Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.64245616518 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.264515440\) \(a_{3}=-0.344758204\) \(a_{4}=-0.930031582\) \(a_{5}=+0.129008322\)
\(a_{6}=-0.091193868\) \(a_{7}=-0.324963913\) \(a_{8}=-0.510523153\) \(a_{9}=-0.881141780\) \(a_{10}=+0.034124693\)
\(a_{11}=-0.540640545\) \(a_{12}=+0.320636018\) \(a_{13}=+0.482721175\) \(a_{14}=-0.085957973\) \(a_{15}=-0.044476678\)
\(a_{16}=+0.794990325\) \(a_{17}=+0.031836732\) \(a_{18}=-0.233075606\) \(a_{19}=+0.229415734\) \(a_{20}=-0.119981814\)
\(a_{21}=+0.112033976\) \(a_{22}=-0.143007772\) \(a_{23}=-1.526741005\) \(a_{24}=+0.176007046\) \(a_{25}=-0.983356853\)
\(a_{26}=+0.127687204\) \(a_{27}=+0.648539063\) \(a_{28}=+0.302226702\) \(a_{29}=+0.000755401\) \(a_{30}=-0.011764768\)
\(a_{31}=+0.399218681\) \(a_{32}=+0.720810370\) \(a_{33}=+0.186390261\) \(a_{34}=+0.008421308\) \(a_{35}=-0.041923047\)
\(a_{36}=+0.819489683\) \(a_{37}=-1.133156407\) \(a_{38}=+0.060684002\) \(a_{39}=-0.166422076\) \(a_{40}=-0.065861741\)
\(a_{41}=+0.868577176\) \(a_{42}=+0.029634732\) \(a_{43}=-0.954663589\) \(a_{44}=+0.502812785\) \(a_{45}=-0.113674618\)
\(a_{46}=-0.403846576\) \(a_{47}=-0.309598419\) \(a_{48}=-0.274079434\) \(a_{49}=-0.894398451\) \(a_{50}=-0.260113076\)
\(a_{51}=-0.010975974\) \(a_{52}=-0.448945931\) \(a_{53}=+1.173864640\) \(a_{54}=+0.171548582\) \(a_{55}=-0.069747107\)
\(a_{56}=+0.165901620\) \(a_{57}=-0.079092993\) \(a_{58}=+0.000199796\) \(a_{59}=+0.863322711\) \(a_{60}=+0.041364734\)
\(a_{61}=+0.884765612\) \(a_{62}=+0.105599516\) \(a_{63}=+0.286339382\) \(a_{64}=-0.604324929\) \(a_{65}=+0.062274942\)
\(a_{66}=+0.049303213\) \(a_{67}=-0.370367977\) \(a_{68}=-0.029609170\) \(a_{69}=+0.526356470\) \(a_{70}=-0.011089316\)
\(a_{71}=-1.757411371\) \(a_{72}=+0.449843337\) \(a_{73}=+1.188333231\) \(a_{74}=-0.299737455\) \(a_{75}=+0.339020345\)
\(a_{76}=-0.213363838\) \(a_{77}=+0.175688675\) \(a_{78}=-0.044021251\) \(a_{79}=-1.707052099\) \(a_{80}=+0.102560397\)
\(a_{81}=+0.657552569\) \(a_{82}=+0.229752048\) \(a_{83}=-1.311841353\) \(a_{84}=-0.104195104\) \(a_{85}=+0.004107192\)
\(a_{86}=-0.252523308\) \(a_{87}=-0.000260371\) \(a_{88}=+0.276009536\) \(a_{89}=-0.942020717\) \(a_{90}=-0.030068620\)
\(a_{91}=-0.156866982\) \(a_{92}=+1.419917268\) \(a_{93}=-0.137633981\) \(a_{94}=-0.081893510\) \(a_{95}=+0.029596656\)
\(a_{96}=-0.248505353\) \(a_{97}=+1.496530809\) \(a_{98}=-0.236582165\) \(a_{99}=+0.476381045\) \(a_{100}=+0.914552952\)

Showing 100 of 1500 available coefficients

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