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: \( 4.53086807747 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.743668240\) \(a_{3}=+0.577350269\) \(a_{4}=+2.040378930\) \(a_{5}=+0.447213596\)
\(a_{6}=+1.006707328\) \(a_{7}=-1.409062745\) \(a_{8}=+1.814075698\) \(a_{9}=+0.333333333\) \(a_{10}=+0.779792143\)
\(a_{11}=+0.559122870\) \(a_{12}=+1.178013325\) \(a_{13}=-1.487572364\) \(a_{14}=-2.456937957\) \(a_{15}=+0.258198890\)
\(a_{16}=+1.122767249\) \(a_{17}=+0.185400480\) \(a_{18}=+0.581222747\) \(a_{19}=-0.235938790\) \(a_{20}=+0.912485198\)
\(a_{21}=-0.813522755\) \(a_{22}=+0.974924791\) \(a_{23}=+0.322809249\) \(a_{24}=+1.047357093\) \(a_{25}=+0.199951172\)
\(a_{26}=-2.593832685\) \(a_{27}=+0.192450090\) \(a_{28}=-2.875021937\) \(a_{29}=+0.688962531\) \(a_{30}=+0.450213204\)
\(a_{31}=+1.287660608\) \(a_{32}=+0.143657895\) \(a_{33}=+0.322809740\) \(a_{34}=+0.323276929\) \(a_{35}=-0.630152017\)
\(a_{36}=+0.680126310\) \(a_{37}=+1.249363730\) \(a_{38}=-0.411398975\) \(a_{39}=-0.858850305\) \(a_{40}=+0.811279316\)
\(a_{41}=-0.676961270\) \(a_{42}=-1.418513791\) \(a_{43}=-1.277015740\) \(a_{44}=+1.140822524\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.562872235\) \(a_{47}=+1.063840534\) \(a_{48}=+0.648229974\) \(a_{49}=+0.985457820\) \(a_{50}=+0.348733648\)
\(a_{51}=+0.107041017\) \(a_{52}=-3.035211308\) \(a_{53}=-0.544451560\) \(a_{54}=+0.335569109\) \(a_{55}=+0.250047349\)
\(a_{56}=-2.556146484\) \(a_{57}=-0.136219324\) \(a_{58}=+1.201322085\) \(a_{59}=-0.768121140\) \(a_{60}=+0.526823575\)
\(a_{61}=+0.924944236\) \(a_{62}=+2.245252906\) \(a_{63}=-0.469687582\) \(a_{64}=-0.872275540\) \(a_{65}=-0.665262585\)
\(a_{66}=+0.562873091\) \(a_{67}=+1.222525257\) \(a_{68}=+0.378287233\) \(a_{69}=+0.186374007\) \(a_{70}=-1.098776058\)
\(a_{71}=+0.259384147\) \(a_{72}=+0.604691899\) \(a_{73}=-1.128575760\) \(a_{74}=+2.178475857\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.481404537\) \(a_{77}=-0.787839207\) \(a_{78}=-1.497549999\) \(a_{79}=+0.754968490\) \(a_{80}=+0.502116779\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.180395867\) \(a_{83}=-0.656499050\) \(a_{84}=-1.659894689\) \(a_{85}=+0.082913615\)
\(a_{86}=-2.226691787\) \(a_{87}=+0.397772703\) \(a_{88}=+1.014291212\) \(a_{89}=-0.559731800\) \(a_{90}=+0.259930714\)
\(a_{91}=+2.096082799\) \(a_{92}=+0.658653190\) \(a_{93}=+0.743431199\) \(a_{94}=+1.854984951\) \(a_{95}=-0.105515035\)
\(a_{96}=+0.082940924\) \(a_{97}=-1.623309000\) \(a_{98}=+1.718311503\) \(a_{99}=+0.186374290\) \(a_{100}=+0.408075786\)

Showing 100 of 172 available coefficients

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