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: \( 5.04639152422 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.126382881\) \(a_{3}=-0.577350269\) \(a_{4}=+0.268738395\) \(a_{5}=-0.447213596\)
\(a_{6}=-0.650317460\) \(a_{7}=-1.679900272\) \(a_{8}=-0.823680553\) \(a_{9}=+0.333333333\) \(a_{10}=-0.503733738\)
\(a_{11}=+1.335847518\) \(a_{12}=-0.155156185\) \(a_{13}=-0.399699069\) \(a_{14}=-1.892210909\) \(a_{15}=+0.258198890\)
\(a_{16}=-1.196518070\) \(a_{17}=+0.922256139\) \(a_{18}=+0.375460960\) \(a_{19}=-0.482418753\) \(a_{20}=-0.120183464\)
\(a_{21}=+0.969890874\) \(a_{22}=+1.504675776\) \(a_{23}=-1.475554387\) \(a_{24}=+0.475552189\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.450214189\) \(a_{27}=-0.192450090\) \(a_{28}=-0.451453703\) \(a_{29}=-0.576070641\) \(a_{30}=+0.290830809\)
\(a_{31}=+0.034126129\) \(a_{32}=-0.524056918\) \(a_{33}=-0.771251924\) \(a_{34}=+1.038813527\) \(a_{35}=+0.751274241\)
\(a_{36}=+0.089579466\) \(a_{37}=-0.152440835\) \(a_{38}=-0.543388225\) \(a_{39}=+0.230766363\) \(a_{40}=+0.368361142\)
\(a_{41}=-0.208746902\) \(a_{42}=+1.092468477\) \(a_{43}=-0.328735328\) \(a_{44}=+0.358993518\) \(a_{45}=-0.149071198\)
\(a_{46}=-1.662039202\) \(a_{47}=-0.298400223\) \(a_{48}=+0.690810030\) \(a_{49}=+1.822064924\) \(a_{50}=+0.225276576\)
\(a_{51}=-0.532464830\) \(a_{52}=-0.107414485\) \(a_{53}=-1.768678671\) \(a_{54}=-0.216772485\) \(a_{55}=-0.597409173\)
\(a_{56}=+1.383701186\) \(a_{57}=+0.278524596\) \(a_{58}=-0.648876109\) \(a_{59}=-0.265926328\) \(a_{60}=+0.069387956\)
\(a_{61}=-0.336159064\) \(a_{62}=+0.038439083\) \(a_{63}=-0.559966750\) \(a_{64}=+0.606229314\) \(a_{65}=+0.178750874\)
\(a_{66}=-0.868724970\) \(a_{67}=+0.996108146\) \(a_{68}=+0.247845638\) \(a_{69}=+0.851911669\) \(a_{70}=+0.846222480\)
\(a_{71}=+0.846859256\) \(a_{72}=-0.274560129\) \(a_{73}=+1.296378738\) \(a_{74}=-0.171706687\) \(a_{75}=-0.115470054\)
\(a_{76}=-0.129644443\) \(a_{77}=-2.244090607\) \(a_{78}=+0.259931287\) \(a_{79}=-1.714628756\) \(a_{80}=+0.535099146\)
\(a_{81}=+0.111111109\) \(a_{82}=-0.235128939\) \(a_{83}=-0.798565998\) \(a_{84}=+0.260646915\) \(a_{85}=-0.412445469\)
\(a_{86}=-0.370281844\) \(a_{87}=+0.332594514\) \(a_{88}=-1.100311631\) \(a_{89}=+1.133069306\) \(a_{90}=-0.167911243\)
\(a_{91}=+0.671454562\) \(a_{92}=-0.396538114\) \(a_{93}=-0.019702698\) \(a_{94}=-0.336112929\) \(a_{95}=+0.215744131\)
\(a_{96}=+0.302564479\) \(a_{97}=+1.615984869\) \(a_{98}=+2.052342678\) \(a_{99}=+0.445282426\) \(a_{100}=+0.053747744\)

Showing 100 of 1500 available coefficients

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