Properties

Level $33$
Weight $0$
Character 33.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.673141432593 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.143867981\) \(a_{3}=+0.577350269\) \(a_{4}=-0.979302004\) \(a_{5}=+0.257039480\)
\(a_{6}=+0.083062218\) \(a_{7}=-0.730544151\) \(a_{8}=-0.284758184\) \(a_{9}=+0.333333333\) \(a_{10}=+0.036979751\)
\(a_{11}=-0.301511345\) \(a_{12}=-0.565400276\) \(a_{13}=+0.189879323\) \(a_{14}=-0.105101912\) \(a_{15}=+0.148401813\)
\(a_{16}=+0.938334419\) \(a_{17}=+1.008266882\) \(a_{18}=+0.047955994\) \(a_{19}=+1.148506172\) \(a_{20}=-0.251719278\)
\(a_{21}=-0.421779862\) \(a_{22}=-0.043377829\) \(a_{23}=-0.654153294\) \(a_{24}=-0.164405214\) \(a_{25}=-0.933930705\)
\(a_{26}=+0.027317556\) \(a_{27}=+0.192450090\) \(a_{28}=+0.715423351\) \(a_{29}=-1.087910391\) \(a_{30}=+0.021350270\)
\(a_{31}=-0.211652560\) \(a_{32}=+0.419754462\) \(a_{33}=-0.174077655\) \(a_{34}=+0.145057320\) \(a_{35}=-0.187778688\)
\(a_{36}=-0.326434007\) \(a_{37}=-0.370644593\) \(a_{38}=+0.165233267\) \(a_{39}=+0.109626869\) \(a_{40}=-0.073194079\)
\(a_{41}=-0.703086696\) \(a_{42}=-0.060680604\) \(a_{43}=+0.101262882\) \(a_{44}=+0.295270658\) \(a_{45}=+0.085679823\)
\(a_{46}=-0.094111696\) \(a_{47}=+1.731247522\) \(a_{48}=+0.541747656\) \(a_{49}=-0.466305156\) \(a_{50}=-0.134362754\)
\(a_{51}=+0.582123184\) \(a_{52}=-0.185949136\) \(a_{53}=+1.457801160\) \(a_{54}=+0.027687342\) \(a_{55}=-0.077500103\)
\(a_{56}=+0.208028527\) \(a_{57}=+0.663089958\) \(a_{58}=-0.156515397\) \(a_{59}=-1.004498562\) \(a_{60}=-0.145330360\)
\(a_{61}=-0.987846620\) \(a_{62}=-0.030450155\) \(a_{63}=-0.243513750\) \(a_{64}=-0.877945275\) \(a_{65}=+0.048807256\)
\(a_{66}=-0.025044050\) \(a_{67}=+0.743831804\) \(a_{68}=-0.987397764\) \(a_{69}=-0.377674223\) \(a_{70}=-0.027015817\)
\(a_{71}=-0.421918994\) \(a_{72}=-0.094919283\) \(a_{73}=+1.254108206\) \(a_{74}=-0.053323819\) \(a_{75}=-0.539205149\)
\(a_{76}=-1.124734391\) \(a_{77}=+0.220267250\) \(a_{78}=+0.015771879\) \(a_{79}=+1.289053393\) \(a_{80}=+0.241188962\)
\(a_{81}=+0.111110828\) \(a_{82}=-0.101152035\) \(a_{83}=-1.642374732\) \(a_{84}=+0.413049905\) \(a_{85}=+0.259164197\)
\(a_{86}=+0.014568652\) \(a_{87}=-0.628105314\) \(a_{88}=+0.085857787\) \(a_{89}=+1.013047927\) \(a_{90}=+0.012326692\)
\(a_{91}=-0.138715101\) \(a_{92}=+0.640613613\) \(a_{93}=-0.122198367\) \(a_{94}=+0.249071133\) \(a_{95}=+0.295211698\)
\(a_{96}=+0.242345242\) \(a_{97}=+0.240672811\) \(a_{98}=-0.067084682\) \(a_{99}=-0.100503653\) \(a_{100}=+0.914600292\)

Showing 100 of 2000 available coefficients

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