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: \( 8.96246431384 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.823565912\) \(a_{4}=+0.500000000\) \(a_{5}=-1.355416371\)
\(a_{6}=+1.289455822\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+2.325392634\) \(a_{10}=-0.958424108\)
\(a_{11}=+1.262021722\) \(a_{12}=+0.911782956\) \(a_{13}=+0.241836769\) \(a_{14}=+0.267261242\) \(a_{15}=-2.471691091\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.964561200\) \(a_{18}=+1.644300901\) \(a_{19}=+0.836729951\) \(a_{20}=-0.677708186\)
\(a_{21}=+0.689243129\) \(a_{22}=+0.892384117\) \(a_{23}=-1.178677956\) \(a_{24}=+0.644727911\) \(a_{25}=+0.837153540\)
\(a_{26}=+0.171004420\) \(a_{27}=+2.416940828\) \(a_{28}=+0.188982237\) \(a_{29}=-0.182562179\) \(a_{30}=-1.747749531\)
\(a_{31}=-0.958663575\) \(a_{32}=+0.176776695\) \(a_{33}=+2.301379791\) \(a_{34}=+0.682047766\) \(a_{35}=-0.512299235\)
\(a_{36}=+1.162696317\) \(a_{37}=-0.424182121\) \(a_{38}=+0.591657422\) \(a_{39}=+0.441005289\) \(a_{40}=-0.479212054\)
\(a_{41}=-0.482789221\) \(a_{42}=+0.487368490\) \(a_{43}=-0.203233607\) \(a_{44}=+0.631010861\) \(a_{45}=-3.151875247\)
\(a_{46}=-0.833451176\) \(a_{47}=+1.277660728\) \(a_{48}=+0.455891478\) \(a_{49}=+0.142857143\) \(a_{50}=+0.591956945\)
\(a_{51}=+1.758940925\) \(a_{52}=+0.120918385\) \(a_{53}=-1.436453873\) \(a_{54}=+1.709035249\) \(a_{55}=-1.710564903\)
\(a_{56}=+0.133630621\) \(a_{57}=+1.525832215\) \(a_{58}=-0.129090955\) \(a_{59}=+0.327233108\) \(a_{60}=-1.235845546\)
\(a_{61}=-1.021592561\) \(a_{62}=-0.677877515\) \(a_{63}=+0.878915802\) \(a_{64}=+0.125000000\) \(a_{65}=-0.327789517\)
\(a_{66}=+1.627321257\) \(a_{67}=-0.508237052\) \(a_{68}=+0.482280600\) \(a_{69}=-2.149396942\) \(a_{70}=-0.362250263\)
\(a_{71}=+0.219759522\) \(a_{72}=+0.822150450\) \(a_{73}=-1.688029226\) \(a_{74}=-0.299942054\) \(a_{75}=+1.526604658\)
\(a_{76}=+0.418364975\) \(a_{77}=+0.476999375\) \(a_{78}=+0.311837830\) \(a_{79}=+0.032253637\) \(a_{80}=-0.338854093\)
\(a_{81}=+2.082058270\) \(a_{82}=-0.341383532\) \(a_{83}=+0.213095173\) \(a_{84}=+0.344621564\) \(a_{85}=-1.307382041\)
\(a_{86}=-0.143707861\) \(a_{87}=-0.332914166\) \(a_{88}=+0.446192059\) \(a_{89}=+1.357537159\) \(a_{90}=-2.228712360\)
\(a_{91}=+0.091405707\) \(a_{92}=-0.589338978\) \(a_{93}=-1.748186213\) \(a_{94}=+0.903442565\) \(a_{95}=-1.134117485\)
\(a_{96}=+0.322363956\) \(a_{97}=-0.830184424\) \(a_{98}=+0.101015254\) \(a_{99}=+2.934696012\) \(a_{100}=+0.418576770\)

Showing 100 of 190 available coefficients

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