Properties

Level $293$
Weight $0$
Character 293.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 293 \)
Weight: \( 0 \)
Character: 293.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.95512306675 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.285200795\) \(a_{3}=-0.050164140\) \(a_{4}=+0.651741066\) \(a_{5}=-0.174898474\)
\(a_{6}=+0.064470991\) \(a_{7}=+0.554160515\) \(a_{8}=+0.447582679\) \(a_{9}=-0.997483566\) \(a_{10}=+0.224779663\)
\(a_{11}=-0.613686233\) \(a_{12}=-0.032694016\) \(a_{13}=+1.933354294\) \(a_{14}=-0.712207529\) \(a_{15}=+0.008773627\)
\(a_{16}=-1.226974658\) \(a_{17}=-0.899086356\) \(a_{18}=+1.281966665\) \(a_{19}=+0.185135082\) \(a_{20}=-0.113988517\)
\(a_{21}=-0.027798979\) \(a_{22}=+0.788710024\) \(a_{23}=-0.981380542\) \(a_{24}=-0.022452597\) \(a_{25}=-0.969410528\)
\(a_{26}=-2.484748460\) \(a_{27}=+0.100202045\) \(a_{28}=+0.361169157\) \(a_{29}=-1.459372634\) \(a_{30}=-0.011275881\)
\(a_{31}=+0.202718765\) \(a_{32}=+1.129326121\) \(a_{33}=+0.030785042\) \(a_{34}=+1.155506484\) \(a_{35}=-0.096921824\)
\(a_{36}=-0.650100997\) \(a_{37}=-0.916422504\) \(a_{38}=-0.237935764\) \(a_{39}=-0.096985051\) \(a_{40}=-0.078281529\)
\(a_{41}=-0.855829448\) \(a_{42}=+0.035727278\) \(a_{43}=-1.034367584\) \(a_{44}=-0.399964519\) \(a_{45}=+0.174458346\)
\(a_{46}=+1.261271066\) \(a_{47}=-0.632717452\) \(a_{48}=+0.061550117\) \(a_{49}=-0.692906132\) \(a_{50}=+1.245887177\)
\(a_{51}=+0.045101887\) \(a_{52}=+1.260046368\) \(a_{53}=+0.802586461\) \(a_{54}=-0.128779736\) \(a_{55}=+0.107332787\)
\(a_{56}=+0.248032644\) \(a_{57}=-0.009287140\) \(a_{58}=+1.875586846\) \(a_{59}=+1.455483277\) \(a_{60}=+0.005718127\)
\(a_{61}=-1.132157650\) \(a_{62}=-0.260534314\) \(a_{63}=-0.552766003\) \(a_{64}=-0.224436177\) \(a_{65}=-0.338140706\)
\(a_{66}=-0.039564947\) \(a_{67}=+0.492960158\) \(a_{68}=-0.585971497\) \(a_{69}=+0.049230119\) \(a_{70}=+0.124564012\)
\(a_{71}=+0.187800706\) \(a_{72}=-0.446456356\) \(a_{73}=-0.407037060\) \(a_{74}=+1.177786910\) \(a_{75}=+0.048629647\)
\(a_{76}=+0.120660152\) \(a_{77}=-0.340080689\) \(a_{78}=+0.124645244\) \(a_{79}=+0.904275840\) \(a_{80}=+0.214596004\)
\(a_{81}=+0.992457019\) \(a_{82}=+1.099912704\) \(a_{83}=+1.833522119\) \(a_{84}=-0.018117733\) \(a_{85}=+0.157248828\)
\(a_{86}=+1.329370018\) \(a_{87}=+0.073208171\) \(a_{88}=-0.274675331\) \(a_{89}=-0.064420261\) \(a_{90}=-0.224214012\)
\(a_{91}=+1.071388612\) \(a_{92}=-0.639605999\) \(a_{93}=-0.010169220\) \(a_{94}=+0.813168968\) \(a_{95}=-0.032379836\)
\(a_{96}=-0.056651650\) \(a_{97}=-0.557455370\) \(a_{98}=+0.890523495\) \(a_{99}=+0.612141921\) \(a_{100}=-0.631804644\)

Showing 100 of 976 available coefficients

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