731381309 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.538488033\) \(a_{3}=-0.084567072\) \(a_{4}=+1.366945428\) \(a_{5}=-1.610526615\)
\(a_{6}=-0.130105428\) \(a_{7}=+0.742108209\) \(a_{8}=+0.564541149\) \(a_{9}=-0.992848410\) \(a_{10}=-2.477775924\)
\(a_{11}=+1.286826094\) \(a_{12}=-0.115598572\) \(a_{13}=+0.288600104\) \(a_{14}=+1.141724599\) \(a_{15}=+0.136197520\)
\(a_{16}=-0.498405625\) \(a_{17}=+0.454834791\) \(a_{18}=-1.527485398\) \(a_{19}=+0.574964882\) \(a_{20}=-2.201501993\)
\(a_{21}=-0.062757918\) \(a_{22}=+1.979766546\) \(a_{23}=-1.059710960\) \(a_{24}=-0.047741592\) \(a_{25}=+1.593795979\)
\(a_{26}=+0.444007806\) \(a_{27}=+0.168529355\) \(a_{28}=+1.014421423\) \(a_{29}=+0.277548047\) \(a_{30}=+0.209538255\)
\(a_{31}=-0.466271873\) \(a_{32}=-1.331332240\) \(a_{33}=-0.108823115\) \(a_{34}=+0.699757883\) \(a_{35}=-1.195185022\)
\(a_{36}=-1.357169595\) \(a_{37}=-0.742519613\) \(a_{38}=+0.884576591\) \(a_{39}=-0.024406066\) \(a_{40}=-0.909208546\)
\(a_{41}=+0.775284151\) \(a_{42}=-0.096552306\) \(a_{43}=+1.590773453\) \(a_{44}=+1.759021045\) \(a_{45}=+1.599008790\)
\(a_{46}=-1.630352630\) \(a_{47}=-0.016209717\) \(a_{48}=+0.042148704\) \(a_{49}=-0.449275406\) \(a_{50}=+2.452036040\)
\(a_{51}=-0.038464047\) \(a_{52}=+0.394500593\) \(a_{53}=-0.060342301\) \(a_{54}=+0.259280396\) \(a_{55}=-2.072467674\)
\(a_{56}=+0.418950621\) \(a_{57}=-0.048623097\) \(a_{58}=+0.427004348\) \(a_{59}=-0.207844435\) \(a_{60}=+0.186174578\)
\(a_{61}=-0.471481965\) \(a_{62}=-0.717353697\) \(a_{63}=-0.736800956\) \(a_{64}=-1.549833093\) \(a_{65}=-0.464798149\)
\(a_{66}=-0.167423060\) \(a_{67}=+0.122169444\) \(a_{68}=+0.621734338\) \(a_{69}=+0.089616653\) \(a_{70}=-1.838777854\)
\(a_{71}=-0.559551566\) \(a_{72}=-0.560503783\) \(a_{73}=-1.689321002\) \(a_{74}=-1.142357539\) \(a_{75}=-0.134782659\)
\(a_{76}=+0.785945617\) \(a_{77}=+0.954964208\) \(a_{78}=-0.037548440\) \(a_{79}=-0.318363101\) \(a_{80}=+0.802695525\)
\(a_{81}=+0.978596376\) \(a_{82}=+1.192765389\) \(a_{83}=+0.821930302\) \(a_{84}=-0.085786650\) \(a_{85}=-0.732523536\)
\(a_{86}=+2.447385921\) \(a_{87}=-0.023471426\) \(a_{88}=+0.726466282\) \(a_{89}=-1.156172991\) \(a_{90}=+2.460055888\)
\(a_{91}=+0.214172506\) \(a_{92}=-1.448567051\) \(a_{93}=+0.039431247\) \(a_{94}=-0.024938455\) \(a_{95}=-0.925996246\)
\(a_{96}=+0.112586869\) \(a_{97}=-1.381292353\) \(a_{98}=-0.691204836\) \(a_{99}=-1.277623242\) \(a_{100}=+2.178632126\)

Showing 100 of 546 available coefficients

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