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: \( 5.44142257111 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.462799563\) \(a_{3}=-0.962449783\) \(a_{4}=+1.139782561\) \(a_{5}=+0.354653541\)
\(a_{6}=-1.407871121\) \(a_{7}=-1.795982511\) \(a_{8}=+0.204473869\) \(a_{9}=-0.073690416\) \(a_{10}=+0.518787045\)
\(a_{11}=-0.544226569\) \(a_{12}=-1.096983478\) \(a_{13}=+0.235515146\) \(a_{14}=-2.627162431\) \(a_{15}=-0.341336224\)
\(a_{16}=-0.840678275\) \(a_{17}=+1.194545000\) \(a_{18}=-0.107794309\) \(a_{19}=+0.229415732\) \(a_{20}=+0.404227921\)
\(a_{21}=+1.728542977\) \(a_{22}=-0.796094387\) \(a_{23}=-0.931066489\) \(a_{24}=-0.196795831\) \(a_{25}=-0.874220866\)
\(a_{26}=+0.344511452\) \(a_{27}=+1.033373108\) \(a_{28}=-2.047029545\) \(a_{29}=+0.973871473\) \(a_{30}=-0.499306479\)
\(a_{31}=-0.077957938\) \(a_{32}=-1.434217682\) \(a_{33}=+0.523790743\) \(a_{34}=+1.747379904\) \(a_{35}=-0.636951557\)
\(a_{36}=-0.083991051\) \(a_{37}=+0.440517410\) \(a_{38}=+0.335589232\) \(a_{39}=-0.226671501\) \(a_{40}=+0.072517382\)
\(a_{41}=-0.533218842\) \(a_{42}=+2.528511911\) \(a_{43}=-0.137598560\) \(a_{44}=-0.620299953\) \(a_{45}=-0.026134567\)
\(a_{46}=-1.361963653\) \(a_{47}=-1.991552740\) \(a_{48}=+0.809110623\) \(a_{49}=+2.225553178\) \(a_{50}=-1.278809900\)
\(a_{51}=-1.149689575\) \(a_{52}=+0.268436056\) \(a_{53}=+0.401581217\) \(a_{54}=+1.511617730\) \(a_{55}=-0.193011880\)
\(a_{56}=-0.367231493\) \(a_{57}=-0.220801121\) \(a_{58}=+1.424578765\) \(a_{59}=-1.128694716\) \(a_{60}=-0.389049075\)
\(a_{61}=-1.243157417\) \(a_{62}=-0.114036838\) \(a_{63}=+0.132346699\) \(a_{64}=-1.257294723\) \(a_{65}=+0.083526280\)
\(a_{66}=+0.766200870\) \(a_{67}=+1.432647868\) \(a_{68}=+1.361521559\) \(a_{69}=+0.896104740\) \(a_{70}=-0.931732460\)
\(a_{71}=-0.909260099\) \(a_{72}=-0.015067765\) \(a_{73}=-1.238351757\) \(a_{74}=+0.644388674\) \(a_{75}=+0.841393682\)
\(a_{76}=+0.261484050\) \(a_{77}=+0.977421400\) \(a_{78}=-0.331574972\) \(a_{79}=+1.027980272\) \(a_{80}=-0.298149527\)
\(a_{81}=-0.920879306\) \(a_{82}=-0.779992289\) \(a_{83}=-0.470415154\) \(a_{84}=+1.970163141\) \(a_{85}=+0.423649614\)
\(a_{86}=-0.201279113\) \(a_{87}=-0.937302387\) \(a_{88}=-0.111280112\) \(a_{89}=-1.989437624\) \(a_{90}=-0.038229633\)
\(a_{91}=-0.422981083\) \(a_{92}=-1.061213347\) \(a_{93}=+0.075030601\) \(a_{94}=-2.913242477\) \(a_{95}=+0.081363102\)
\(a_{96}=+1.380362496\) \(a_{97}=+0.288790185\) \(a_{98}=+3.255538216\) \(a_{99}=+0.040104282\) \(a_{100}=-0.996421697\)

Showing 100 of 546 available coefficients

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