Properties

Level $45$
Weight $0$
Character 45.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 45 = 3^{2} \cdot 5 \)
Weight: \( 0 \)
Character: 45.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.9520288783 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.950527953\) \(a_{3}=+0.000000000\) \(a_{4}=-0.096496610\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.467578234\) \(a_{8}=+1.042250679\) \(a_{9}=+0.000000000\) \(a_{10}=+0.425089024\)
\(a_{11}=+0.580540082\) \(a_{12}=+0.000000000\) \(a_{13}=+1.319546394\) \(a_{14}=+0.444446181\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.894191794\) \(a_{17}=-0.661588898\) \(a_{18}=+0.000000000\) \(a_{19}=-0.380734605\) \(a_{20}=+0.043154596\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.551819576\) \(a_{23}=-1.165407904\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.254265733\) \(a_{27}=+0.000000000\) \(a_{28}=+0.045119714\) \(a_{29}=+0.955011365\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.320983084\) \(a_{32}=-0.192296383\) \(a_{33}=+0.000000000\) \(a_{34}=+0.628858741\) \(a_{35}=+0.209107343\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.720452505\) \(a_{38}=+0.361898885\) \(a_{39}=+0.000000000\) \(a_{40}=-0.466108673\)
\(a_{41}=+1.404486198\) \(a_{42}=+0.000000000\) \(a_{43}=-1.390961177\) \(a_{44}=-0.056020150\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.107752790\) \(a_{47}=+0.480583080\) \(a_{48}=+0.000000000\) \(a_{49}=-0.781370596\) \(a_{50}=-0.190105591\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.127331754\) \(a_{53}=+0.863111752\) \(a_{54}=+0.000000000\) \(a_{55}=-0.259625418\)
\(a_{56}=-0.487333731\) \(a_{57}=+0.000000000\) \(a_{58}=-0.907764998\) \(a_{59}=-1.249902777\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.708330992\) \(a_{62}=-0.305103394\) \(a_{63}=+0.000000000\) \(a_{64}=+1.076974881\) \(a_{65}=-0.590119087\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.276093303\) \(a_{68}=+0.063841086\) \(a_{69}=+0.000000000\) \(a_{70}=-0.198762375\)
\(a_{71}=-0.449401500\) \(a_{72}=+0.000000000\) \(a_{73}=-0.363213780\) \(a_{74}=-0.684810245\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.036739599\) \(a_{77}=-0.271447906\) \(a_{78}=+0.000000000\) \(a_{79}=-0.436686890\) \(a_{80}=+0.399894727\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.335003391\) \(a_{83}=-0.678473570\) \(a_{84}=+0.000000000\) \(a_{85}=+0.295871550\)
\(a_{86}=+1.322147480\) \(a_{87}=+0.000000000\) \(a_{88}=+0.605068295\) \(a_{89}=+1.130848210\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.616991172\) \(a_{92}=+0.112457912\) \(a_{93}=+0.000000000\) \(a_{94}=-0.456807651\) \(a_{95}=+0.170269691\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.092994260\) \(a_{98}=+0.742714593\) \(a_{99}=+0.000000000\) \(a_{100}=-0.019299322\)

Showing 100 of 306 available coefficients

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