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: \( 6.96485168305 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.889366260\) \(a_{4}=+0.500000000\) \(a_{5}=+0.781612315\)
\(a_{6}=+1.335983695\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+2.569704864\) \(a_{10}=-0.552683369\)
\(a_{11}=-1.276779974\) \(a_{12}=-0.944683130\) \(a_{13}=+0.782306518\) \(a_{14}=-0.267261242\) \(a_{15}=-1.476751937\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.069925018\) \(a_{18}=-1.817055735\) \(a_{19}=+0.232289492\) \(a_{20}=+0.390806158\)
\(a_{21}=-0.714113323\) \(a_{22}=+0.902819778\) \(a_{23}=+0.554902866\) \(a_{24}=+0.667991847\) \(a_{25}=-0.389082188\)
\(a_{26}=-0.553174244\) \(a_{27}=-2.965747409\) \(a_{28}=+0.188982237\) \(a_{29}=+0.361351312\) \(a_{30}=+1.044221309\)
\(a_{31}=-1.604762289\) \(a_{32}=-0.176776695\) \(a_{33}=+2.412305004\) \(a_{34}=-0.049444455\) \(a_{35}=+0.295421687\)
\(a_{36}=+1.284852432\) \(a_{37}=+0.203623863\) \(a_{38}=-0.164253475\) \(a_{39}=-1.478063540\) \(a_{40}=-0.276341684\)
\(a_{41}=-1.886172217\) \(a_{42}=+0.504954374\) \(a_{43}=+0.595888137\) \(a_{44}=-0.638389984\) \(a_{45}=+2.008512965\)
\(a_{46}=-0.392375576\) \(a_{47}=-1.204659533\) \(a_{48}=-0.472341564\) \(a_{49}=+0.142857148\) \(a_{50}=+0.275122651\)
\(a_{51}=-0.132113956\) \(a_{52}=+0.391153222\) \(a_{53}=+0.021749511\) \(a_{54}=+2.097100011\) \(a_{55}=-0.997946952\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.438879930\) \(a_{58}=-0.255513963\) \(a_{59}=+0.582093522\) \(a_{60}=-0.738375969\)
\(a_{61}=-0.350027856\) \(a_{62}=+1.134738297\) \(a_{63}=+0.971257145\) \(a_{64}=+0.125000000\) \(a_{65}=+0.611460409\)
\(a_{66}=-1.705757227\) \(a_{67}=+0.497855070\) \(a_{68}=+0.034962510\) \(a_{69}=-1.048414750\) \(a_{70}=-0.208894680\)
\(a_{71}=-0.568760438\) \(a_{72}=-0.908527872\) \(a_{73}=-0.149520536\) \(a_{74}=-0.143983806\) \(a_{75}=+0.735118756\)
\(a_{76}=+0.116144736\) \(a_{77}=-0.482577470\) \(a_{78}=+1.045148765\) \(a_{79}=-1.070437449\) \(a_{80}=+0.195403069\)
\(a_{81}=+3.033678185\) \(a_{82}=+1.333725157\) \(a_{83}=-1.146881408\) \(a_{84}=-0.357056603\) \(a_{85}=+0.054654233\)
\(a_{86}=-0.421356600\) \(a_{87}=-0.682724978\) \(a_{88}=+0.451409890\) \(a_{89}=-1.671006632\) \(a_{90}=-1.420233137\)
\(a_{91}=+0.295684069\) \(a_{92}=+0.277451431\) \(a_{93}=+3.031983723\) \(a_{94}=+0.851822923\) \(a_{95}=+0.181560329\)
\(a_{96}=+0.333995921\) \(a_{97}=+0.231690220\) \(a_{98}=-0.101015258\) \(a_{99}=-3.280947704\) \(a_{100}=-0.194541103\)

Showing 100 of 2000 available coefficients

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