Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.79416536046 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.367822243\) \(a_{4}=+0.500000000\) \(a_{5}=+0.916030570\)
\(a_{6}=-0.967196383\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.870937687\) \(a_{10}=+0.647731428\)
\(a_{11}=+0.266099030\) \(a_{12}=-0.683911121\) \(a_{13}=-0.595269200\) \(a_{14}=-0.267261242\) \(a_{15}=-1.252966988\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.519686578\) \(a_{18}=+0.615845945\) \(a_{19}=+1.108976617\) \(a_{20}=+0.458015285\)
\(a_{21}=+0.516988213\) \(a_{22}=+0.188160429\) \(a_{23}=-0.131238363\) \(a_{24}=-0.483598192\) \(a_{25}=-0.160887995\)
\(a_{26}=-0.420918889\) \(a_{27}=+0.176534303\) \(a_{28}=-0.188982237\) \(a_{29}=+1.581960633\) \(a_{30}=-0.885981453\)
\(a_{31}=-1.483913338\) \(a_{32}=+0.176776701\) \(a_{33}=-0.363976184\) \(a_{34}=-0.367473886\) \(a_{35}=-0.346227031\)
\(a_{36}=+0.435468856\) \(a_{37}=+0.022889900\) \(a_{38}=+0.784164887\) \(a_{39}=+0.814222451\) \(a_{40}=+0.323865713\)
\(a_{41}=+0.364198269\) \(a_{42}=+0.365565868\) \(a_{43}=-1.372534578\) \(a_{44}=+0.133049517\) \(a_{45}=+0.797805533\)
\(a_{46}=-0.092799548\) \(a_{47}=-0.200306282\) \(a_{48}=-0.341955646\) \(a_{49}=+0.142857056\) \(a_{50}=-0.113764924\)
\(a_{51}=+0.710838483\) \(a_{52}=-0.297634875\) \(a_{53}=-1.217849063\) \(a_{54}=+0.124829648\) \(a_{55}=+0.243753710\)
\(a_{56}=-0.133627986\) \(a_{57}=-1.516883491\) \(a_{58}=+1.118606795\) \(a_{59}=+1.027712274\) \(a_{60}=-0.626485191\)
\(a_{61}=+0.364852592\) \(a_{62}=-1.049278011\) \(a_{63}=-0.329185613\) \(a_{64}=+0.125008526\) \(a_{65}=-0.545192038\)
\(a_{66}=-0.257562685\) \(a_{67}=+1.246894904\) \(a_{68}=-0.259952451\) \(a_{69}=+0.179442699\) \(a_{70}=-0.244215151\)
\(a_{71}=+1.485195924\) \(a_{72}=+0.307923154\) \(a_{73}=+1.061820200\) \(a_{74}=+0.016184175\) \(a_{75}=+0.220066302\)
\(a_{76}=+0.554488844\) \(a_{77}=-0.100568510\) \(a_{78}=+0.575734646\) \(a_{79}=-1.767667845\) \(a_{80}=+0.229012133\)
\(a_{81}=-1.112425521\) \(a_{82}=+0.257525635\) \(a_{83}=-0.619256443\) \(a_{84}=+0.258508516\) \(a_{85}=-0.476068204\)
\(a_{86}=-0.970518078\) \(a_{87}=-2.163848569\) \(a_{88}=+0.094081599\) \(a_{89}=-0.169943008\) \(a_{90}=+0.564301270\)
\(a_{91}=+0.225427241\) \(a_{92}=-0.065530592\) \(a_{93}=+2.029642625\) \(a_{94}=-0.141635699\) \(a_{95}=+1.015866667\)
\(a_{96}=-0.241790008\) \(a_{97}=+0.763927222\) \(a_{98}=+0.101010699\) \(a_{99}=+0.231686932\) \(a_{100}=-0.080439797\)

Showing 100 of 2000 available coefficients

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