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: \( 4.6113780114 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.700842659\) \(a_{3}=+0.577350269\) \(a_{4}=-0.508819567\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.404631698\) \(a_{7}=+1.110557015\) \(a_{8}=+1.057445118\) \(a_{9}=+0.333333333\) \(a_{10}=-0.313426365\)
\(a_{11}=-0.102154788\) \(a_{12}=-0.293767114\) \(a_{13}=+1.363587961\) \(a_{14}=-0.778325731\) \(a_{15}=+0.258198890\)
\(a_{16}=-0.232283081\) \(a_{17}=-0.996956436\) \(a_{18}=-0.233614220\) \(a_{19}=+1.580835818\) \(a_{20}=-0.227551028\)
\(a_{21}=+0.641180392\) \(a_{22}=+0.071594433\) \(a_{23}=-0.394969776\) \(a_{24}=+0.610516223\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.955660612\) \(a_{27}=+0.192450090\) \(a_{28}=-0.565073140\) \(a_{29}=+0.962414644\) \(a_{30}=-0.180956796\)
\(a_{31}=-1.270957139\) \(a_{32}=-0.894651226\) \(a_{33}=-0.058979094\) \(a_{34}=+0.698709600\) \(a_{35}=+0.496656196\)
\(a_{36}=-0.169606522\) \(a_{37}=+0.975008928\) \(a_{38}=-1.107917178\) \(a_{39}=+0.787267876\) \(a_{40}=+0.472903833\)
\(a_{41}=+0.866049520\) \(a_{42}=-0.449366571\) \(a_{43}=+0.362787286\) \(a_{44}=+0.051978355\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.276811668\) \(a_{47}=-1.290368170\) \(a_{48}=-0.134108699\) \(a_{49}=+0.233336884\) \(a_{50}=-0.140168532\)
\(a_{51}=-0.575593067\) \(a_{52}=-0.693820236\) \(a_{53}=-1.098030780\) \(a_{54}=-0.134877233\) \(a_{55}=-0.045685010\)
\(a_{56}=+1.174353093\) \(a_{57}=+0.912695985\) \(a_{58}=-0.674501238\) \(a_{59}=+0.468593270\) \(a_{60}=-0.131376647\)
\(a_{61}=-0.962021400\) \(a_{62}=+0.890740981\) \(a_{63}=+0.370185672\) \(a_{64}=+0.859292824\) \(a_{65}=+0.609815075\)
\(a_{66}=+0.041335065\) \(a_{67}=-0.065515200\) \(a_{68}=+0.507270942\) \(a_{69}=-0.228035906\) \(a_{70}=-0.348077849\)
\(a_{71}=-1.261823500\) \(a_{72}=+0.352481706\) \(a_{73}=+0.523779988\) \(a_{74}=-0.683327849\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.804360197\) \(a_{77}=-0.113448716\) \(a_{78}=-0.551750912\) \(a_{79}=+1.610292003\) \(a_{80}=-0.103880152\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.606964448\) \(a_{83}=+0.335701998\) \(a_{84}=-0.326245129\) \(a_{85}=-0.445852472\)
\(a_{86}=-0.254256806\) \(a_{87}=+0.555650354\) \(a_{88}=-0.108023082\) \(a_{89}=-1.447040999\) \(a_{90}=-0.104475455\)
\(a_{91}=+1.514342176\) \(a_{92}=+0.200968350\) \(a_{93}=-0.733787446\) \(a_{94}=+0.904345059\) \(a_{95}=+0.706971270\)
\(a_{96}=-0.516527126\) \(a_{97}=-1.283540000\) \(a_{98}=-0.163532442\) \(a_{99}=-0.034051596\) \(a_{100}=-0.101763913\)

Showing 100 of 136 available coefficients

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