Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.6208081452 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.903773753\) \(a_{4}=+0.500000000\) \(a_{5}=-0.750276638\)
\(a_{6}=-0.639064549\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.183193003\) \(a_{10}=-0.530525699\)
\(a_{11}=+0.324157171\) \(a_{12}=-0.451886876\) \(a_{13}=+1.249407732\) \(a_{14}=+0.267261242\) \(a_{15}=+0.678080333\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.247638187\) \(a_{18}=-0.129537015\) \(a_{19}=+1.341532845\) \(a_{20}=-0.375138319\)
\(a_{21}=-0.341594370\) \(a_{22}=+0.229213733\) \(a_{23}=+0.455491727\) \(a_{24}=-0.319532275\) \(a_{25}=-0.437084966\)
\(a_{26}=+0.883464680\) \(a_{27}=+1.069338781\) \(a_{28}=+0.188982237\) \(a_{29}=-0.415341021\) \(a_{30}=+0.479475202\)
\(a_{31}=-0.336056678\) \(a_{32}=+0.176776695\) \(a_{33}=-0.292964743\) \(a_{34}=+0.882213423\) \(a_{35}=-0.283577914\)
\(a_{36}=-0.091596502\) \(a_{37}=-1.122192338\) \(a_{38}=+0.948606972\) \(a_{39}=-1.129181915\) \(a_{40}=-0.265262849\)
\(a_{41}=+1.338867245\) \(a_{42}=-0.241543696\) \(a_{43}=-0.719331116\) \(a_{44}=+0.162078585\) \(a_{45}=+0.137445431\)
\(a_{46}=+0.322081289\) \(a_{47}=+0.768579278\) \(a_{48}=-0.225943438\) \(a_{49}=+0.142857143\) \(a_{50}=-0.309065743\)
\(a_{51}=-1.127582647\) \(a_{52}=+0.624703866\) \(a_{53}=+1.707674936\) \(a_{54}=+0.756136704\) \(a_{55}=-0.243207552\)
\(a_{56}=+0.133630621\) \(a_{57}=-1.212442174\) \(a_{58}=-0.293690453\) \(a_{59}=-1.224833601\) \(a_{60}=+0.339040167\)
\(a_{61}=-0.789839447\) \(a_{62}=-0.237627956\) \(a_{63}=-0.069240447\) \(a_{64}=+0.125000000\) \(a_{65}=-0.937401433\)
\(a_{66}=-0.207157356\) \(a_{67}=+1.888664567\) \(a_{68}=+0.623819094\) \(a_{69}=-0.411661468\) \(a_{70}=-0.200519866\)
\(a_{71}=+0.891875927\) \(a_{72}=-0.064768508\) \(a_{73}=+1.616423116\) \(a_{74}=-0.793509812\) \(a_{75}=+0.395025920\)
\(a_{76}=+0.670766422\) \(a_{77}=+0.122519894\) \(a_{78}=-0.798452189\) \(a_{79}=-0.286029175\) \(a_{80}=-0.187569160\)
\(a_{81}=-0.783247320\) \(a_{82}=+0.946722108\) \(a_{83}=-1.171506210\) \(a_{84}=-0.170797185\) \(a_{85}=-0.936073785\)
\(a_{86}=-0.508643910\) \(a_{87}=+0.375374313\) \(a_{88}=+0.114606867\) \(a_{89}=-0.203009120\) \(a_{90}=+0.097188596\)
\(a_{91}=+0.472231735\) \(a_{92}=+0.227745864\) \(a_{93}=+0.303719205\) \(a_{94}=+0.543467619\) \(a_{95}=-1.006520753\)
\(a_{96}=-0.159766137\) \(a_{97}=+1.282100600\) \(a_{98}=+0.101015254\) \(a_{99}=-0.059383326\) \(a_{100}=-0.218542483\)

Showing 100 of 172 available coefficients

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