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: \( 8.39388640634 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.870043352\) \(a_{3}=-0.577350269\) \(a_{4}=-0.243024566\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.502319763\) \(a_{7}=+1.500607350\) \(a_{8}=-1.081485260\) \(a_{9}=+0.333333333\) \(a_{10}=+0.389095215\)
\(a_{11}=-1.364053266\) \(a_{12}=+0.140310299\) \(a_{13}=+0.205524631\) \(a_{14}=+1.305593448\) \(a_{15}=-0.258198890\)
\(a_{16}=-0.697914494\) \(a_{17}=-1.754224765\) \(a_{18}=+0.290014451\) \(a_{19}=-0.004254399\) \(a_{20}=-0.108683890\)
\(a_{21}=-0.866376057\) \(a_{22}=-1.186785476\) \(a_{23}=-1.298794235\) \(a_{24}=+0.624395806\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.178815339\) \(a_{27}=-0.192450090\) \(a_{28}=-0.364684451\) \(a_{29}=-0.340750765\) \(a_{30}=-0.224644227\)
\(a_{31}=-1.277169683\) \(a_{32}=+0.474269395\) \(a_{33}=+0.787536521\) \(a_{34}=-1.526251594\) \(a_{35}=+0.671092008\)
\(a_{36}=-0.081008189\) \(a_{37}=-0.819217511\) \(a_{38}=-0.003701511\) \(a_{39}=-0.118659701\) \(a_{40}=-0.483654912\)
\(a_{41}=+1.000418607\) \(a_{42}=-0.753784728\) \(a_{43}=+1.201269781\) \(a_{44}=+0.331498454\) \(a_{45}=+0.149071198\)
\(a_{46}=-1.130007290\) \(a_{47}=-0.783806379\) \(a_{48}=+0.402941121\) \(a_{49}=+1.251822418\) \(a_{50}=+0.174008670\)
\(a_{51}=+1.012802140\) \(a_{52}=-0.049947534\) \(a_{53}=-1.103489091\) \(a_{54}=-0.167439921\) \(a_{55}=-0.610023166\)
\(a_{56}=-1.622884729\) \(a_{57}=+0.002456278\) \(a_{58}=-0.296467937\) \(a_{59}=+1.296592432\) \(a_{60}=+0.062748673\)
\(a_{61}=-0.596461328\) \(a_{62}=-1.111192991\) \(a_{63}=+0.500202450\) \(a_{64}=+1.110549427\) \(a_{65}=+0.091913409\)
\(a_{66}=+0.685190914\) \(a_{67}=-0.127830625\) \(a_{68}=+0.426319713\) \(a_{69}=+0.749859201\) \(a_{70}=+0.583879140\)
\(a_{71}=+0.178124678\) \(a_{72}=-0.360495087\) \(a_{73}=+0.707982903\) \(a_{74}=-0.712754749\) \(a_{75}=-0.115470054\)
\(a_{76}=+0.001033924\) \(a_{77}=-2.046908357\) \(a_{78}=-0.103239084\) \(a_{79}=-0.111313298\) \(a_{80}=-0.312116850\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.870407558\) \(a_{83}=-1.888977056\) \(a_{84}=+0.210550666\) \(a_{85}=-0.784513164\)
\(a_{86}=+1.045156786\) \(a_{87}=+0.196732546\) \(a_{88}=+1.475203503\) \(a_{89}=-0.774481793\) \(a_{90}=+0.129698405\)
\(a_{91}=+0.308411770\) \(a_{92}=+0.315638903\) \(a_{93}=+0.737374260\) \(a_{94}=-0.681945533\) \(a_{95}=-0.001902625\)
\(a_{96}=-0.273819563\) \(a_{97}=-0.028290477\) \(a_{98}=+1.089139769\) \(a_{99}=-0.454684422\) \(a_{100}=-0.048604913\)

Showing 100 of 210 available coefficients

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