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: \( 9.47558282076 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.353923244\) \(a_{4}=+0.500000000\) \(a_{5}=+0.732736590\)
\(a_{6}=+0.957368307\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.833108151\) \(a_{10}=-0.518123012\)
\(a_{11}=-1.095503536\) \(a_{12}=-0.676961622\) \(a_{13}=-0.511116315\) \(a_{14}=+0.267261242\) \(a_{15}=-0.992069101\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.425535472\) \(a_{18}=-0.589096423\) \(a_{19}=-0.747196476\) \(a_{20}=+0.366368295\)
\(a_{21}=+0.511734886\) \(a_{22}=+0.774637979\) \(a_{23}=+1.876730675\) \(a_{24}=+0.478684154\) \(a_{25}=-0.463097090\)
\(a_{26}=+0.361413812\) \(a_{27}=+0.225958753\) \(a_{28}=-0.188982237\) \(a_{29}=-0.903862066\) \(a_{30}=+0.701498789\)
\(a_{31}=+0.847481589\) \(a_{32}=-0.176776695\) \(a_{33}=+1.483227702\) \(a_{34}=+1.008005799\) \(a_{35}=-0.276948399\)
\(a_{36}=+0.416554076\) \(a_{37}=-0.868883361\) \(a_{38}=+0.528347695\) \(a_{39}=+0.692012260\) \(a_{40}=-0.259061506\)
\(a_{41}=+0.082624673\) \(a_{42}=-0.361851208\) \(a_{43}=+0.770960334\) \(a_{44}=-0.547751768\) \(a_{45}=+0.610448826\)
\(a_{46}=-1.327048987\) \(a_{47}=+0.039438726\) \(a_{48}=-0.338480811\) \(a_{49}=+0.142857143\) \(a_{50}=+0.327459092\)
\(a_{51}=+1.930065611\) \(a_{52}=-0.255558158\) \(a_{53}=-1.067659286\) \(a_{54}=-0.159776967\) \(a_{55}=-0.802715525\)
\(a_{56}=+0.133630621\) \(a_{57}=+1.011646677\) \(a_{58}=+0.639126996\) \(a_{59}=+0.109533112\) \(a_{60}=-0.496034551\)
\(a_{61}=+1.752774233\) \(a_{62}=-0.599259978\) \(a_{63}=-0.314885283\) \(a_{64}=+0.125000000\) \(a_{65}=-0.374513626\)
\(a_{66}=-1.048800366\) \(a_{67}=+1.052690010\) \(a_{68}=-0.712767736\) \(a_{69}=-2.540949284\) \(a_{70}=+0.195832091\)
\(a_{71}=+1.828683931\) \(a_{72}=-0.294548212\) \(a_{73}=-0.547667269\) \(a_{74}=+0.614393317\) \(a_{75}=+0.626997914\)
\(a_{76}=-0.373598238\) \(a_{77}=+0.414061417\) \(a_{78}=-0.489326561\) \(a_{79}=+1.565428831\) \(a_{80}=+0.183184148\)
\(a_{81}=-1.139038960\) \(a_{82}=-0.058424467\) \(a_{83}=-0.012799613\) \(a_{84}=+0.255867443\) \(a_{85}=-1.044541999\)
\(a_{86}=-0.545151280\) \(a_{87}=+1.223759863\) \(a_{88}=+0.387318990\) \(a_{89}=+1.483468325\) \(a_{90}=-0.431652504\)
\(a_{91}=+0.193183809\) \(a_{92}=+0.938365337\) \(a_{93}=-1.147425025\) \(a_{94}=-0.027887391\) \(a_{95}=-0.547498202\)
\(a_{96}=+0.239342077\) \(a_{97}=-1.216022973\) \(a_{98}=-0.101015254\) \(a_{99}=-0.912672933\) \(a_{100}=-0.231548545\)

Showing 100 of 192 available coefficients

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