Properties

Level $51$
Weight $0$
Character 51.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.58273406161 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.398768961\) \(a_{3}=-0.577350269\) \(a_{4}=-0.840983316\) \(a_{5}=-0.887064769\)
\(a_{6}=+0.230229367\) \(a_{7}=-0.119382215\) \(a_{8}=+0.734127003\) \(a_{9}=+0.333333333\) \(a_{10}=+0.353733896\)
\(a_{11}=-1.071433007\) \(a_{12}=+0.485541944\) \(a_{13}=-0.314296097\) \(a_{14}=+0.047605922\) \(a_{15}=+0.512147083\)
\(a_{16}=+0.548236254\) \(a_{17}=-0.242535625\) \(a_{18}=-0.132922987\) \(a_{19}=+0.177890040\) \(a_{20}=+0.746006671\)
\(a_{21}=+0.068925354\) \(a_{22}=+0.427254227\) \(a_{23}=+1.676983539\) \(a_{24}=-0.423848423\) \(a_{25}=-0.213116096\)
\(a_{26}=+0.125331528\) \(a_{27}=-0.192450090\) \(a_{28}=+0.100398451\) \(a_{29}=+1.272234901\) \(a_{30}=-0.204228360\)
\(a_{31}=-0.877225213\) \(a_{32}=-0.952746604\) \(a_{33}=+0.618592135\) \(a_{34}=+0.096715679\) \(a_{35}=+0.105899757\)
\(a_{36}=-0.280327772\) \(a_{37}=+0.145631301\) \(a_{38}=-0.070937026\) \(a_{39}=+0.181458936\) \(a_{40}=-0.651218200\)
\(a_{41}=-0.137756684\) \(a_{42}=-0.027485292\) \(a_{43}=-1.282689205\) \(a_{44}=+0.901057284\) \(a_{45}=-0.295688256\)
\(a_{46}=-0.668728982\) \(a_{47}=+1.122493075\) \(a_{48}=-0.316524349\) \(a_{49}=-0.985747887\) \(a_{50}=+0.084984084\)
\(a_{51}=+0.140028008\) \(a_{52}=+0.264317774\) \(a_{53}=+1.551677415\) \(a_{54}=+0.076743122\) \(a_{55}=+0.950430473\)
\(a_{56}=-0.087641708\) \(a_{57}=-0.102704863\) \(a_{58}=-0.507327789\) \(a_{59}=-0.571005523\) \(a_{60}=-0.430707152\)
\(a_{61}=+1.090897015\) \(a_{62}=+0.349810186\) \(a_{63}=-0.039794072\) \(a_{64}=-0.168310481\) \(a_{65}=+0.278800995\)
\(a_{66}=-0.246675343\) \(a_{67}=+1.407455560\) \(a_{68}=+0.203968414\) \(a_{69}=-0.968206897\) \(a_{70}=-0.042229536\)
\(a_{71}=-0.530619538\) \(a_{72}=+0.244709001\) \(a_{73}=-0.172366985\) \(a_{74}=-0.058073242\) \(a_{75}=+0.123042635\)
\(a_{76}=-0.149602556\) \(a_{77}=+0.127910045\) \(a_{78}=-0.072360191\) \(a_{79}=+0.389804382\) \(a_{80}=-0.486321066\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.054933090\) \(a_{83}=+0.503775001\) \(a_{84}=-0.057965073\) \(a_{85}=+0.215144808\)
\(a_{86}=+0.511496641\) \(a_{87}=-0.734525162\) \(a_{88}=-0.786567903\) \(a_{89}=-0.725081860\) \(a_{90}=+0.117911299\)
\(a_{91}=+0.037521364\) \(a_{92}=-1.410315177\) \(a_{93}=+0.506466213\) \(a_{94}=-0.447615397\) \(a_{95}=-0.157799987\)
\(a_{96}=+0.550068509\) \(a_{97}=-0.511534496\) \(a_{98}=+0.393085660\) \(a_{99}=-0.357144336\) \(a_{100}=+0.179227081\)

Showing 100 of 486 available coefficients

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