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: \( 7.39439295726 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.833074209\) \(a_{3}=-0.577350269\) \(a_{4}=+2.360161056\) \(a_{5}=+0.447213596\)
\(a_{6}=+1.058325888\) \(a_{7}=-1.370774512\) \(a_{8}=-2.493276152\) \(a_{9}=+0.333333333\) \(a_{10}=-0.819775708\)
\(a_{11}=+0.094105484\) \(a_{12}=-1.362639621\) \(a_{13}=-1.145409585\) \(a_{14}=+2.512731405\) \(a_{15}=-0.258198890\)
\(a_{16}=+2.210199154\) \(a_{17}=-0.355454894\) \(a_{18}=-0.611024736\) \(a_{19}=-1.704230320\) \(a_{20}=+1.055496112\)
\(a_{21}=+0.791417034\) \(a_{22}=-0.172502336\) \(a_{23}=+1.006403161\) \(a_{24}=+1.439493657\) \(a_{25}=+0.199951172\)
\(a_{26}=+2.099620770\) \(a_{27}=-0.192450090\) \(a_{28}=-3.235248620\) \(a_{29}=-0.546227361\) \(a_{30}=+0.473297726\)
\(a_{31}=+1.125481015\) \(a_{32}=-1.558182914\) \(a_{33}=-0.054331826\) \(a_{34}=+0.651575198\) \(a_{35}=-0.613028998\)
\(a_{36}=+0.786720352\) \(a_{37}=-1.011594252\) \(a_{38}=+3.123980646\) \(a_{39}=+0.661302532\) \(a_{40}=-1.115026992\)
\(a_{41}=+0.813550607\) \(a_{42}=-1.450726153\) \(a_{43}=+0.983547341\) \(a_{44}=+0.222104098\) \(a_{45}=+0.149071198\)
\(a_{46}=-1.844811679\) \(a_{47}=+0.532719770\) \(a_{48}=-1.276059077\) \(a_{49}=+0.879022763\) \(a_{50}=-0.366614842\)
\(a_{51}=+0.205221978\) \(a_{52}=-2.703351096\) \(a_{53}=-0.159036100\) \(a_{54}=+0.352775296\) \(a_{55}=+0.042085252\)
\(a_{56}=+3.417719401\) \(a_{57}=+0.983937834\) \(a_{58}=+1.001275289\) \(a_{59}=+0.742338342\) \(a_{60}=-0.609390964\)
\(a_{61}=-1.306472936\) \(a_{62}=-2.063090222\) \(a_{63}=-0.456924837\) \(a_{64}=+0.646065759\) \(a_{65}=-0.512242739\)
\(a_{66}=+0.099594270\) \(a_{67}=+0.809750176\) \(a_{68}=-0.838930797\) \(a_{69}=-0.581047136\) \(a_{70}=+1.123727646\)
\(a_{71}=+1.623671722\) \(a_{72}=-0.831092051\) \(a_{73}=+0.984532363\) \(a_{74}=+1.854327334\) \(a_{75}=-0.115470054\)
\(a_{76}=-4.022258031\) \(a_{77}=-0.128997399\) \(a_{78}=-1.212216616\) \(a_{79}=+1.248984960\) \(a_{80}=+0.988431110\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.491298635\) \(a_{83}=-0.151109912\) \(a_{84}=+1.867871662\) \(a_{85}=-0.158964261\)
\(a_{86}=-1.802915264\) \(a_{87}=+0.315364514\) \(a_{88}=-0.234630959\) \(a_{89}=-0.109499898\) \(a_{90}=-0.273258569\)
\(a_{91}=+1.570098266\) \(a_{92}=+2.375273548\) \(a_{93}=-0.649796767\) \(a_{94}=-0.976514870\) \(a_{95}=-0.762154969\)
\(a_{96}=+0.899617325\) \(a_{97}=+0.628482709\) \(a_{98}=-1.611313957\) \(a_{99}=+0.031368495\) \(a_{100}=+0.472032211\)

Showing 100 of 210 available coefficients

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