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: \( 20.5301600346 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.529364338\) \(a_{4}=+0.500000000\) \(a_{5}=-0.027494485\)
\(a_{6}=-1.081423894\) \(a_{7}=-1.760981245\) \(a_{8}=-0.353553390\) \(a_{9}=+1.338955280\) \(a_{10}=+0.019441537\)
\(a_{11}=-0.447837093\) \(a_{12}=+0.764682168\) \(a_{13}=-0.094456559\) \(a_{14}=+1.245201779\) \(a_{15}=-0.042049085\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.289824275\) \(a_{18}=-0.946784357\) \(a_{19}=-0.323556432\) \(a_{20}=-0.013747242\)
\(a_{21}=-2.693181917\) \(a_{22}=+0.316668645\) \(a_{23}=+0.635656021\) \(a_{24}=-0.540711946\) \(a_{25}=-0.999244053\)
\(a_{26}=+0.066790873\) \(a_{27}=+0.518386117\) \(a_{28}=-0.880490621\) \(a_{29}=+0.798924044\) \(a_{30}=+0.029733193\)
\(a_{31}=-0.335709486\) \(a_{32}=-0.176776695\) \(a_{33}=-0.684906079\) \(a_{34}=+0.912043490\) \(a_{35}=+0.048417272\)
\(a_{36}=+0.669477639\) \(a_{37}=-1.107292450\) \(a_{38}=+0.228788947\) \(a_{39}=-0.144458493\) \(a_{40}=+0.009720768\)
\(a_{41}=-0.897298956\) \(a_{42}=+1.904367195\) \(a_{43}=-0.256336883\) \(a_{44}=-0.223918546\) \(a_{45}=-0.036813886\)
\(a_{46}=-0.449476683\) \(a_{47}=-1.355270793\) \(a_{48}=+0.382341084\) \(a_{49}=+2.101054945\) \(a_{50}=+0.706572246\)
\(a_{51}=-1.972611248\) \(a_{52}=-0.047228279\) \(a_{53}=+0.367445703\) \(a_{54}=-0.366554339\) \(a_{55}=+0.012313050\)
\(a_{56}=+0.622600889\) \(a_{57}=-0.494835669\) \(a_{58}=-0.564924609\) \(a_{59}=+0.862648615\) \(a_{60}=-0.021024542\)
\(a_{61}=+1.065263407\) \(a_{62}=+0.237382454\) \(a_{63}=-2.357875136\) \(a_{64}=+0.125000000\) \(a_{65}=+0.002597034\)
\(a_{66}=+0.484301733\) \(a_{67}=+0.653893248\) \(a_{68}=-0.644912136\) \(a_{69}=+0.972149650\) \(a_{70}=-0.034236181\)
\(a_{71}=+0.074968389\) \(a_{72}=-0.473392178\) \(a_{73}=-0.530064765\) \(a_{74}=+0.782974000\) \(a_{75}=-1.528208221\)
\(a_{76}=-0.161778216\) \(a_{77}=+0.788632721\) \(a_{78}=+0.102147580\) \(a_{79}=+1.334378374\) \(a_{80}=-0.006873621\)
\(a_{81}=-0.546154038\) \(a_{82}=+0.634486176\) \(a_{83}=-0.809576700\) \(a_{84}=-1.346590957\) \(a_{85}=+0.035463054\)
\(a_{86}=+0.181257548\) \(a_{87}=+1.221845942\) \(a_{88}=+0.158334322\) \(a_{89}=-0.736689424\) \(a_{90}=+0.026031348\)
\(a_{91}=+0.166336229\) \(a_{92}=+0.317828010\) \(a_{93}=-0.513422116\) \(a_{94}=+0.958321168\) \(a_{95}=+0.008896017\)
\(a_{96}=-0.270355973\) \(a_{97}=+0.408763335\) \(a_{98}=-1.485670198\) \(a_{99}=-0.599633840\) \(a_{100}=-0.499622026\)

Showing 100 of 1228 available coefficients

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