Properties

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

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 9.01223427143 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.326056511\) \(a_{4}=+0.500000000\) \(a_{5}=+0.067783169\)
\(a_{6}=-0.230556770\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.893687152\) \(a_{10}=-0.047929938\)
\(a_{11}=+0.912131808\) \(a_{12}=+0.163028255\) \(a_{13}=+1.667648891\) \(a_{14}=+0.267261242\) \(a_{15}=+0.022101143\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.537057397\) \(a_{18}=+0.631932245\) \(a_{19}=+0.042541840\) \(a_{20}=+0.033891584\)
\(a_{21}=-0.123237777\) \(a_{22}=-0.644974587\) \(a_{23}=+0.105182637\) \(a_{24}=-0.115278385\) \(a_{25}=-0.995405442\)
\(a_{26}=-1.179205840\) \(a_{27}=-0.617449025\) \(a_{28}=-0.188982237\) \(a_{29}=-0.151692895\) \(a_{30}=-0.015627868\)
\(a_{31}=-0.950628841\) \(a_{32}=-0.176776695\) \(a_{33}=+0.297406515\) \(a_{34}=+1.086863708\) \(a_{35}=-0.025619630\)
\(a_{36}=-0.446843576\) \(a_{37}=-0.063477186\) \(a_{38}=-0.030081624\) \(a_{39}=+0.543747778\) \(a_{40}=-0.023964969\)
\(a_{41}=-1.455576537\) \(a_{42}=+0.087142268\) \(a_{43}=-1.565754856\) \(a_{44}=+0.456065904\) \(a_{45}=-0.060576947\)
\(a_{46}=-0.074375356\) \(a_{47}=+0.625119887\) \(a_{48}=+0.081514128\) \(a_{49}=+0.142857143\) \(a_{50}=+0.703857938\)
\(a_{51}=-0.501167571\) \(a_{52}=+0.833824446\) \(a_{53}=-0.911062712\) \(a_{54}=+0.436602392\) \(a_{55}=+0.061827184\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.013871044\) \(a_{58}=+0.107263075\) \(a_{59}=-0.888683448\) \(a_{60}=+0.011050572\)
\(a_{61}=-0.251314534\) \(a_{62}=+0.672196100\) \(a_{63}=+0.337781993\) \(a_{64}=+0.125000000\) \(a_{65}=+0.113038526\)
\(a_{66}=-0.210298163\) \(a_{67}=-0.914614659\) \(a_{68}=-0.768528698\) \(a_{69}=+0.034295484\) \(a_{70}=+0.018115814\)
\(a_{71}=+0.476789422\) \(a_{72}=+0.315966123\) \(a_{73}=-0.349527983\) \(a_{74}=+0.044885149\) \(a_{75}=-0.324558425\)
\(a_{76}=+0.021270920\) \(a_{77}=-0.344753418\) \(a_{78}=-0.384487741\) \(a_{79}=+1.652468014\) \(a_{80}=+0.016945792\)
\(a_{81}=+0.692363877\) \(a_{82}=+1.029248040\) \(a_{83}=-0.978576316\) \(a_{84}=-0.061618889\) \(a_{85}=-0.104186619\)
\(a_{86}=+1.107155876\) \(a_{87}=-0.049460456\) \(a_{88}=-0.322487294\) \(a_{89}=-0.707802916\) \(a_{90}=+0.042834370\)
\(a_{91}=-0.630312034\) \(a_{92}=+0.052591319\) \(a_{93}=-0.309958725\) \(a_{94}=-0.442026511\) \(a_{95}=+0.002883632\)
\(a_{96}=-0.057639192\) \(a_{97}=+0.757411534\) \(a_{98}=-0.101015254\) \(a_{99}=-0.815160467\) \(a_{100}=-0.497702721\)

Showing 100 of 196 available coefficients

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