Properties

Level $42$
Weight $0$
Character 42.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( 0 \)
Character: 42.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.07255726908 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.342044581\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.948968824\)
\(a_{11}=-0.027159149\) \(a_{12}=-0.288675135\) \(a_{13}=-1.053900303\) \(a_{14}=-0.267261242\) \(a_{15}=+0.774829800\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.978014873\) \(a_{18}=+0.235702260\) \(a_{19}=+0.440280912\) \(a_{20}=-0.671022290\)
\(a_{21}=+0.218217890\) \(a_{22}=-0.019204419\) \(a_{23}=-1.442695473\) \(a_{24}=-0.204124145\) \(a_{25}=+0.801083657\)
\(a_{26}=-0.745220051\) \(a_{27}=-0.192450090\) \(a_{28}=-0.188982237\) \(a_{29}=+0.794313441\) \(a_{30}=+0.547887406\)
\(a_{31}=+1.358333326\) \(a_{32}=+0.176776695\) \(a_{33}=+0.015680342\) \(a_{34}=-0.691560949\) \(a_{35}=+0.507245173\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.603593564\) \(a_{38}=+0.311325618\) \(a_{39}=+0.608469624\) \(a_{40}=-0.474484412\)
\(a_{41}=-1.755328099\) \(a_{42}=+0.154303350\) \(a_{43}=-1.453720372\) \(a_{44}=-0.013579575\) \(a_{45}=-0.447348194\)
\(a_{46}=-1.020139752\) \(a_{47}=-1.025812928\) \(a_{48}=-0.144337567\) \(a_{49}=+0.142857143\) \(a_{50}=+0.566451686\)
\(a_{51}=+0.564657150\) \(a_{52}=-0.526950151\) \(a_{53}=+1.035010686\) \(a_{54}=-0.136082763\) \(a_{55}=+0.036448789\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.254196303\) \(a_{58}=+0.561664421\) \(a_{59}=-0.995666318\) \(a_{60}=+0.387414900\)
\(a_{61}=-0.626704624\) \(a_{62}=+0.960486706\) \(a_{63}=-0.125988158\) \(a_{64}=+0.125000000\) \(a_{65}=+1.414381190\)
\(a_{66}=+0.011087676\) \(a_{67}=-0.399064618\) \(a_{68}=-0.489007436\) \(a_{69}=+0.832940620\) \(a_{70}=+0.358676501\)
\(a_{71}=-1.793445804\) \(a_{72}=+0.117851130\) \(a_{73}=+1.650580134\) \(a_{74}=+1.133911884\) \(a_{75}=-0.462505865\)
\(a_{76}=+0.220140456\) \(a_{77}=+0.010265194\) \(a_{78}=+0.430252997\) \(a_{79}=+0.927789821\) \(a_{80}=-0.335511145\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.241204402\) \(a_{83}=-0.733262210\) \(a_{84}=+0.109108945\) \(a_{85}=+1.312539560\)
\(a_{86}=-1.027935533\) \(a_{87}=-0.458597079\) \(a_{88}=-0.009602209\) \(a_{89}=+0.561606526\) \(a_{90}=-0.316322941\)
\(a_{91}=+0.398336873\) \(a_{92}=-0.721347736\) \(a_{93}=-0.784234112\) \(a_{94}=-0.725359278\) \(a_{95}=-0.590876612\)
\(a_{96}=-0.102062073\) \(a_{97}=-1.003891387\) \(a_{98}=+0.101015254\) \(a_{99}=-0.009053050\) \(a_{100}=+0.400541829\)

Showing 100 of 618 available coefficients

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