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: \( 20.8248391133 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.335812086\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.237455003\) \(a_{7}=+1.284574848\) \(a_{8}=+0.353553391\) \(a_{9}=-0.887230243\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.566797354\) \(a_{12}=-0.167906043\) \(a_{13}=+0.948010385\) \(a_{14}=+0.908331586\) \(a_{15}=+0.150179731\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.490007779\) \(a_{18}=-0.627366521\) \(a_{19}=+1.128241613\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.431375760\) \(a_{22}=-1.107893034\) \(a_{23}=+0.837516592\) \(a_{24}=-0.118727502\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.670344572\) \(a_{27}=+0.633754725\) \(a_{28}=+0.642287424\) \(a_{29}=-0.760208117\) \(a_{30}=+0.106193106\)
\(a_{31}=-0.996995580\) \(a_{32}=+0.176776695\) \(a_{33}=+0.526149488\) \(a_{34}=-0.346487823\) \(a_{35}=-0.574479336\)
\(a_{36}=-0.443615121\) \(a_{37}=-0.845781979\) \(a_{38}=+0.797787295\) \(a_{39}=-0.318353345\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.616645743\) \(a_{42}=-0.305028725\) \(a_{43}=+0.082731371\) \(a_{44}=-0.783398677\) \(a_{45}=+0.396781427\)
\(a_{46}=+0.592213661\) \(a_{47}=-1.471934069\) \(a_{48}=-0.083953022\) \(a_{49}=+0.650132540\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.164550534\) \(a_{52}=+0.474005193\) \(a_{53}=+1.500432318\) \(a_{54}=+0.448132264\) \(a_{55}=+0.700693078\)
\(a_{56}=+0.454165793\) \(a_{57}=-0.378877170\) \(a_{58}=-0.537548315\) \(a_{59}=+1.668301531\) \(a_{60}=+0.075089865\)
\(a_{61}=+0.493674676\) \(a_{62}=-0.704982336\) \(a_{63}=-1.139713654\) \(a_{64}=+0.125000000\) \(a_{65}=-0.423963133\)
\(a_{66}=+0.372043871\) \(a_{67}=+1.452239401\) \(a_{68}=-0.245003889\) \(a_{69}=-0.281248194\) \(a_{70}=-0.406218234\)
\(a_{71}=+0.112805964\) \(a_{72}=-0.313683261\) \(a_{73}=-1.461966494\) \(a_{74}=-0.598058173\) \(a_{75}=-0.067162417\)
\(a_{76}=+0.564120806\) \(a_{77}=-2.012668473\) \(a_{78}=-0.225109809\) \(a_{79}=+0.897560508\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.674407746\) \(a_{82}=+1.143141168\) \(a_{83}=-0.069150448\) \(a_{84}=-0.215687880\) \(a_{85}=+0.219138141\)
\(a_{86}=+0.058499913\) \(a_{87}=+0.255287074\) \(a_{88}=-0.553946517\) \(a_{89}=+1.466099826\) \(a_{90}=+0.280566838\)
\(a_{91}=+1.217790297\) \(a_{92}=+0.418758296\) \(a_{93}=+0.334803166\) \(a_{94}=-1.040814562\) \(a_{95}=-0.504564988\)
\(a_{96}=-0.059363751\) \(a_{97}=+1.385395994\) \(a_{98}=+0.459713127\) \(a_{99}=+1.390109997\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

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