Properties

Level $78$
Weight $0$
Character 78.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( 0 \)
Character: 78.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.36813279635 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.058776030\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.353141422\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.041560929\)
\(a_{11}=+0.297413987\) \(a_{12}=-0.288675135\) \(a_{13}=+0.277350098\) \(a_{14}=-0.249708694\) \(a_{15}=+0.033934357\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.683001200\) \(a_{18}=+0.235702260\) \(a_{19}=-0.211502732\) \(a_{20}=-0.029388015\)
\(a_{21}=+0.203886295\) \(a_{22}=+0.210303447\) \(a_{23}=-0.070476419\) \(a_{24}=-0.204124145\) \(a_{25}=-0.996545378\)
\(a_{26}=+0.196116135\) \(a_{27}=-0.192450090\) \(a_{28}=-0.176570711\) \(a_{29}=+1.231528969\) \(a_{30}=+0.023995214\)
\(a_{31}=-1.889934675\) \(a_{32}=+0.176776695\) \(a_{33}=-0.171712045\) \(a_{34}=+1.190061561\) \(a_{35}=+0.020756251\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.034733128\) \(a_{38}=-0.149555016\) \(a_{39}=-0.160128154\) \(a_{40}=-0.020780465\)
\(a_{41}=-0.139796283\) \(a_{42}=+0.144169382\) \(a_{43}=+1.081092200\) \(a_{44}=+0.148706993\) \(a_{45}=-0.019592010\)
\(a_{46}=-0.049834353\) \(a_{47}=-1.475920458\) \(a_{48}=-0.144337567\) \(a_{49}=-0.875291136\) \(a_{50}=-0.704663995\)
\(a_{51}=-0.971681196\) \(a_{52}=+0.138675049\) \(a_{53}=+1.379583861\) \(a_{54}=-0.136082763\) \(a_{55}=-0.017480813\)
\(a_{56}=-0.124854347\) \(a_{57}=+0.122111159\) \(a_{58}=+0.870822485\) \(a_{59}=-1.697923105\) \(a_{60}=+0.016967178\)
\(a_{61}=+0.457776060\) \(a_{62}=-1.336385625\) \(a_{63}=-0.117713807\) \(a_{64}=+0.125000000\) \(a_{65}=-0.016301538\)
\(a_{66}=-0.121418752\) \(a_{67}=+0.671425697\) \(a_{68}=+0.841500600\) \(a_{69}=+0.040689579\) \(a_{70}=+0.014676886\)
\(a_{71}=+0.647375987\) \(a_{72}=+0.117851130\) \(a_{73}=+0.904300986\) \(a_{74}=-0.024560030\) \(a_{75}=+0.575355742\)
\(a_{76}=-0.105751366\) \(a_{77}=-0.105029198\) \(a_{78}=-0.113227703\) \(a_{79}=+1.226994689\) \(a_{80}=-0.014694007\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.098850900\) \(a_{83}=+1.231167339\) \(a_{84}=+0.101943148\) \(a_{85}=-0.098920129\)
\(a_{86}=+0.764447625\) \(a_{87}=-0.711023582\) \(a_{88}=+0.105151723\) \(a_{89}=+0.233729340\) \(a_{90}=-0.013853643\)
\(a_{91}=-0.097943808\) \(a_{92}=-0.035238209\) \(a_{93}=+1.091154293\) \(a_{94}=-1.043633365\) \(a_{95}=+0.012431291\)
\(a_{96}=-0.102062073\) \(a_{97}=+0.807330124\) \(a_{98}=-0.618924298\) \(a_{99}=+0.099137996\) \(a_{100}=-0.498272689\)

Showing 100 of 1200 available coefficients

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