Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 31.8329099691 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.474645239\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.042731649\) \(a_{7}=-0.182247535\) \(a_{8}=+0.353553391\) \(a_{9}=+1.174578582\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.788238470\) \(a_{12}=-0.737322620\) \(a_{13}=+1.759367229\) \(a_{14}=-0.128868468\) \(a_{15}=+0.659481400\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.146066095\) \(a_{18}=+0.830552480\) \(a_{19}=+0.172561157\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.268750461\) \(a_{22}=+0.557368767\) \(a_{23}=+0.152359681\) \(a_{24}=-0.521365824\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.244060498\) \(a_{27}=-0.257441475\) \(a_{28}=-0.091123768\) \(a_{29}=+1.640612499\) \(a_{30}=+0.466323770\)
\(a_{31}=-0.068770895\) \(a_{32}=+0.176776695\) \(a_{33}=-1.162372107\) \(a_{34}=+0.810391108\) \(a_{35}=+0.081503576\)
\(a_{36}=+0.587289291\) \(a_{37}=+0.363798661\) \(a_{38}=+0.122019164\) \(a_{39}=-2.594442508\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.012985273\) \(a_{42}=+0.190035273\) \(a_{43}=+0.456649020\) \(a_{44}=+0.394119235\) \(a_{45}=-0.525287511\)
\(a_{46}=+0.107734564\) \(a_{47}=-0.223977153\) \(a_{48}=-0.368661310\) \(a_{49}=-0.966785836\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.690040911\) \(a_{52}=+0.879683614\) \(a_{53}=-0.973327865\) \(a_{54}=-0.182038613\) \(a_{55}=-0.352510960\)
\(a_{56}=-0.064434234\) \(a_{57}=-0.254466489\) \(a_{58}=+1.160088223\) \(a_{59}=+1.693681340\) \(a_{60}=+0.329740700\)
\(a_{61}=+1.872047954\) \(a_{62}=-0.048628366\) \(a_{63}=-0.214064052\) \(a_{64}=+0.125000000\) \(a_{65}=-0.786812944\)
\(a_{66}=-0.821921199\) \(a_{67}=+0.401589237\) \(a_{68}=+0.573033048\) \(a_{69}=-0.224676479\) \(a_{70}=+0.057631731\)
\(a_{71}=+0.525410893\) \(a_{72}=+0.415276240\) \(a_{73}=-1.654289275\) \(a_{74}=+0.257244500\) \(a_{75}=-0.294929048\)
\(a_{76}=+0.086280579\) \(a_{77}=-0.143654518\) \(a_{78}=-1.834547891\) \(a_{79}=-0.722762049\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.794943737\) \(a_{82}=-0.716288756\) \(a_{83}=+0.541127127\) \(a_{84}=+0.134375230\) \(a_{85}=-0.512536339\)
\(a_{86}=+0.322899619\) \(a_{87}=-2.419321411\) \(a_{88}=+0.278684384\) \(a_{89}=+0.264539070\) \(a_{90}=-0.371434361\)
\(a_{91}=-0.320640341\) \(a_{92}=+0.076179841\) \(a_{93}=+0.101412673\) \(a_{94}=-0.158375763\) \(a_{95}=-0.077171696\)
\(a_{96}=-0.260682912\) \(a_{97}=-1.340619241\) \(a_{98}=-0.683620820\) \(a_{99}=+0.925848024\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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