Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.23047412065 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.112503877\) \(a_{3}=-0.577350269\) \(a_{4}=+0.237664875\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.642304413\) \(a_{7}=+0.414660075\) \(a_{8}=-0.848100781\) \(a_{9}=+0.333333333\) \(a_{10}=+0.497526859\)
\(a_{11}=+1.625600848\) \(a_{12}=-0.137215880\) \(a_{13}=-1.202297057\) \(a_{14}=+0.461310940\) \(a_{15}=-0.258198890\)
\(a_{16}=-1.181180282\) \(a_{17}=-0.860170034\) \(a_{18}=+0.370834626\) \(a_{19}=-0.027439980\) \(a_{20}=+0.106286963\)
\(a_{21}=-0.239404106\) \(a_{22}=+1.808487245\) \(a_{23}=+0.734074443\) \(a_{24}=+0.489651214\) \(a_{25}=+0.200000000\)
\(a_{26}=-1.337560136\) \(a_{27}=-0.192450090\) \(a_{28}=+0.098550135\) \(a_{29}=+0.340220303\) \(a_{30}=-0.287247266\)
\(a_{31}=+0.327010022\) \(a_{32}=-0.465966861\) \(a_{33}=-0.938541085\) \(a_{34}=-0.956942499\) \(a_{35}=+0.185441623\)
\(a_{36}=+0.079221625\) \(a_{37}=+0.371667101\) \(a_{38}=-0.030527084\) \(a_{39}=+0.694146529\) \(a_{40}=-0.379282200\)
\(a_{41}=+1.255683096\) \(a_{42}=-0.266337996\) \(a_{43}=-0.689766703\) \(a_{44}=+0.386348223\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.816660663\) \(a_{47}=-0.817739706\) \(a_{48}=+0.681954755\) \(a_{49}=-0.828057023\) \(a_{50}=+0.222500776\)
\(a_{51}=+0.496619401\) \(a_{52}=-0.285743780\) \(a_{53}=-0.096419316\) \(a_{54}=-0.214101472\) \(a_{55}=+0.726990803\)
\(a_{56}=-0.351673533\) \(a_{57}=+0.015842480\) \(a_{58}=+0.378496403\) \(a_{59}=-0.459391654\) \(a_{60}=-0.061364812\)
\(a_{61}=-1.444968495\) \(a_{62}=+0.363799919\) \(a_{63}=+0.138220028\) \(a_{64}=+0.662790353\) \(a_{65}=-0.537683610\)
\(a_{66}=-1.044130584\) \(a_{67}=-0.011501305\) \(a_{68}=-0.204432196\) \(a_{69}=-0.423818105\) \(a_{70}=+0.206304559\)
\(a_{71}=+1.068772630\) \(a_{72}=-0.282700295\) \(a_{73}=+0.366289073\) \(a_{74}=+0.413481037\) \(a_{75}=-0.115469945\)
\(a_{76}=-0.006521514\) \(a_{77}=+0.674071903\) \(a_{78}=+0.772240510\) \(a_{79}=+1.398916707\) \(a_{80}=-0.528240973\)
\(a_{81}=+0.111111175\) \(a_{82}=+1.396952085\) \(a_{83}=-0.599000460\) \(a_{84}=-0.056898252\) \(a_{85}=-0.384679756\)
\(a_{86}=-0.767369605\) \(a_{87}=-0.196424222\) \(a_{88}=-1.378672077\) \(a_{89}=-0.556251417\) \(a_{90}=+0.165834679\)
\(a_{91}=-0.498551039\) \(a_{92}=+0.174469916\) \(a_{93}=-0.188832683\) \(a_{94}=-0.909733928\) \(a_{95}=-0.012256014\)
\(a_{96}=+0.269011768\) \(a_{97}=-0.937178375\) \(a_{98}=-0.921021793\) \(a_{99}=+0.541942691\) \(a_{100}=+0.047570610\)

Showing 100 of 1500 available coefficients

Rows: Cols: