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: \( 17.4931127227 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106782\) \(a_{3}=-1.681219554\) \(a_{4}=+0.500000001\) \(a_{5}=+0.816028158\)
\(a_{6}=+1.188801748\) \(a_{7}=+0.330768917\) \(a_{8}=-0.353553391\) \(a_{9}=+1.826499187\) \(a_{10}=-0.577019045\)
\(a_{11}=+0.798626596\) \(a_{12}=-0.840609778\) \(a_{13}=-1.418503271\) \(a_{14}=-0.233888944\) \(a_{15}=-1.371922496\)
\(a_{16}=+0.250000001\) \(a_{17}=-0.483988115\) \(a_{18}=-1.291529962\) \(a_{19}=+0.792586323\) \(a_{20}=+0.408014080\)
\(a_{21}=-0.556095171\) \(a_{22}=-0.564714282\) \(a_{23}=+0.073038396\) \(a_{24}=+0.594400874\) \(a_{25}=-0.334098045\)
\(a_{26}=+1.003033283\) \(a_{27}=-1.389526594\) \(a_{28}=+0.165384459\) \(a_{29}=-0.415023701\) \(a_{30}=+0.970095701\)
\(a_{31}=+0.497632095\) \(a_{32}=-0.176776696\) \(a_{33}=-1.342666649\) \(a_{34}=+0.342231278\) \(a_{35}=+0.269916750\)
\(a_{36}=+0.913249595\) \(a_{37}=-1.219543698\) \(a_{38}=-0.560443164\) \(a_{39}=+2.384815436\) \(a_{40}=-0.288509523\)
\(a_{41}=-1.866451367\) \(a_{42}=+0.393218667\) \(a_{43}=-0.585664325\) \(a_{44}=+0.399313298\) \(a_{45}=+1.490474768\)
\(a_{46}=-0.051645945\) \(a_{47}=-0.349432162\) \(a_{48}=-0.420304889\) \(a_{49}=-0.890591924\) \(a_{50}=+0.236242993\)
\(a_{51}=+0.813690282\) \(a_{52}=-0.709251636\) \(a_{53}=-0.131437554\) \(a_{54}=+0.982543678\) \(a_{55}=+0.651701790\)
\(a_{56}=-0.116944472\) \(a_{57}=-1.332511623\) \(a_{58}=+0.293466073\) \(a_{59}=-0.388209150\) \(a_{60}=-0.685961249\)
\(a_{61}=+1.417587720\) \(a_{62}=-0.351879029\) \(a_{63}=+0.604149158\) \(a_{64}=+0.125000000\) \(a_{65}=-1.157538612\)
\(a_{66}=+0.949408693\) \(a_{67}=+0.091988289\) \(a_{68}=-0.241994058\) \(a_{69}=-0.122793579\) \(a_{70}=-0.190859965\)
\(a_{71}=-0.962560999\) \(a_{72}=-0.645764982\) \(a_{73}=+1.269806360\) \(a_{74}=+0.862347619\) \(a_{75}=+0.561692165\)
\(a_{76}=+0.396293162\) \(a_{77}=+0.264160854\) \(a_{78}=-1.686319167\) \(a_{79}=-1.551483647\) \(a_{80}=+0.204007040\)
\(a_{81}=+0.509600094\) \(a_{82}=+1.319780419\) \(a_{83}=-0.223939213\) \(a_{84}=-0.278047586\) \(a_{85}=-0.394947930\)
\(a_{86}=+0.414127216\) \(a_{87}=+0.697745961\) \(a_{88}=-0.282357141\) \(a_{89}=+0.826713633\) \(a_{90}=-1.053924816\)
\(a_{91}=-0.469196791\) \(a_{92}=+0.036519198\) \(a_{93}=-0.836628809\) \(a_{94}=+0.247085851\) \(a_{95}=+0.646772757\)
\(a_{96}=+0.297200438\) \(a_{97}=-0.785982533\) \(a_{98}=+0.629743589\) \(a_{99}=+1.458690828\) \(a_{100}=-0.167049022\)

Showing 100 of 1228 available coefficients

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