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: \( 9.56689697161 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.416363525\) \(a_{4}=+0.500000000\) \(a_{5}=-0.691155149\)
\(a_{6}=+0.294413472\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.826641415\) \(a_{10}=-0.488720493\)
\(a_{11}=-1.276310390\) \(a_{12}=+0.208181762\) \(a_{13}=+0.135479872\) \(a_{14}=+0.267261242\) \(a_{15}=-0.287771794\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.782026369\) \(a_{18}=-0.584523750\) \(a_{19}=+1.157136633\) \(a_{20}=-0.345577574\)
\(a_{21}=+0.157370620\) \(a_{22}=-0.902487732\) \(a_{23}=-1.018109384\) \(a_{24}=+0.147206736\) \(a_{25}=-0.522304560\)
\(a_{26}=+0.095798736\) \(a_{27}=-0.760546858\) \(a_{28}=+0.188982237\) \(a_{29}=-1.087543304\) \(a_{30}=-0.203485387\)
\(a_{31}=-1.238474942\) \(a_{32}=+0.176776695\) \(a_{33}=-0.531409093\) \(a_{34}=-0.552976149\) \(a_{35}=-0.261232092\)
\(a_{36}=-0.413320708\) \(a_{37}=+1.027653499\) \(a_{38}=+0.818219160\) \(a_{39}=+0.056408877\) \(a_{40}=-0.244360246\)
\(a_{41}=-1.049698085\) \(a_{42}=+0.111277833\) \(a_{43}=+0.370274611\) \(a_{44}=-0.638155195\) \(a_{45}=+0.571337470\)
\(a_{46}=-0.719912049\) \(a_{47}=-1.325226161\) \(a_{48}=+0.104090881\) \(a_{49}=+0.142857143\) \(a_{50}=-0.369325096\)
\(a_{51}=-0.325607256\) \(a_{52}=+0.067739936\) \(a_{53}=+1.355878847\) \(a_{54}=-0.537787841\) \(a_{55}=+0.882128498\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.481789487\) \(a_{58}=-0.769009245\) \(a_{59}=+0.582115526\) \(a_{60}=-0.143885897\)
\(a_{61}=+0.978474300\) \(a_{62}=-0.875734030\) \(a_{63}=-0.312441087\) \(a_{64}=+0.125000000\) \(a_{65}=-0.093637611\)
\(a_{66}=-0.375762973\) \(a_{67}=+0.232798887\) \(a_{68}=-0.391013185\) \(a_{69}=-0.423903612\) \(a_{70}=-0.184718983\)
\(a_{71}=-1.148998936\) \(a_{72}=-0.292261875\) \(a_{73}=+0.448691919\) \(a_{74}=+0.726660758\) \(a_{75}=-0.217468568\)
\(a_{76}=+0.578568317\) \(a_{77}=-0.482399984\) \(a_{78}=+0.039887099\) \(a_{79}=+1.751554308\) \(a_{80}=-0.172788787\)
\(a_{81}=+0.509977444\) \(a_{82}=-0.742248634\) \(a_{83}=+0.227988344\) \(a_{84}=+0.078685310\) \(a_{85}=+0.540501551\)
\(a_{86}=+0.261823688\) \(a_{87}=-0.452813362\) \(a_{88}=-0.451243866\) \(a_{89}=-0.069283147\) \(a_{90}=+0.403996600\)
\(a_{91}=+0.051206578\) \(a_{92}=-0.509054692\) \(a_{93}=-0.515655796\) \(a_{94}=-0.937076405\) \(a_{95}=-0.799760942\)
\(a_{96}=+0.073603368\) \(a_{97}=+1.194805630\) \(a_{98}=+0.101015254\) \(a_{99}=+1.055051026\) \(a_{100}=-0.261152280\)

Showing 100 of 198 available coefficients

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