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: \( 6.1871464447 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.892712310\) \(a_{4}=+0.500000000\) \(a_{5}=+1.471525428\)
\(a_{6}=+0.631242928\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.203064732\) \(a_{10}=-1.040525609\)
\(a_{11}=+0.582544985\) \(a_{12}=-0.446356155\) \(a_{13}=-0.604207698\) \(a_{14}=+0.267261242\) \(a_{15}=-1.313648864\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.217823114\) \(a_{18}=+0.143588449\) \(a_{19}=-1.859231214\) \(a_{20}=+0.735762714\)
\(a_{21}=+0.337413538\) \(a_{22}=-0.411921509\) \(a_{23}=-0.980153016\) \(a_{24}=+0.315621464\) \(a_{25}=+1.165387087\)
\(a_{26}=+0.427239360\) \(a_{27}=+1.073990696\) \(a_{28}=-0.188982237\) \(a_{29}=-1.023261338\) \(a_{30}=+0.928890020\)
\(a_{31}=-1.975226303\) \(a_{32}=-0.176776695\) \(a_{33}=-0.520045079\) \(a_{34}=-0.154024201\) \(a_{35}=-0.556184333\)
\(a_{36}=-0.101532366\) \(a_{37}=+0.763099048\) \(a_{38}=+1.314674999\) \(a_{39}=+0.539383649\) \(a_{40}=-0.520262805\)
\(a_{41}=+0.530777515\) \(a_{42}=-0.238587401\) \(a_{43}=-0.058254903\) \(a_{44}=+0.291272493\) \(a_{45}=-0.298814917\)
\(a_{46}=+0.693072844\) \(a_{47}=+0.068970512\) \(a_{48}=-0.223178077\) \(a_{49}=+0.142857143\) \(a_{50}=-0.824053112\)
\(a_{51}=-0.194453375\) \(a_{52}=-0.302103849\) \(a_{53}=-1.367394755\) \(a_{54}=-0.759426104\) \(a_{55}=+0.857229759\)
\(a_{56}=+0.133630621\) \(a_{57}=+1.659758591\) \(a_{58}=+0.723555031\) \(a_{59}=-1.271688805\) \(a_{60}=-0.656824432\)
\(a_{61}=-0.225216060\) \(a_{62}=+1.396695913\) \(a_{63}=+0.076751254\) \(a_{64}=+0.125000000\) \(a_{65}=-0.889106991\)
\(a_{66}=+0.367727402\) \(a_{67}=-0.876331990\) \(a_{68}=+0.108911557\) \(a_{69}=+0.874994663\) \(a_{70}=+0.393281714\)
\(a_{71}=+0.679182600\) \(a_{72}=+0.071794225\) \(a_{73}=+1.832487300\) \(a_{74}=-0.539592512\) \(a_{75}=-1.040355398\)
\(a_{76}=-0.929615607\) \(a_{77}=-0.220181308\) \(a_{78}=-0.381401836\) \(a_{79}=-0.776501900\) \(a_{80}=+0.367881357\)
\(a_{81}=-0.755699982\) \(a_{82}=-0.375316380\) \(a_{83}=+0.451580835\) \(a_{84}=+0.168706769\) \(a_{85}=+0.320532251\)
\(a_{86}=+0.041192437\) \(a_{87}=+0.913477993\) \(a_{88}=-0.205960755\) \(a_{89}=-0.983556100\) \(a_{90}=+0.211294054\)
\(a_{91}=+0.228369044\) \(a_{92}=-0.490076508\) \(a_{93}=+1.763308835\) \(a_{94}=-0.048769517\) \(a_{95}=-2.735906009\)
\(a_{96}=+0.157810732\) \(a_{97}=+1.349810000\) \(a_{98}=-0.101015254\) \(a_{99}=-0.118294341\) \(a_{100}=+0.582693543\)

Showing 100 of 156 available coefficients

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