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: \( 27.1480324512 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.276042755\) \(a_{4}=+0.500000000\) \(a_{5}=+0.408220455\)
\(a_{6}=-0.902298485\) \(a_{7}=+0.813251944\) \(a_{8}=-0.353553391\) \(a_{9}=+0.628285113\) \(a_{10}=-0.288655452\)
\(a_{11}=+1.482634347\) \(a_{12}=+0.638021378\) \(a_{13}=+1.335703006\) \(a_{14}=-0.575055965\) \(a_{15}=+0.520906754\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.467009398\) \(a_{18}=-0.444264664\) \(a_{19}=-0.988801948\) \(a_{20}=+0.204110227\)
\(a_{21}=+1.037744252\) \(a_{22}=-1.048380801\) \(a_{23}=+1.342760171\) \(a_{24}=-0.451149243\) \(a_{25}=-0.833356060\)
\(a_{26}=-0.944484654\) \(a_{27}=-0.474324089\) \(a_{28}=+0.406625972\) \(a_{29}=+0.216415267\) \(a_{30}=-0.368336698\)
\(a_{31}=+1.113616040\) \(a_{32}=-0.176776695\) \(a_{33}=+1.891904817\) \(a_{34}=+1.037332293\) \(a_{35}=+0.331986079\)
\(a_{36}=+0.314142556\) \(a_{37}=+0.030981662\) \(a_{38}=+0.699188563\) \(a_{39}=+1.704414144\) \(a_{40}=-0.144327726\)
\(a_{41}=-0.011352617\) \(a_{42}=-0.733795997\) \(a_{43}=+0.490968429\) \(a_{44}=+0.741317174\) \(a_{45}=+0.256478834\)
\(a_{46}=-0.949474822\) \(a_{47}=+0.750086892\) \(a_{48}=+0.319010689\) \(a_{49}=-0.338621275\) \(a_{50}=+0.589271721\)
\(a_{51}=-1.871966714\) \(a_{52}=+0.667851503\) \(a_{53}=+0.628562898\) \(a_{54}=+0.335397780\) \(a_{55}=+0.605241668\)
\(a_{56}=-0.287527982\) \(a_{57}=-1.261753562\) \(a_{58}=-0.153028703\) \(a_{59}=+0.208830124\) \(a_{60}=+0.260453377\)
\(a_{61}=+0.859550046\) \(a_{62}=-0.787445453\) \(a_{63}=+0.510954089\) \(a_{64}=+0.125000000\) \(a_{65}=+0.545261289\)
\(a_{66}=-1.337778725\) \(a_{67}=-0.367889491\) \(a_{68}=-0.733504699\) \(a_{69}=+1.713419388\) \(a_{70}=-0.234749607\)
\(a_{71}=+0.550571308\) \(a_{72}=-0.222132332\) \(a_{73}=+0.241755804\) \(a_{74}=-0.021907343\) \(a_{75}=-1.063397963\)
\(a_{76}=-0.494400974\) \(a_{77}=+1.205755265\) \(a_{78}=-1.205202799\) \(a_{79}=+1.519161202\) \(a_{80}=+0.102055114\)
\(a_{81}=-1.233542930\) \(a_{82}=+0.008027512\) \(a_{83}=+1.052498188\) \(a_{84}=+0.518872126\) \(a_{85}=-0.598863244\)
\(a_{86}=-0.347167105\) \(a_{87}=+0.276155133\) \(a_{88}=-0.524190400\) \(a_{89}=-1.122775083\) \(a_{90}=-0.181357923\)
\(a_{91}=+1.086263067\) \(a_{92}=+0.671380086\) \(a_{93}=+1.421021680\) \(a_{94}=-0.530391528\) \(a_{95}=-0.403649181\)
\(a_{96}=-0.225574621\) \(a_{97}=-1.646412336\) \(a_{98}=+0.239441400\) \(a_{99}=+0.931517088\) \(a_{100}=-0.416678030\)

Showing 100 of 1228 available coefficients

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