Properties

Level $65$
Weight $0$
Character 65.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.4772609848 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.844245536\) \(a_{3}=-1.195020476\) \(a_{4}=+2.401241599\) \(a_{5}=-0.447213595\)
\(a_{6}=-2.203911179\) \(a_{7}=-1.531173913\) \(a_{8}=+2.584233564\) \(a_{9}=+0.428073938\) \(a_{10}=-0.824771677\)
\(a_{11}=-1.314812201\) \(a_{12}=-2.869532879\) \(a_{13}=-0.277350098\) \(a_{14}=-2.823860654\) \(a_{15}=+0.534429404\)
\(a_{16}=+2.364719617\) \(a_{17}=-0.613124523\) \(a_{18}=+0.789473450\) \(a_{19}=+1.757496333\) \(a_{20}=-1.073867889\)
\(a_{21}=+1.829784178\) \(a_{22}=-2.424836534\) \(a_{23}=-0.367903266\) \(a_{24}=-3.088212024\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.511501680\) \(a_{27}=+0.683463355\) \(a_{28}=-3.676718494\) \(a_{29}=-0.677025779\) \(a_{30}=+0.985619042\)
\(a_{31}=+0.745375093\) \(a_{32}=+1.776890035\) \(a_{33}=+1.571227503\) \(a_{34}=-1.130752166\) \(a_{35}=+0.684761791\)
\(a_{36}=+1.027908947\) \(a_{37}=-0.692464955\) \(a_{38}=+3.241254768\) \(a_{39}=+0.331439046\) \(a_{40}=-1.155704384\)
\(a_{41}=-0.845509143\) \(a_{42}=+3.374571303\) \(a_{43}=-0.339926456\) \(a_{44}=-3.157181753\) \(a_{45}=-0.191440485\)
\(a_{46}=-0.678503956\) \(a_{47}=+0.459393905\) \(a_{48}=-2.825888363\) \(a_{49}=+1.344493551\) \(a_{50}=+0.368849107\)
\(a_{51}=+0.732696360\) \(a_{52}=-0.665984593\) \(a_{53}=-1.474526511\) \(a_{54}=+1.260474241\) \(a_{55}=+0.588001892\)
\(a_{56}=-3.956911018\) \(a_{57}=-2.100244104\) \(a_{58}=-1.248601771\) \(a_{59}=-0.453604144\) \(a_{60}=+1.283294116\)
\(a_{61}=-0.401806427\) \(a_{62}=+1.374654688\) \(a_{63}=-0.655455647\) \(a_{64}=+0.912301899\) \(a_{65}=+0.124034735\)
\(a_{66}=+2.897729309\) \(a_{67}=-0.784969596\) \(a_{68}=-1.472260111\) \(a_{69}=+0.439651936\) \(a_{70}=+1.262868876\)
\(a_{71}=+1.244017519\) \(a_{72}=+1.106243039\) \(a_{73}=+0.328369402\) \(a_{74}=-1.277075403\) \(a_{75}=-0.239004095\)
\(a_{76}=+4.220173305\) \(a_{77}=+2.013206143\) \(a_{78}=+0.611254982\) \(a_{79}=-1.645771374\) \(a_{80}=-1.057534762\)
\(a_{81}=-1.244826642\) \(a_{82}=-1.559326463\) \(a_{83}=-0.914670142\) \(a_{84}=+4.393753885\) \(a_{85}=+0.274197623\)
\(a_{86}=-0.626907849\) \(a_{87}=+0.809059669\) \(a_{88}=-3.397781822\) \(a_{89}=-0.023865742\) \(a_{90}=-0.353063260\)
\(a_{91}=+0.424671235\) \(a_{92}=-0.883424626\) \(a_{93}=-0.890738498\) \(a_{94}=+0.847235159\) \(a_{95}=-0.785976254\)
\(a_{96}=-2.123419976\) \(a_{97}=-0.733264816\) \(a_{98}=+2.479576230\) \(a_{99}=-0.562836837\) \(a_{100}=+0.480248320\)

Showing 100 of 502 available coefficients

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