Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 22.3339312805 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.499493682\) \(a_{3}=+0.577350269\) \(a_{4}=+1.248481302\) \(a_{5}=-1.786559870\)
\(a_{6}=+0.865733081\) \(a_{7}=+0.327717240\) \(a_{8}=+0.372596142\) \(a_{9}=+0.333333333\) \(a_{10}=-2.678935238\)
\(a_{11}=+0.438024485\) \(a_{12}=+0.720811016\) \(a_{13}=-0.748542179\) \(a_{14}=+0.491409930\) \(a_{15}=-1.031470822\)
\(a_{16}=-0.689775741\) \(a_{17}=-1.270239383\) \(a_{18}=+0.499831227\) \(a_{19}=-1.479519146\) \(a_{20}=-2.230486593\)
\(a_{21}=+0.189207637\) \(a_{22}=+0.656814948\) \(a_{23}=-0.986941234\) \(a_{24}=+0.215118483\) \(a_{25}=+2.191796170\)
\(a_{26}=-1.122434267\) \(a_{27}=+0.192450090\) \(a_{28}=+0.409148846\) \(a_{29}=+0.582174569\) \(a_{30}=-1.546683981\)
\(a_{31}=+0.058940172\) \(a_{32}=-1.406910507\) \(a_{33}=+0.252893554\) \(a_{34}=-1.904715929\) \(a_{35}=-0.585486469\)
\(a_{36}=+0.416160434\) \(a_{37}=+0.672089450\) \(a_{38}=-2.218529612\) \(a_{39}=-0.432171028\) \(a_{40}=-0.665665315\)
\(a_{41}=-0.566454886\) \(a_{42}=+0.283715656\) \(a_{43}=+0.917666691\) \(a_{44}=+0.546865380\) \(a_{45}=-0.595519957\)
\(a_{46}=-1.479912145\) \(a_{47}=-0.082906398\) \(a_{48}=-0.398242210\) \(a_{49}=-0.892601411\) \(a_{50}=+3.286584509\)
\(a_{51}=-0.733373050\) \(a_{52}=-0.934540914\) \(a_{53}=+0.247712598\) \(a_{54}=+0.288577694\) \(a_{55}=-0.782556968\)
\(a_{56}=+0.122106179\) \(a_{57}=-0.854200777\) \(a_{58}=+0.872967087\) \(a_{59}=+0.905337963\) \(a_{60}=-1.287772035\)
\(a_{61}=+0.660212081\) \(a_{62}=+0.088380415\) \(a_{63}=+0.109239080\) \(a_{64}=-1.419877676\) \(a_{65}=+1.337315417\)
\(a_{66}=+0.379212287\) \(a_{67}=+0.862100781\) \(a_{68}=-1.585870119\) \(a_{69}=-0.569810787\) \(a_{70}=-0.877933261\)
\(a_{71}=+0.735527479\) \(a_{72}=+0.124198714\) \(a_{73}=+0.522069879\) \(a_{74}=+1.007793884\) \(a_{75}=+1.265434109\)
\(a_{76}=-1.847151990\) \(a_{77}=+0.143548175\) \(a_{78}=-0.648037726\) \(a_{79}=-0.705579965\) \(a_{80}=+1.232325658\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.849395523\) \(a_{83}=-1.914806265\) \(a_{84}=+0.236222196\) \(a_{85}=+2.269358707\)
\(a_{86}=+1.376035405\) \(a_{87}=+0.336118644\) \(a_{88}=+0.163206233\) \(a_{89}=-1.205617187\) \(a_{90}=-0.892978413\)
\(a_{91}=-0.245310177\) \(a_{92}=-1.232177677\) \(a_{93}=+0.034029124\) \(a_{94}=-0.124317621\) \(a_{95}=+2.643249534\)
\(a_{96}=-0.812280160\) \(a_{97}=+0.392606709\) \(a_{98}=-1.338450176\) \(a_{99}=+0.146008162\) \(a_{100}=+2.736416536\)

Showing 100 of 1228 available coefficients

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