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: \( 13.8221167093 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.461639468\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.326428398\) \(a_{7}=-0.215020653\) \(a_{8}=-0.353553391\) \(a_{9}=-0.786889002\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.124202660\) \(a_{12}=+0.230819734\) \(a_{13}=+1.363876039\) \(a_{14}=+0.152042562\) \(a_{15}=-0.206451446\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.124964084\) \(a_{18}=+0.556414549\) \(a_{19}=+0.842811281\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.099262020\) \(a_{22}=+0.087824543\) \(a_{23}=-1.190663896\) \(a_{24}=-0.163214199\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.964405996\) \(a_{27}=-0.824898487\) \(a_{28}=-0.107510327\) \(a_{29}=-0.604757462\) \(a_{30}=+0.145983218\)
\(a_{31}=+0.213566518\) \(a_{32}=-0.176776695\) \(a_{33}=-0.057336850\) \(a_{34}=+0.795469732\) \(a_{35}=+0.096160160\)
\(a_{36}=-0.393444501\) \(a_{37}=+0.753576545\) \(a_{38}=-0.595957572\) \(a_{39}=+0.629619008\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.529101041\) \(a_{42}=+0.070188847\) \(a_{43}=+1.754380426\) \(a_{44}=-0.062101330\) \(a_{45}=+0.351907460\)
\(a_{46}=+0.841926515\) \(a_{47}=+0.281474979\) \(a_{48}=+0.115409867\) \(a_{49}=-0.953766119\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.519327821\) \(a_{52}=+0.681938019\) \(a_{53}=+0.758559699\) \(a_{54}=+0.583291314\) \(a_{55}=+0.055545118\)
\(a_{56}=+0.076021281\) \(a_{57}=+0.389074951\) \(a_{58}=+0.427628102\) \(a_{59}=+0.627697312\) \(a_{60}=-0.103225723\)
\(a_{61}=+0.305090709\) \(a_{62}=-0.151014333\) \(a_{63}=+0.169197387\) \(a_{64}=+0.125000000\) \(a_{65}=-0.609943907\)
\(a_{66}=+0.040543275\) \(a_{67}=-0.843445355\) \(a_{68}=-0.562482042\) \(a_{69}=-0.549657447\) \(a_{70}=-0.067995501\)
\(a_{71}=+1.454710227\) \(a_{72}=+0.278207275\) \(a_{73}=+0.564005592\) \(a_{74}=-0.532859085\) \(a_{75}=+0.092327894\)
\(a_{76}=+0.421405640\) \(a_{77}=+0.026706137\) \(a_{78}=-0.445207870\) \(a_{79}=+0.980754319\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.406083303\) \(a_{82}=-1.081237715\) \(a_{83}=+0.466283254\) \(a_{84}=-0.049631010\) \(a_{85}=+0.503099233\)
\(a_{86}=-1.240534296\) \(a_{87}=-0.279179914\) \(a_{88}=+0.043912271\) \(a_{89}=+0.777058232\) \(a_{90}=-0.248836151\)
\(a_{91}=-0.293261519\) \(a_{92}=-0.595331948\) \(a_{93}=+0.098590733\) \(a_{94}=-0.199032866\) \(a_{95}=-0.376916663\)
\(a_{96}=-0.081607099\) \(a_{97}=+1.239016667\) \(a_{98}=+0.674414490\) \(a_{99}=+0.097733753\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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