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: \( 5.03074918113 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.754254979\) \(a_{4}=+0.500000000\) \(a_{5}=-0.959868572\)
\(a_{6}=+1.240445592\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553390\) \(a_{9}=+2.077410532\) \(a_{10}=+0.678729577\)
\(a_{11}=+0.495518362\) \(a_{12}=-0.877127489\) \(a_{13}=-1.695877019\) \(a_{14}=+0.267261242\) \(a_{15}=+1.683854222\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.358678956\) \(a_{18}=-1.468951074\) \(a_{19}=+0.499696178\) \(a_{20}=-0.479934286\)
\(a_{21}=+0.663046060\) \(a_{22}=-0.350384394\) \(a_{23}=+0.748171124\) \(a_{24}=+0.620222793\) \(a_{25}=-0.078652324\)
\(a_{26}=+1.199166148\) \(a_{27}=-1.890052781\) \(a_{28}=-0.188982250\) \(a_{29}=+0.006038258\) \(a_{30}=-1.190664729\)
\(a_{31}=+0.565405835\) \(a_{32}=-0.176776685\) \(a_{33}=-0.869265414\) \(a_{34}=-0.253624375\) \(a_{35}=+0.362796218\)
\(a_{36}=+1.038705273\) \(a_{37}=+0.514887922\) \(a_{38}=-0.353338564\) \(a_{39}=+2.975000705\) \(a_{40}=+0.339364790\)
\(a_{41}=-0.551235335\) \(a_{42}=-0.468844371\) \(a_{43}=-1.345448157\) \(a_{44}=+0.247759164\) \(a_{45}=-1.994041081\)
\(a_{46}=-0.529036884\) \(a_{47}=+1.674491742\) \(a_{48}=-0.438563741\) \(a_{49}=+0.142857166\) \(a_{50}=+0.055615575\)
\(a_{51}=-0.629214370\) \(a_{52}=-0.847938495\) \(a_{53}=+0.667960655\) \(a_{54}=+1.336469155\) \(a_{55}=-0.475632495\)
\(a_{56}=+0.133630616\) \(a_{57}=-0.876594505\) \(a_{58}=-0.004269717\) \(a_{59}=+1.444901413\) \(a_{60}=+0.841927073\)
\(a_{61}=-1.326605169\) \(a_{62}=-0.399802233\) \(a_{63}=-0.785187414\) \(a_{64}=+0.125000015\) \(a_{65}=+1.627819071\)
\(a_{66}=+0.614663600\) \(a_{67}=+0.825874257\) \(a_{68}=+0.179339428\) \(a_{69}=-1.312482890\) \(a_{70}=-0.256535704\)
\(a_{71}=+1.052484967\) \(a_{72}=-0.734475550\) \(a_{73}=-0.600641086\) \(a_{74}=-0.364080767\) \(a_{75}=+0.137976225\)
\(a_{76}=+0.249848059\) \(a_{77}=-0.187288323\) \(a_{78}=-2.103643164\) \(a_{79}=+0.154191893\) \(a_{80}=-0.239967177\)
\(a_{81}=+1.238224026\) \(a_{82}=+0.389782203\) \(a_{83}=-1.088998150\) \(a_{84}=+0.331523077\) \(a_{85}=-0.344284618\)
\(a_{86}=+0.951375556\) \(a_{87}=-0.010592759\) \(a_{88}=-0.175192171\) \(a_{89}=+0.182345569\) \(a_{90}=+1.409999914\)
\(a_{91}=+0.640981260\) \(a_{92}=+0.374085544\) \(a_{93}=-0.991866046\) \(a_{94}=-1.184044460\) \(a_{95}=-0.479642632\)
\(a_{96}=+0.310111408\) \(a_{97}=+0.128086915\) \(a_{98}=-0.101015265\) \(a_{99}=+1.029395066\) \(a_{100}=-0.039326200\)

Showing 100 of 2000 available coefficients

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