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: \( 2.91653733402 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.900588001\) \(a_{3}=+0.577350269\) \(a_{4}=-0.188941253\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.519954725\) \(a_{7}=+0.852894740\) \(a_{8}=-1.070746226\) \(a_{9}=+0.333333333\) \(a_{10}=+0.402755198\)
\(a_{11}=-1.291444519\) \(a_{12}=-0.109085283\) \(a_{13}=-0.287280831\) \(a_{14}=+0.768106769\) \(a_{15}=+0.258198890\)
\(a_{16}=-0.775359950\) \(a_{17}=+1.029571692\) \(a_{18}=+0.300196000\) \(a_{19}=+1.116983159\) \(a_{20}=-0.084497097\)
\(a_{21}=+0.492419008\) \(a_{22}=-1.163059438\) \(a_{23}=-1.309353213\) \(a_{24}=-0.618195622\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.258721669\) \(a_{27}=+0.192450090\) \(a_{28}=-0.161147001\) \(a_{29}=-0.467254258\) \(a_{30}=+0.232530822\)
\(a_{31}=+1.673771193\) \(a_{32}=+0.372466358\) \(a_{33}=-0.745615841\) \(a_{34}=+0.927219912\) \(a_{35}=+0.381426123\)
\(a_{36}=-0.062980418\) \(a_{37}=-1.204046783\) \(a_{38}=+1.005941631\) \(a_{39}=-0.165861665\) \(a_{40}=-0.478852270\)
\(a_{41}=-1.137523503\) \(a_{42}=+0.443466650\) \(a_{43}=+0.813150510\) \(a_{44}=+0.244007145\) \(a_{45}=+0.149071198\)
\(a_{46}=-1.179187792\) \(a_{47}=+0.181140449\) \(a_{48}=-0.447654276\) \(a_{49}=-0.272570563\) \(a_{50}=+0.180117600\)
\(a_{51}=+0.594423493\) \(a_{52}=+0.054279200\) \(a_{53}=-0.376739310\) \(a_{54}=+0.173318242\) \(a_{55}=-0.577551547\)
\(a_{56}=-0.913233824\) \(a_{57}=+0.644890528\) \(a_{58}=-0.420803578\) \(a_{59}=+0.194423560\) \(a_{60}=-0.048784422\)
\(a_{61}=+0.891594260\) \(a_{62}=+1.507378253\) \(a_{63}=+0.284298247\) \(a_{64}=+1.110798683\) \(a_{65}=-0.128475893\)
\(a_{66}=-0.671492679\) \(a_{67}=-0.541214030\) \(a_{68}=-0.194528565\) \(a_{69}=-0.755955430\) \(a_{70}=+0.343507790\)
\(a_{71}=+1.205504800\) \(a_{72}=-0.356915409\) \(a_{73}=-0.133024800\) \(a_{74}=-1.084350085\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.211044197\) \(a_{77}=-1.101466237\) \(a_{78}=-0.149373025\) \(a_{79}=+0.551285997\) \(a_{80}=-0.346751511\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.024440018\) \(a_{83}=-0.542236000\) \(a_{84}=-0.093038264\) \(a_{85}=+0.460438458\)
\(a_{86}=+0.732313592\) \(a_{87}=-0.269769372\) \(a_{88}=+1.382809345\) \(a_{89}=-0.040835000\) \(a_{90}=+0.134251733\)
\(a_{91}=-0.245020310\) \(a_{92}=+0.247390836\) \(a_{93}=+0.966352249\) \(a_{94}=+0.163132915\) \(a_{95}=+0.499530055\)
\(a_{96}=+0.215043552\) \(a_{97}=+0.178920001\) \(a_{98}=-0.245473778\) \(a_{99}=-0.430481506\) \(a_{100}=-0.037788251\)

Showing 100 of 148 available coefficients

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