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: \( 6.84293956587 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.056377348\) \(a_{3}=+0.577350269\) \(a_{4}=-0.996821595\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.032549477\) \(a_{7}=+0.504904610\) \(a_{8}=+0.112575507\) \(a_{9}=+0.333333333\) \(a_{10}=-0.025212717\)
\(a_{11}=-1.248835561\) \(a_{12}=-0.575515216\) \(a_{13}=-0.811786821\) \(a_{14}=-0.028465183\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.990474886\) \(a_{17}=-1.542521987\) \(a_{18}=-0.018792449\) \(a_{19}=-1.484613540\) \(a_{20}=-0.445792169\)
\(a_{21}=+0.291506813\) \(a_{22}=+0.070406037\) \(a_{23}=-0.714898422\) \(a_{24}=+0.064995499\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.045766388\) \(a_{27}=+0.192450090\) \(a_{28}=-0.503299819\) \(a_{29}=+0.640019448\) \(a_{30}=-0.014556569\)
\(a_{31}=+0.732403225\) \(a_{32}=-0.168415854\) \(a_{33}=-0.721015547\) \(a_{34}=+0.086963299\) \(a_{35}=+0.225800206\)
\(a_{36}=-0.332273865\) \(a_{37}=-0.973433980\) \(a_{38}=+0.083698575\) \(a_{39}=-0.468685340\) \(a_{40}=+0.050345297\)
\(a_{41}=+0.642060178\) \(a_{42}=-0.016434381\) \(a_{43}=-1.310461628\) \(a_{44}=+1.244866255\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.040304077\) \(a_{47}=+0.986162484\) \(a_{48}=+0.571850942\) \(a_{49}=-0.745071335\) \(a_{50}=-0.011275470\)
\(a_{51}=-0.890575484\) \(a_{52}=+0.809206633\) \(a_{53}=+1.093560778\) \(a_{54}=-0.010849826\) \(a_{55}=-0.558496241\)
\(a_{56}=+0.056839892\) \(a_{57}=-0.857142027\) \(a_{58}=-0.036082599\) \(a_{59}=-1.103376843\) \(a_{60}=-0.257378229\)
\(a_{61}=+0.658164579\) \(a_{62}=-0.041290952\) \(a_{63}=+0.168301537\) \(a_{64}=-0.980980047\) \(a_{65}=-0.363042103\)
\(a_{66}=+0.040648945\) \(a_{67}=+0.410760288\) \(a_{68}=+1.537619226\) \(a_{69}=-0.412746796\) \(a_{70}=-0.012730017\)
\(a_{71}=+0.439445017\) \(a_{72}=+0.037525169\) \(a_{73}=-0.174226753\) \(a_{74}=+0.054879627\) \(a_{75}=+0.115470054\)
\(a_{76}=+1.479894836\) \(a_{77}=-0.630542832\) \(a_{78}=+0.026423237\) \(a_{79}=-1.324897863\) \(a_{80}=+0.442953835\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.036197650\) \(a_{83}=+1.063746763\) \(a_{84}=-0.290580286\) \(a_{85}=-0.689836804\)
\(a_{86}=+0.073880352\) \(a_{87}=+0.369515400\) \(a_{88}=-0.140588296\) \(a_{89}=-1.355025009\) \(a_{90}=-0.008404239\)
\(a_{91}=-0.409874908\) \(a_{92}=+0.712626184\) \(a_{93}=+0.422853199\) \(a_{94}=-0.055597226\) \(a_{95}=-0.663939359\)
\(a_{96}=-0.097234939\) \(a_{97}=-1.118821868\) \(a_{98}=+0.042005146\) \(a_{99}=-0.416278520\) \(a_{100}=-0.199364319\)

Showing 100 of 190 available coefficients

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