Properties

Level $47$
Weight $0$
Character 47.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 47 \)
Weight: \( 0 \)
Character: 47.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.43722726343 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.821739443\) \(a_{3}=+1.612193465\) \(a_{4}=+2.318734596\) \(a_{5}=+1.429044265\)
\(a_{6}=-2.936996460\) \(a_{7}=+0.297373608\) \(a_{8}=-2.402390819\) \(a_{9}=+1.599167768\) \(a_{10}=-2.603346299\)
\(a_{11}=+0.937955179\) \(a_{12}=+3.738248767\) \(a_{13}=-0.758984045\) \(a_{14}=-0.541737226\) \(a_{15}=+2.303895830\)
\(a_{16}=+2.057795524\) \(a_{17}=-0.144818104\) \(a_{18}=-2.913267001\) \(a_{19}=-1.429745622\) \(a_{20}=+3.313574376\)
\(a_{21}=+0.479423780\) \(a_{22}=-1.708709954\) \(a_{23}=+0.666043564\) \(a_{24}=-3.873118791\) \(a_{25}=+1.042167508\)
\(a_{26}=+1.382671167\) \(a_{27}=+0.965974366\) \(a_{28}=+0.689530470\) \(a_{29}=-0.557923688\) \(a_{30}=-4.197097900\)
\(a_{31}=-1.449558404\) \(a_{32}=-1.346376448\) \(a_{33}=+1.512165221\) \(a_{34}=+0.263820865\) \(a_{35}=+0.424960037\)
\(a_{36}=+3.708045627\) \(a_{37}=+0.919288509\) \(a_{38}=+2.604623991\) \(a_{39}=-1.223629114\) \(a_{40}=-3.433122846\)
\(a_{41}=+0.747207485\) \(a_{42}=-0.873385221\) \(a_{43}=-0.700955071\) \(a_{44}=+2.174869146\) \(a_{45}=+2.285281534\)
\(a_{46}=-1.213357801\) \(a_{47}=-0.145865002\) \(a_{48}=+3.317564500\) \(a_{49}=-0.911568963\) \(a_{50}=-1.898557646\)
\(a_{51}=-0.233474753\) \(a_{52}=-1.759882585\) \(a_{53}=-1.173668080\) \(a_{54}=-1.759753650\) \(a_{55}=+1.340379484\)
\(a_{56}=-0.714407627\) \(a_{57}=-2.305026563\) \(a_{58}=+1.016391605\) \(a_{59}=-1.003008400\) \(a_{60}=+5.342123043\)
\(a_{61}=+0.267304827\) \(a_{62}=+2.640717697\) \(a_{63}=+0.475550234\) \(a_{64}=+0.394951562\) \(a_{65}=-1.084621806\)
\(a_{66}=-2.754771015\) \(a_{67}=+0.996510751\) \(a_{68}=-0.335794732\) \(a_{69}=+1.073791062\) \(a_{70}=-0.774166456\)
\(a_{71}=+0.487666085\) \(a_{72}=-3.841825976\) \(a_{73}=+1.415731315\) \(a_{74}=-1.674704091\) \(a_{75}=+1.680175661\)
\(a_{76}=-3.315200710\) \(a_{77}=+0.278923180\) \(a_{78}=+2.229133406\) \(a_{79}=+0.274991445\) \(a_{80}=+2.940680892\)
\(a_{81}=-0.041830224\) \(a_{82}=-1.361217361\) \(a_{83}=+1.515454687\) \(a_{84}=+1.111656541\) \(a_{85}=-0.206951505\)
\(a_{86}=+1.276957520\) \(a_{87}=-0.899480857\) \(a_{88}=-2.253334960\) \(a_{89}=-0.353343329\) \(a_{90}=-4.163187590\)
\(a_{91}=-0.225701788\) \(a_{92}=+1.544378182\) \(a_{93}=-2.336968520\) \(a_{94}=+0.265728038\) \(a_{95}=-2.043169822\)
\(a_{96}=-2.170619321\) \(a_{97}=-0.478934497\) \(a_{98}=+1.660641125\) \(a_{99}=+1.499947663\) \(a_{100}=+2.416509892\)

Showing 100 of 2000 available coefficients

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