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: \( 6.34752444631 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.028621227\) \(a_{4}=+0.500000000\) \(a_{5}=+0.225254369\)
\(a_{6}=+0.727345045\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.058061629\) \(a_{10}=+0.159278892\)
\(a_{11}=+1.029160790\) \(a_{12}=+0.514310613\) \(a_{13}=+1.381896218\) \(a_{14}=+0.267261242\) \(a_{15}=+0.231701425\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.736362424\) \(a_{18}=+0.041055771\) \(a_{19}=-0.643696960\) \(a_{20}=+0.112627185\)
\(a_{21}=+0.388782280\) \(a_{22}=+0.727726574\) \(a_{23}=+1.091394423\) \(a_{24}=+0.363672522\) \(a_{25}=-0.949260469\)
\(a_{26}=+0.977148186\) \(a_{27}=-0.968897803\) \(a_{28}=+0.188982237\) \(a_{29}=-0.735520676\) \(a_{30}=+0.163837649\)
\(a_{31}=-0.444574784\) \(a_{32}=+0.176776695\) \(a_{33}=+1.058616635\) \(a_{34}=-0.520686863\) \(a_{35}=+0.085138149\)
\(a_{36}=+0.029030814\) \(a_{37}=-0.869750063\) \(a_{38}=-0.455162485\) \(a_{39}=+1.421447783\) \(a_{40}=+0.079639446\)
\(a_{41}=-1.773161254\) \(a_{42}=+0.274910587\) \(a_{43}=+0.951763388\) \(a_{44}=+0.514580395\) \(a_{45}=+0.013078636\)
\(a_{46}=+0.771732398\) \(a_{47}=+0.388625112\) \(a_{48}=+0.257155307\) \(a_{49}=+0.142857143\) \(a_{50}=-0.671228515\)
\(a_{51}=-0.757438020\) \(a_{52}=+0.690948109\) \(a_{53}=-1.597749745\) \(a_{54}=-0.685114207\) \(a_{55}=+0.231822965\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.662120356\) \(a_{58}=-0.520091658\) \(a_{59}=+0.376329123\) \(a_{60}=+0.115850713\)
\(a_{61}=+1.643602369\) \(a_{62}=-0.314361845\) \(a_{63}=+0.021945233\) \(a_{64}=+0.125000000\) \(a_{65}=+0.311278161\)
\(a_{66}=+0.748555001\) \(a_{67}=-1.464193150\) \(a_{68}=-0.368181212\) \(a_{69}=+1.122631471\) \(a_{70}=+0.060201762\)
\(a_{71}=+0.820660804\) \(a_{72}=+0.020527886\) \(a_{73}=+1.211221867\) \(a_{74}=-0.615006167\) \(a_{75}=-0.976429469\)
\(a_{76}=-0.321848480\) \(a_{77}=+0.388986216\) \(a_{78}=+1.005115366\) \(a_{79}=-1.666424303\) \(a_{80}=+0.056313592\)
\(a_{81}=-1.054690476\) \(a_{82}=-1.253814347\) \(a_{83}=+0.573999782\) \(a_{84}=+0.194391140\) \(a_{85}=-0.165868853\)
\(a_{86}=+0.672998346\) \(a_{87}=-0.756572181\) \(a_{88}=+0.363863287\) \(a_{89}=-0.352386670\) \(a_{90}=+0.009247992\)
\(a_{91}=+0.522307676\) \(a_{92}=+0.545697212\) \(a_{93}=-0.457299060\) \(a_{94}=+0.274799452\) \(a_{95}=-0.144995552\)
\(a_{96}=+0.181836261\) \(a_{97}=+1.932977935\) \(a_{98}=+0.101015254\) \(a_{99}=+0.059754752\) \(a_{100}=-0.474630235\)

Showing 100 of 180 available coefficients

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