Properties

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

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.0764219866 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.923031221\) \(a_{3}=-0.577350269\) \(a_{4}=+2.698049075\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.110262593\) \(a_{7}=+0.232222027\) \(a_{8}=+3.265401386\) \(a_{9}=+0.333333333\) \(a_{10}=+0.860005706\)
\(a_{11}=+0.894844545\) \(a_{12}=-1.557719360\) \(a_{13}=+0.172304831\) \(a_{14}=+0.446570208\) \(a_{15}=-0.258198890\)
\(a_{16}=+3.581419738\) \(a_{17}=-1.246699135\) \(a_{18}=+0.641010407\) \(a_{19}=-1.272132149\) \(a_{20}=+1.206604228\)
\(a_{21}=-0.134073450\) \(a_{22}=+1.720813997\) \(a_{23}=-1.385856376\) \(a_{24}=-1.885280369\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.331347569\) \(a_{27}=-0.192450090\) \(a_{28}=+0.626546425\) \(a_{29}=-0.134428099\) \(a_{30}=-0.496524526\)
\(a_{31}=+0.386432210\) \(a_{32}=+3.621780584\) \(a_{33}=-0.516638739\) \(a_{34}=-2.397441359\) \(a_{35}=+0.103852848\)
\(a_{36}=+0.899349692\) \(a_{37}=-0.411229274\) \(a_{38}=-2.446349839\) \(a_{39}=-0.099480240\) \(a_{40}=+1.460331895\)
\(a_{41}=+0.027673861\) \(a_{42}=-0.257827430\) \(a_{43}=+1.652339116\) \(a_{44}=+2.414334496\) \(a_{45}=+0.149071199\)
\(a_{46}=-2.665045079\) \(a_{47}=-0.383020417\) \(a_{48}=-2.067733650\) \(a_{49}=-0.946072930\) \(a_{50}=+0.384606244\)
\(a_{51}=+0.719782081\) \(a_{52}=+0.464886889\) \(a_{53}=+0.413123543\) \(a_{54}=-0.370087531\) \(a_{55}=+0.400186645\)
\(a_{56}=+0.758298130\) \(a_{57}=+0.734465839\) \(a_{58}=-0.258509430\) \(a_{59}=-0.258392811\) \(a_{60}=-0.696633277\)
\(a_{61}=-0.126710250\) \(a_{62}=+0.743121204\) \(a_{63}=+0.077407343\) \(a_{64}=+3.383377398\) \(a_{65}=+0.077057079\)
\(a_{66}=-0.993512424\) \(a_{67}=-1.140394200\) \(a_{68}=-3.363655458\) \(a_{69}=+0.800124552\) \(a_{70}=+0.199712268\)
\(a_{71}=+0.867057338\) \(a_{72}=+1.088467129\) \(a_{73}=-0.794323173\) \(a_{74}=-0.790806735\) \(a_{75}=-0.115470056\)
\(a_{76}=-3.432274968\) \(a_{77}=+0.207802617\) \(a_{78}=-0.191303609\) \(a_{79}=+0.247898868\) \(a_{80}=+1.601659603\)
\(a_{81}=+0.111111114\) \(a_{82}=+0.053217692\) \(a_{83}=+1.382506831\) \(a_{84}=-0.361736734\) \(a_{85}=-0.557540794\)
\(a_{86}=+3.177499699\) \(a_{87}=+0.077612097\) \(a_{88}=+2.922026636\) \(a_{89}=+0.466793762\) \(a_{90}=+0.286668532\)
\(a_{91}=+0.040012978\) \(a_{92}=-3.739108496\) \(a_{93}=-0.223106678\) \(a_{94}=-0.736560256\) \(a_{95}=-0.568914823\)
\(a_{96}=-2.091035993\) \(a_{97}=+0.526315001\) \(a_{98}=-1.819327780\) \(a_{99}=+0.298281508\) \(a_{100}=+0.539609809\)

Showing 100 of 1500 available coefficients

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