Properties

Level $33$
Weight $0$
Character 33.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.67574985339 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.387175607\) \(a_{3}=+0.577350269\) \(a_{4}=-0.850095049\) \(a_{5}=+1.692073635\)
\(a_{6}=-0.223535941\) \(a_{7}=-0.296757183\) \(a_{8}=+0.716311674\) \(a_{9}=+0.333333333\) \(a_{10}=-0.655129637\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.490802606\) \(a_{13}=+1.244835652\) \(a_{14}=+0.114897143\) \(a_{15}=+0.976919169\)
\(a_{16}=+0.572756642\) \(a_{17}=+1.617010985\) \(a_{18}=-0.129058536\) \(a_{19}=-0.647537161\) \(a_{20}=-1.438423420\)
\(a_{21}=-0.171332840\) \(a_{22}=-0.116737838\) \(a_{23}=-1.559333600\) \(a_{24}=+0.413562738\) \(a_{25}=+1.863113186\)
\(a_{26}=-0.481969999\) \(a_{27}=+0.192450090\) \(a_{28}=+0.252271812\) \(a_{29}=+0.244283948\) \(a_{30}=-0.378239272\)
\(a_{31}=+0.543666110\) \(a_{32}=-0.938069074\) \(a_{33}=+0.174077656\) \(a_{34}=-0.626067210\) \(a_{35}=-0.502135005\)
\(a_{36}=-0.283365016\) \(a_{37}=-0.219217269\) \(a_{38}=+0.250710593\) \(a_{39}=+0.718706199\) \(a_{40}=+1.212052098\)
\(a_{41}=+0.831509233\) \(a_{42}=+0.066335896\) \(a_{43}=-0.536377286\) \(a_{44}=-0.256313301\) \(a_{45}=+0.564024545\)
\(a_{46}=+0.603735933\) \(a_{47}=+0.799919007\) \(a_{48}=+0.330681201\) \(a_{49}=-0.911935174\) \(a_{50}=-0.721351979\)
\(a_{51}=+0.933581727\) \(a_{52}=-1.058228625\) \(a_{53}=-1.678704765\) \(a_{54}=-0.074511980\) \(a_{55}=+0.510179397\)
\(a_{56}=-0.212570635\) \(a_{57}=-0.373855754\) \(a_{58}=-0.094580786\) \(a_{59}=+0.685553853\) \(a_{60}=-0.830474149\)
\(a_{61}=+0.470448553\) \(a_{62}=-0.210494256\) \(a_{63}=-0.098919061\) \(a_{64}=-0.209559179\) \(a_{65}=+2.106353587\)
\(a_{66}=-0.067398622\) \(a_{67}=-0.362430532\) \(a_{68}=-1.374613033\) \(a_{69}=-0.900281674\) \(a_{70}=+0.194414426\)
\(a_{71}=-0.770153726\) \(a_{72}=+0.238770558\) \(a_{73}=-0.118955969\) \(a_{74}=+0.084875579\) \(a_{75}=+1.075668900\)
\(a_{76}=+0.550468135\) \(a_{77}=-0.089475657\) \(a_{78}=-0.278265509\) \(a_{79}=+0.659620916\) \(a_{80}=+0.969146413\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.321940092\) \(a_{83}=-1.043816180\) \(a_{84}=+0.145649199\) \(a_{85}=+2.736101655\)
\(a_{86}=+0.207672201\) \(a_{87}=+0.141037403\) \(a_{88}=+0.215976096\) \(a_{89}=-1.343890603\) \(a_{90}=-0.218376546\)
\(a_{91}=-0.369413922\) \(a_{92}=+1.325581774\) \(a_{93}=+0.313885775\) \(a_{94}=-0.309709127\) \(a_{95}=-1.095680558\)
\(a_{96}=-0.541594433\) \(a_{97}=+0.208681596\) \(a_{98}=+0.353079055\) \(a_{99}=+0.100503782\) \(a_{100}=-1.583823296\)

Showing 100 of 336 available coefficients

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