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: \( 2.29012783647 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.533427392\) \(a_{4}=+0.500000000\) \(a_{5}=+0.926402520\)
\(a_{6}=-0.377190126\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.715455218\) \(a_{10}=-0.655065504\)
\(a_{11}=+1.795577045\) \(a_{12}=+0.266713696\) \(a_{13}=-0.799626677\) \(a_{14}=+0.267261242\) \(a_{15}=+0.494168480\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.644200140\) \(a_{18}=+0.505903236\) \(a_{19}=-0.267389365\) \(a_{20}=+0.463201260\)
\(a_{21}=-0.201616603\) \(a_{22}=-1.269664705\) \(a_{23}=+0.320697632\) \(a_{24}=-0.188595063\) \(a_{25}=-0.141778371\)
\(a_{26}=+0.565421445\) \(a_{27}=-0.915070803\) \(a_{28}=-0.188982237\) \(a_{29}=+0.554645537\) \(a_{30}=-0.349429883\)
\(a_{31}=+1.403755326\) \(a_{32}=-0.176776696\) \(a_{33}=+0.957809980\) \(a_{34}=+0.455518286\) \(a_{35}=-0.350147242\)
\(a_{36}=-0.357727603\) \(a_{37}=+0.098216111\) \(a_{38}=+0.189072833\) \(a_{39}=-0.426542768\) \(a_{40}=-0.327532752\)
\(a_{41}=-1.054530773\) \(a_{42}=+0.142564467\) \(a_{43}=-0.180016305\) \(a_{44}=+0.897788522\) \(a_{45}=-0.662799517\)
\(a_{46}=-0.226767470\) \(a_{47}=-1.041653772\) \(a_{48}=+0.133356851\) \(a_{49}=+0.142857145\) \(a_{50}=+0.100252449\)
\(a_{51}=-0.343634001\) \(a_{52}=-0.399813336\) \(a_{53}=+1.657304994\) \(a_{54}=+0.647052762\) \(a_{55}=+1.663427145\)
\(a_{56}=+0.133630592\) \(a_{57}=-0.142632824\) \(a_{58}=-0.392193711\) \(a_{59}=+0.024661633\) \(a_{60}=+0.247084013\)
\(a_{61}=-0.329622069\) \(a_{62}=-0.992604818\) \(a_{63}=+0.270414567\) \(a_{64}=+0.125000446\) \(a_{65}=-0.740772435\)
\(a_{66}=-0.677277705\) \(a_{67}=-0.488347479\) \(a_{68}=-0.322102957\) \(a_{69}=+0.171026990\) \(a_{70}=+0.247596513\)
\(a_{71}=+1.316182432\) \(a_{72}=+0.252952777\) \(a_{73}=-0.902754016\) \(a_{74}=-0.069491634\) \(a_{75}=-0.075697410\)
\(a_{76}=-0.133730249\) \(a_{77}=-0.678777303\) \(a_{78}=+0.301688273\) \(a_{79}=-0.216230735\) \(a_{80}=+0.233812918\)
\(a_{81}=+0.227331629\) \(a_{82}=+0.745666010\) \(a_{83}=+0.251642212\) \(a_{84}=-0.100808244\) \(a_{85}=-0.596788515\)
\(a_{86}=+0.127290940\) \(a_{87}=+0.295862558\) \(a_{88}=-0.634831822\) \(a_{89}=+0.575118169\) \(a_{90}=+0.468671198\)
\(a_{91}=+0.302230423\) \(a_{92}=+0.160346519\) \(a_{93}=+0.748801183\) \(a_{94}=+0.736562356\) \(a_{95}=-0.247706104\)
\(a_{96}=-0.094296057\) \(a_{97}=-1.229124800\) \(a_{98}=-0.101027566\) \(a_{99}=-1.284640915\) \(a_{100}=-0.070892889\)

Showing 100 of 2000 available coefficients

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