Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 19.2387335253 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.509151297\) \(a_{4}=+0.500000000\) \(a_{5}=+1.135683252\)
\(a_{6}=+1.067131116\) \(a_{7}=+0.378200920\) \(a_{8}=+0.353553391\) \(a_{9}=+1.277537636\) \(a_{10}=+0.803049329\)
\(a_{11}=-1.345237866\) \(a_{12}=+0.754575648\) \(a_{13}=-1.274446771\) \(a_{14}=+0.267428435\) \(a_{15}=+1.713917852\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.732913678\) \(a_{18}=+0.903355526\) \(a_{19}=+0.532842883\) \(a_{20}=+0.567841626\)
\(a_{21}=+0.570762408\) \(a_{22}=-0.951226818\) \(a_{23}=+0.631678748\) \(a_{24}=+0.533565558\) \(a_{25}=+0.289776448\)
\(a_{26}=-0.901169954\) \(a_{27}=+0.418846283\) \(a_{28}=+0.189100460\) \(a_{29}=-1.098632221\) \(a_{30}=+1.211922935\)
\(a_{31}=+0.432283878\) \(a_{32}=+0.176776695\) \(a_{33}=-2.030167470\) \(a_{34}=+0.518248232\) \(a_{35}=+0.429516450\)
\(a_{36}=+0.638768818\) \(a_{37}=+0.119621645\) \(a_{38}=+0.376776816\) \(a_{39}=-1.923332997\) \(a_{40}=+0.401524664\)
\(a_{41}=+0.584078565\) \(a_{42}=+0.403589969\) \(a_{43}=-0.491836700\) \(a_{44}=-0.672618933\) \(a_{45}=+1.450878097\)
\(a_{46}=+0.446664327\) \(a_{47}=-1.541852483\) \(a_{48}=+0.377287824\) \(a_{49}=-0.856964064\) \(a_{50}=+0.204902892\)
\(a_{51}=+1.106077628\) \(a_{52}=-0.637223386\) \(a_{53}=+0.965520567\) \(a_{54}=+0.296169047\) \(a_{55}=-1.527764115\)
\(a_{56}=+0.133714217\) \(a_{57}=+0.804140527\) \(a_{58}=-0.776850293\) \(a_{59}=-1.065722925\) \(a_{60}=+0.856958926\)
\(a_{61}=+0.883425542\) \(a_{62}=+0.305670862\) \(a_{63}=+0.483165909\) \(a_{64}=+0.125000000\) \(a_{65}=-1.447367853\)
\(a_{66}=-1.435545185\) \(a_{67}=+0.701507344\) \(a_{68}=+0.366456839\) \(a_{69}=+0.953298802\) \(a_{70}=+0.303713995\)
\(a_{71}=-0.866067847\) \(a_{72}=+0.451677763\) \(a_{73}=-0.364265408\) \(a_{74}=+0.084585277\) \(a_{75}=+0.437316503\)
\(a_{76}=+0.266421441\) \(a_{77}=-0.508770198\) \(a_{78}=-1.360001805\) \(a_{79}=+0.636780518\) \(a_{80}=+0.283920813\)
\(a_{81}=-0.645435225\) \(a_{82}=+0.413005914\) \(a_{83}=+0.937084226\) \(a_{84}=+0.285381204\) \(a_{85}=+0.832357789\)
\(a_{86}=-0.347781066\) \(a_{87}=-1.658002241\) \(a_{88}=-0.475613409\) \(a_{89}=-0.250778653\) \(a_{90}=+1.025925741\)
\(a_{91}=-0.481996941\) \(a_{92}=+0.315839374\) \(a_{93}=+0.652381775\) \(a_{94}=-1.090254346\) \(a_{95}=+0.605140738\)
\(a_{96}=+0.266782779\) \(a_{97}=+1.964474004\) \(a_{98}=-0.605965101\) \(a_{99}=-1.718592004\) \(a_{100}=+0.144888224\)

Showing 100 of 1228 available coefficients

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