Properties

Level $9$
Weight $0$
Character 9.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 6.64658135561 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.795425706\) \(a_{3}=+0.000000000\) \(a_{4}=+2.223553462\) \(a_{5}=+0.185279035\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.839669004\) \(a_{8}=+2.196799339\) \(a_{9}=+0.000000000\) \(a_{10}=+0.332654743\)
\(a_{11}=+0.154427065\) \(a_{12}=+0.000000000\) \(a_{13}=-1.076664577\) \(a_{14}=+1.507563313\) \(a_{15}=+0.000000000\)
\(a_{16}=+1.720636539\) \(a_{17}=-1.111924248\) \(a_{18}=+0.000000000\) \(a_{19}=-1.198649755\) \(a_{20}=+0.411977842\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.277262313\) \(a_{23}=+1.225143144\) \(a_{24}=+0.000000000\) \(a_{25}=-0.965671640\)
\(a_{26}=-1.933071213\) \(a_{27}=+0.000000000\) \(a_{28}=+1.867048727\) \(a_{29}=+0.628941658\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.074702174\) \(a_{32}=+0.892475733\) \(a_{33}=+0.000000000\) \(a_{34}=-1.996377377\) \(a_{35}=+0.155573064\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.629136227\) \(a_{38}=-2.152086587\) \(a_{39}=+0.000000000\) \(a_{40}=+0.407020858\)
\(a_{41}=+1.339090972\) \(a_{42}=+0.000000000\) \(a_{43}=-0.716118407\) \(a_{44}=+0.343376833\) \(a_{45}=+0.000000000\)
\(a_{46}=+2.199653500\) \(a_{47}=+0.953385941\) \(a_{48}=+0.000000000\) \(a_{49}=-0.294955998\) \(a_{50}=-1.733791697\)
\(a_{51}=+0.000000000\) \(a_{52}=-2.394021090\) \(a_{53}=-1.024445849\) \(a_{54}=+0.000000000\) \(a_{55}=+0.028612099\)
\(a_{56}=+1.844584304\) \(a_{57}=+0.000000000\) \(a_{58}=+1.129218022\) \(a_{59}=+0.273889996\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.040031444\) \(a_{62}=+0.134122258\) \(a_{63}=+0.000000000\) \(a_{64}=-0.118262640\) \(a_{65}=-0.199483450\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.028939369\) \(a_{68}=-2.472423068\) \(a_{69}=+0.000000000\) \(a_{70}=+0.279319731\)
\(a_{71}=+1.398536465\) \(a_{72}=+0.000000000\) \(a_{73}=-0.288236356\) \(a_{74}=+1.129567339\) \(a_{75}=+0.000000000\)
\(a_{76}=-2.665261820\) \(a_{77}=+0.129667609\) \(a_{78}=+0.000000000\) \(a_{79}=-0.262597440\) \(a_{80}=+0.318797893\)
\(a_{81}=+0.000000000\) \(a_{82}=+2.404238245\) \(a_{83}=-1.082323790\) \(a_{84}=+0.000000000\) \(a_{85}=-0.206016169\)
\(a_{86}=-1.285737269\) \(a_{87}=+0.000000000\) \(a_{88}=+0.339245257\) \(a_{89}=-0.375991152\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.904041754\) \(a_{92}=+2.724171381\) \(a_{93}=+0.000000000\) \(a_{94}=+1.711733524\) \(a_{95}=-0.222084513\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.526911203\) \(a_{98}=-0.529571821\) \(a_{99}=+0.000000000\) \(a_{100}=-2.147222200\)

Showing 100 of 1500 available coefficients

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