Properties

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

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.53928284159 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.495344571\) \(a_{3}=+0.577350269\) \(a_{4}=+1.236055386\) \(a_{5}=+0.965097197\)
\(a_{6}=+0.863337591\) \(a_{7}=+0.812816059\) \(a_{8}=+0.352984140\) \(a_{9}=+0.333333333\) \(a_{10}=+1.443152854\)
\(a_{11}=-0.040807703\) \(a_{12}=+0.713636910\) \(a_{13}=-0.357624107\) \(a_{14}=+1.215440081\) \(a_{15}=+0.557199126\)
\(a_{16}=-0.708222469\) \(a_{17}=+0.242535625\) \(a_{18}=+0.498448190\) \(a_{19}=-1.596390183\) \(a_{20}=+1.192913588\)
\(a_{21}=+0.469279570\) \(a_{22}=-0.061021577\) \(a_{23}=+0.654696892\) \(a_{24}=+0.203795488\) \(a_{25}=-0.068587401\)
\(a_{26}=-0.534771267\) \(a_{27}=+0.192450090\) \(a_{28}=+1.004685667\) \(a_{29}=+0.021978715\) \(a_{30}=+0.833204689\)
\(a_{31}=+1.411237390\) \(a_{32}=-1.412020764\) \(a_{33}=-0.023560338\) \(a_{34}=+0.362674330\) \(a_{35}=+0.784446500\)
\(a_{36}=+0.412018462\) \(a_{37}=-0.237662543\) \(a_{38}=-2.387153393\) \(a_{39}=-0.206474374\) \(a_{40}=+0.340664004\)
\(a_{41}=-1.205907271\) \(a_{42}=+0.701734658\) \(a_{43}=-1.477178053\) \(a_{44}=-0.050440581\) \(a_{45}=+0.321699066\)
\(a_{46}=+0.978997443\) \(a_{47}=-0.864475413\) \(a_{48}=-0.408892433\) \(a_{49}=-0.339330054\) \(a_{50}=-0.102561797\)
\(a_{51}=+0.140028008\) \(a_{52}=-0.442043204\) \(a_{53}=+1.294848103\) \(a_{54}=+0.287779197\) \(a_{55}=-0.039383399\)
\(a_{56}=+0.286911177\) \(a_{57}=-0.921676302\) \(a_{58}=+0.032865752\) \(a_{59}=+1.019250408\) \(a_{60}=+0.688728981\)
\(a_{61}=+0.830362250\) \(a_{62}=+2.110286170\) \(a_{63}=+0.270938686\) \(a_{64}=-1.403235114\) \(a_{65}=-0.345142023\)
\(a_{66}=-0.035230824\) \(a_{67}=+0.404704069\) \(a_{68}=+0.299787466\) \(a_{69}=+0.377989427\) \(a_{70}=+1.173017815\)
\(a_{71}=-1.675830169\) \(a_{72}=+0.117661380\) \(a_{73}=+1.851310297\) \(a_{74}=-0.355387394\) \(a_{75}=-0.039598954\)
\(a_{76}=-1.973226684\) \(a_{77}=-0.033169156\) \(a_{78}=-0.308750335\) \(a_{79}=+0.535797456\) \(a_{80}=-0.683503519\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.803246891\) \(a_{83}=+0.467412738\) \(a_{84}=+0.580055541\) \(a_{85}=+0.234070452\)
\(a_{86}=-2.208890181\) \(a_{87}=+0.012689417\) \(a_{88}=-0.014404472\) \(a_{89}=+0.052559039\) \(a_{90}=+0.481050951\)
\(a_{91}=-0.290682617\) \(a_{92}=+0.809241619\) \(a_{93}=+0.814778287\) \(a_{94}=-1.292688615\) \(a_{95}=-1.540671691\)
\(a_{96}=-0.815230568\) \(a_{97}=-1.171871240\) \(a_{98}=-0.507415355\) \(a_{99}=-0.013602568\) \(a_{100}=-0.084777826\)

Showing 100 of 430 available coefficients

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