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: \( 12.821988162 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.528878578\) \(a_{4}=+0.500000000\) \(a_{5}=-0.612659258\)
\(a_{6}=+1.081080410\) \(a_{7}=+0.970776942\) \(a_{8}=+0.353553391\) \(a_{9}=+1.337469706\) \(a_{10}=-0.433215516\)
\(a_{11}=-0.020139615\) \(a_{12}=+0.764439289\) \(a_{13}=-0.583998499\) \(a_{14}=+0.686442959\) \(a_{15}=-0.936681615\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.385460638\) \(a_{18}=+0.945733899\) \(a_{19}=-1.750008236\) \(a_{20}=-0.306329629\)
\(a_{21}=+1.484200071\) \(a_{22}=-0.014240858\) \(a_{23}=-0.664871351\) \(a_{24}=+0.540540205\) \(a_{25}=-0.624648633\)
\(a_{26}=-0.412949299\) \(a_{27}=+0.515950205\) \(a_{28}=+0.485388471\) \(a_{29}=+0.388397027\) \(a_{30}=-0.662333922\)
\(a_{31}=-0.441229730\) \(a_{32}=+0.176776695\) \(a_{33}=-0.030791025\) \(a_{34}=+0.272561831\) \(a_{35}=-0.594755481\)
\(a_{36}=+0.668734853\) \(a_{37}=+1.437832618\) \(a_{38}=-1.237442691\) \(a_{39}=-0.892862794\) \(a_{40}=-0.216607758\)
\(a_{41}=-0.336253756\) \(a_{42}=+1.049487935\) \(a_{43}=+1.099246858\) \(a_{44}=-0.010069807\) \(a_{45}=-0.819413198\)
\(a_{46}=-0.470135041\) \(a_{47}=-0.175962525\) \(a_{48}=+0.382219644\) \(a_{49}=-0.057592128\) \(a_{50}=-0.441693285\)
\(a_{51}=+0.589322511\) \(a_{52}=-0.291999249\) \(a_{53}=+0.633380439\) \(a_{54}=+0.364831889\) \(a_{55}=+0.012338722\)
\(a_{56}=+0.343221475\) \(a_{57}=-2.675550106\) \(a_{58}=+0.274638171\) \(a_{59}=+1.863810672\) \(a_{60}=-0.468340808\)
\(a_{61}=-0.481100841\) \(a_{62}=-0.311996534\) \(a_{63}=+1.298384752\) \(a_{64}=+0.125000000\) \(a_{65}=+0.357792087\)
\(a_{66}=-0.021772542\) \(a_{67}=-1.550775821\) \(a_{68}=+0.192730319\) \(a_{69}=-1.016507566\) \(a_{70}=-0.420555634\)
\(a_{71}=+1.721926576\) \(a_{72}=+0.472866950\) \(a_{73}=+0.143783908\) \(a_{74}=+1.016701195\) \(a_{75}=-0.955011914\)
\(a_{76}=-0.875004118\) \(a_{77}=-0.019551073\) \(a_{78}=-0.631349337\) \(a_{79}=+1.270918618\) \(a_{80}=-0.153164815\)
\(a_{81}=-0.548644491\) \(a_{82}=-0.237767311\) \(a_{83}=-0.329308003\) \(a_{84}=+0.742100035\) \(a_{85}=-0.236156028\)
\(a_{86}=+0.777284908\) \(a_{87}=+0.593811894\) \(a_{88}=-0.007120429\) \(a_{89}=-0.065490051\) \(a_{90}=-0.579412630\)
\(a_{91}=-0.566932276\) \(a_{92}=-0.332435676\) \(a_{93}=-0.674586684\) \(a_{94}=-0.124424295\) \(a_{95}=+1.072158748\)
\(a_{96}=+0.270270107\) \(a_{97}=+0.323506750\) \(a_{98}=-0.040723788\) \(a_{99}=-0.026936122\) \(a_{100}=-0.312324325\)

Showing 100 of 5000 available coefficients

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