Properties

Level $15$
Weight $0$
Character 15.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 8.67808170374 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.626789692\) \(a_{3}=-0.577350269\) \(a_{4}=-0.607134683\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.361877197\) \(a_{7}=-0.976617120\) \(a_{8}=+1.007335452\) \(a_{9}=+0.333333333\) \(a_{10}=-0.280308872\)
\(a_{11}=+1.181382128\) \(a_{12}=+0.350529372\) \(a_{13}=+0.520501130\) \(a_{14}=+0.612133543\) \(a_{15}=-0.258198890\)
\(a_{16}=-0.024252795\) \(a_{17}=+1.878027443\) \(a_{18}=-0.208929897\) \(a_{19}=-1.817670061\) \(a_{20}=-0.271518884\)
\(a_{21}=+0.563850157\) \(a_{22}=-0.740478139\) \(a_{23}=-1.805586257\) \(a_{24}=-0.581585394\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.326244743\) \(a_{27}=-0.192450090\) \(a_{28}=+0.592938125\) \(a_{29}=+0.597197902\) \(a_{30}=+0.161836402\)
\(a_{31}=-0.311604537\) \(a_{32}=-0.992134050\) \(a_{33}=-0.682071289\) \(a_{34}=-1.177128241\) \(a_{35}=-0.436756454\)
\(a_{36}=-0.202378228\) \(a_{37}=-0.368541017\) \(a_{38}=+1.139296857\) \(a_{39}=-0.300511467\) \(a_{40}=+0.450494109\)
\(a_{41}=+0.197668703\) \(a_{42}=-0.353415466\) \(a_{43}=+0.254504390\) \(a_{44}=-0.717258063\) \(a_{45}=+0.149071198\)
\(a_{46}=+1.131722853\) \(a_{47}=+0.118007662\) \(a_{48}=+0.014002357\) \(a_{49}=-0.046219001\) \(a_{50}=-0.125357938\)
\(a_{51}=-1.084279650\) \(a_{52}=-0.316014288\) \(a_{53}=+0.228331804\) \(a_{54}=+0.120625732\) \(a_{55}=+0.528330149\)
\(a_{56}=-0.983781048\) \(a_{57}=+1.049432299\) \(a_{58}=-0.374317489\) \(a_{59}=-0.969837964\) \(a_{60}=+0.156761501\)
\(a_{61}=-0.524927772\) \(a_{62}=+0.195310511\) \(a_{63}=-0.325539040\) \(a_{64}=+0.646112190\) \(a_{65}=+0.232775182\)
\(a_{66}=+0.427515253\) \(a_{67}=+0.928734758\) \(a_{68}=-1.140215595\) \(a_{69}=+1.042455711\) \(a_{70}=+0.273754443\)
\(a_{71}=-0.740950557\) \(a_{72}=+0.335778484\) \(a_{73}=-0.240180447\) \(a_{74}=+0.230997710\) \(a_{75}=-0.115470054\)
\(a_{76}=+1.103570536\) \(a_{77}=-1.153758011\) \(a_{78}=+0.188357490\) \(a_{79}=-0.675195275\) \(a_{80}=-0.010846179\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.123896705\) \(a_{83}=-0.471248153\) \(a_{84}=-0.342332986\) \(a_{85}=+0.839879405\)
\(a_{86}=-0.159520728\) \(a_{87}=-0.344792370\) \(a_{88}=+1.190048099\) \(a_{89}=-1.934268844\) \(a_{90}=-0.093436291\)
\(a_{91}=-0.508330315\) \(a_{92}=+1.096234038\) \(a_{93}=+0.179904963\) \(a_{94}=-0.073965987\) \(a_{95}=-0.812886763\)
\(a_{96}=+0.572808861\) \(a_{97}=+0.300713357\) \(a_{98}=+0.028969596\) \(a_{99}=+0.393794043\) \(a_{100}=-0.121426937\)

Showing 100 of 214 available coefficients

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