Properties

Level $45$
Weight $0$
Character 45.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

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

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.950527953\) \(a_{3}=+0.000000000\) \(a_{4}=-0.096496610\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.467578234\) \(a_{8}=-1.042250679\) \(a_{9}=+0.000000000\) \(a_{10}=+0.425089024\)
\(a_{11}=-0.580540082\) \(a_{12}=+0.000000000\) \(a_{13}=+1.319546394\) \(a_{14}=-0.444446181\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.894191794\) \(a_{17}=+0.661588898\) \(a_{18}=+0.000000000\) \(a_{19}=-0.380734605\) \(a_{20}=-0.043154596\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.551819576\) \(a_{23}=+1.165407904\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.254265733\) \(a_{27}=+0.000000000\) \(a_{28}=+0.045119714\) \(a_{29}=-0.955011365\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.320983084\) \(a_{32}=+0.192296383\) \(a_{33}=+0.000000000\) \(a_{34}=+0.628858741\) \(a_{35}=-0.209107343\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.720452504\) \(a_{38}=-0.361898885\) \(a_{39}=+0.000000000\) \(a_{40}=-0.466108673\)
\(a_{41}=-1.404486198\) \(a_{42}=+0.000000000\) \(a_{43}=-1.390961177\) \(a_{44}=+0.056020150\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.107752790\) \(a_{47}=-0.480583080\) \(a_{48}=+0.000000000\) \(a_{49}=-0.781370595\) \(a_{50}=+0.190105591\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.127331754\) \(a_{53}=-0.863111750\) \(a_{54}=+0.000000000\) \(a_{55}=-0.259625418\)
\(a_{56}=+0.487333731\) \(a_{57}=+0.000000000\) \(a_{58}=-0.907764998\) \(a_{59}=+1.249902780\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.708330990\) \(a_{62}=+0.305103394\) \(a_{63}=+0.000000000\) \(a_{64}=+1.076974881\) \(a_{65}=+0.590119087\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.276093300\) \(a_{68}=-0.063841086\) \(a_{69}=+0.000000000\) \(a_{70}=-0.198762375\)
\(a_{71}=+0.449401500\) \(a_{72}=+0.000000000\) \(a_{73}=-0.363213780\) \(a_{74}=+0.684810244\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.036739599\) \(a_{77}=+0.271447906\) \(a_{78}=+0.000000000\) \(a_{79}=-0.436686890\) \(a_{80}=-0.399894727\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.335003391\) \(a_{83}=+0.678473600\) \(a_{84}=+0.000000000\) \(a_{85}=+0.295871550\)
\(a_{86}=-1.322147480\) \(a_{87}=+0.000000000\) \(a_{88}=+0.605068295\) \(a_{89}=-1.130848200\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.616991172\) \(a_{92}=-0.112457912\) \(a_{93}=+0.000000000\) \(a_{94}=-0.456807651\) \(a_{95}=-0.170269691\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.092994200\) \(a_{98}=-0.742714593\) \(a_{99}=+0.000000000\) \(a_{100}=-0.019299322\)

Showing 100 of 256 available coefficients

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