Properties

Level 10
Weight 0
Character 10.1
Symmetry even
Fricke sign -1

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: \(-1\)
Spectral parameter: \( 4.58236150313 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.663175460\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.176042646\) \(a_{7}=-1.126006458\) \(a_{8}=+0.353553391\) \(a_{9}=+1.766152610\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.438783589\) \(a_{12}=-0.831587730\) \(a_{13}=+0.224726306\) \(a_{14}=-0.796206802\) \(a_{15}=+0.743794677\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.129269801\) \(a_{18}=+1.248858487\) \(a_{19}=-0.340792139\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.872746309\) \(a_{22}=-0.310266851\) \(a_{23}=-0.839585422\) \(a_{24}=-0.588021323\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.158905495\) \(a_{27}=-1.274246220\) \(a_{28}=-0.563003229\) \(a_{29}=+1.282349921\) \(a_{30}=+0.525942261\)
\(a_{31}=-0.512147928\) \(a_{32}=+0.176776699\) \(a_{33}=+0.729774105\) \(a_{34}=-0.798514342\) \(a_{35}=+0.503565385\)
\(a_{36}=+0.883076318\) \(a_{37}=-0.596895753\) \(a_{38}=-0.240976432\) \(a_{39}=-0.373759278\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.422308361\) \(a_{42}=+1.324231615\) \(a_{43}=-0.372685230\) \(a_{44}=-0.219391795\) \(a_{45}=-0.789847459\)
\(a_{46}=-0.593676546\) \(a_{47}=-1.716579952\) \(a_{48}=-0.415793865\) \(a_{49}=+0.267890544\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.878173821\) \(a_{52}=+0.112363153\) \(a_{53}=+1.906683130\) \(a_{54}=-0.901028143\) \(a_{55}=+0.196229987\)
\(a_{56}=-0.398103401\) \(a_{57}=+0.566797123\) \(a_{58}=+0.906758325\) \(a_{59}=+0.158089300\) \(a_{60}=+0.371897339\)
\(a_{61}=-1.927310045\) \(a_{62}=-0.362143270\) \(a_{63}=-1.988699246\) \(a_{64}=+0.125000000\) \(a_{65}=-0.100500661\)
\(a_{66}=+0.516028210\) \(a_{67}=-0.251968329\) \(a_{68}=-0.564634906\) \(a_{69}=+1.396377862\) \(a_{70}=+0.356074469\)
\(a_{71}=+0.784884049\) \(a_{72}=+0.624429278\) \(a_{73}=-0.915462911\) \(a_{74}=-0.422069015\) \(a_{75}=-0.332635223\)
\(a_{76}=-0.170396360\) \(a_{77}=+0.494074874\) \(a_{78}=-0.264287619\) \(a_{79}=-0.302558633\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.353142433\) \(a_{82}=+0.298617106\) \(a_{83}=+1.683734796\) \(a_{84}=+0.936373155\) \(a_{85}=+0.505024808\)
\(a_{86}=-0.263528253\) \(a_{87}=-2.132772920\) \(a_{88}=-0.155133426\) \(a_{89}=-0.003499899\) \(a_{90}=-0.558506495\)
\(a_{91}=-0.253043274\) \(a_{92}=-0.419792710\) \(a_{93}=+0.851791860\) \(a_{94}=-1.213805324\) \(a_{95}=+0.152406885\)
\(a_{96}=-0.294010664\) \(a_{97}=+0.561961966\) \(a_{98}=+0.189427206\) \(a_{99}=-0.774958755\) \(a_{100}=+0.100000014\)

Showing 100 of 2000 available coefficients

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