Properties

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

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 16.9402609464 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.091642619\) \(a_{4}=+0.500000000\) \(a_{5}=+1.161904488\)
\(a_{6}=-0.771907899\) \(a_{7}=-1.000000496\) \(a_{8}=+0.353553391\) \(a_{9}=+0.191683609\) \(a_{10}=+0.821590543\)
\(a_{11}=-1.502301417\) \(a_{12}=-0.545821310\) \(a_{13}=-0.697740661\) \(a_{14}=-0.707107132\) \(a_{15}=-1.268384459\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.019215861\) \(a_{18}=+0.135540780\) \(a_{19}=-1.486703959\) \(a_{20}=+0.580952244\)
\(a_{21}=+1.091643160\) \(a_{22}=-1.062287520\) \(a_{23}=+0.272629200\) \(a_{24}=-0.385953949\) \(a_{25}=+0.350022039\)
\(a_{26}=-0.493377153\) \(a_{27}=+0.882392623\) \(a_{28}=-0.500000248\) \(a_{29}=+0.755819077\) \(a_{30}=-0.896883252\)
\(a_{31}=-0.709364460\) \(a_{32}=+0.176776695\) \(a_{33}=+1.639976254\) \(a_{34}=-0.013587665\) \(a_{35}=-1.161905064\)
\(a_{36}=+0.095841804\) \(a_{37}=+0.255846040\) \(a_{38}=-1.051258451\) \(a_{39}=+0.761683443\) \(a_{40}=+0.410795271\)
\(a_{41}=+0.163580315\) \(a_{42}=+0.771908281\) \(a_{43}=-1.175095950\) \(a_{44}=-0.751150709\) \(a_{45}=+0.222718045\)
\(a_{46}=+0.192777956\) \(a_{47}=+0.707729112\) \(a_{48}=-0.272910655\) \(a_{49}=+0.000000991\) \(a_{50}=+0.247502958\)
\(a_{51}=+0.020976852\) \(a_{52}=-0.348870331\) \(a_{53}=-0.025357784\) \(a_{54}=+0.623945807\) \(a_{55}=-1.745530759\)
\(a_{56}=-0.353553566\) \(a_{57}=+1.622949404\) \(a_{58}=+0.534444795\) \(a_{59}=+0.695301682\) \(a_{60}=-0.634192229\)
\(a_{61}=-0.614606247\) \(a_{62}=-0.501596420\) \(a_{63}=-0.191683704\) \(a_{64}=+0.125000000\) \(a_{65}=-0.810708006\)
\(a_{66}=+1.159638331\) \(a_{67}=+0.901103732\) \(a_{68}=-0.009607930\) \(a_{69}=-0.297613654\) \(a_{70}=-0.821590950\)
\(a_{71}=+0.897414890\) \(a_{72}=+0.067770390\) \(a_{73}=-1.107622459\) \(a_{74}=+0.180910470\) \(a_{75}=-0.382098976\)
\(a_{76}=-0.743351980\) \(a_{77}=+1.502302162\) \(a_{78}=+0.538591528\) \(a_{79}=+0.013449699\) \(a_{80}=+0.290476122\)
\(a_{81}=-1.154941003\) \(a_{82}=+0.115668750\) \(a_{83}=+0.194776632\) \(a_{84}=+0.545821580\) \(a_{85}=-0.022326995\)
\(a_{86}=-0.830918315\) \(a_{87}=-0.825084317\) \(a_{88}=-0.531143760\) \(a_{89}=+1.181686207\) \(a_{90}=+0.157485440\)
\(a_{91}=+0.697741007\) \(a_{92}=+0.136314600\) \(a_{93}=+0.774372477\) \(a_{94}=+0.500440054\) \(a_{95}=-1.727408002\)
\(a_{96}=-0.192976975\) \(a_{97}=-0.875595296\) \(a_{98}=+0.000000701\) \(a_{99}=-0.287966557\) \(a_{100}=+0.175011020\)

Showing 100 of 1228 available coefficients

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