Properties

Level $51$
Weight $0$
Character 51.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.27586456683 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.783281347\) \(a_{3}=-0.577350269\) \(a_{4}=+2.180092364\) \(a_{5}=+0.322329547\)
\(a_{6}=+1.029577966\) \(a_{7}=+0.479517286\) \(a_{8}=-2.104436700\) \(a_{9}=+0.333333333\) \(a_{10}=-0.574804269\)
\(a_{11}=-0.995625750\) \(a_{12}=-1.258676913\) \(a_{13}=+1.253096804\) \(a_{14}=-0.855114232\) \(a_{15}=-0.186097051\)
\(a_{16}=+1.572710351\) \(a_{17}=-0.242535625\) \(a_{18}=-0.594427116\) \(a_{19}=+0.480228515\) \(a_{20}=+0.702708184\)
\(a_{21}=-0.276849434\) \(a_{22}=+1.775480828\) \(a_{23}=-1.589326469\) \(a_{24}=+1.214997095\) \(a_{25}=-0.896103663\)
\(a_{26}=-2.234624158\) \(a_{27}=-0.192450090\) \(a_{28}=+1.045391974\) \(a_{29}=+0.882649195\) \(a_{30}=+0.331863400\)
\(a_{31}=-1.416619031\) \(a_{32}=-0.700148333\) \(a_{33}=+0.574824795\) \(a_{34}=+0.432509256\) \(a_{35}=+0.154562590\)
\(a_{36}=+0.726697455\) \(a_{37}=-0.492751433\) \(a_{38}=-0.856382554\) \(a_{39}=-0.723475777\) \(a_{40}=-0.678322129\)
\(a_{41}=-1.765688804\) \(a_{42}=+0.493700432\) \(a_{43}=+0.443474327\) \(a_{44}=-2.170556094\) \(a_{45}=+0.107443182\)
\(a_{46}=+2.834216246\) \(a_{47}=+1.662637907\) \(a_{48}=-0.908004744\) \(a_{49}=-0.770063172\) \(a_{50}=+1.598004948\)
\(a_{51}=+0.140028008\) \(a_{52}=+2.731866774\) \(a_{53}=+0.405075267\) \(a_{54}=+0.343192655\) \(a_{55}=-0.320919597\)
\(a_{56}=-1.009113776\) \(a_{57}=-0.277260063\) \(a_{58}=-1.574011846\) \(a_{59}=-1.124653906\) \(a_{60}=-0.405708759\)
\(a_{61}=-0.825481855\) \(a_{62}=+2.526230294\) \(a_{63}=+0.159839095\) \(a_{64}=-0.324148889\) \(a_{65}=+0.403910126\)
\(a_{66}=-1.025074334\) \(a_{67}=-0.283254054\) \(a_{68}=-0.528750064\) \(a_{69}=+0.917598065\) \(a_{70}=-0.275628583\)
\(a_{71}=-1.473438591\) \(a_{72}=-0.701478900\) \(a_{73}=-0.132407872\) \(a_{74}=+0.878714440\) \(a_{75}=+0.517365691\)
\(a_{76}=+1.046942519\) \(a_{77}=-0.477419758\) \(a_{78}=+1.290160859\) \(a_{79}=-0.423712134\) \(a_{80}=+0.506931015\)
\(a_{81}=+0.111111111\) \(a_{82}=+3.148719910\) \(a_{83}=-1.706383848\) \(a_{84}=-0.603557338\) \(a_{85}=-0.078176398\)
\(a_{86}=-0.790839496\) \(a_{87}=-0.509597751\) \(a_{88}=+2.095231368\) \(a_{89}=+1.370780803\) \(a_{90}=-0.191601423\)
\(a_{91}=+0.600881579\) \(a_{92}=-3.464878498\) \(a_{93}=+0.817885379\) \(a_{94}=-2.964951168\) \(a_{95}=+0.154791840\)
\(a_{96}=+0.404230828\) \(a_{97}=+0.932208732\) \(a_{98}=+1.373239291\) \(a_{99}=-0.331875250\) \(a_{100}=-1.953588753\)

Showing 100 of 486 available coefficients

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