Properties

Level $1$
Weight $0$
Character 1.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 20.1066946826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.858847619\) \(a_{3}=+0.187278614\) \(a_{4}=-0.262380767\) \(a_{5}=-1.395547932\)
\(a_{6}=+0.160843792\) \(a_{7}=+0.776695055\) \(a_{8}=-1.084192716\) \(a_{9}=-0.964926721\) \(a_{10}=-1.198563019\)
\(a_{11}=-0.387355875\) \(a_{12}=-0.049138306\) \(a_{13}=-0.688244124\) \(a_{14}=+0.667062699\) \(a_{15}=-0.261356282\)
\(a_{16}=-0.668775566\) \(a_{17}=+1.234595249\) \(a_{18}=-0.828725017\) \(a_{19}=-0.094759736\) \(a_{20}=+0.366164937\)
\(a_{21}=+0.145458373\) \(a_{22}=-0.332679671\) \(a_{23}=-0.033821564\) \(a_{24}=-0.203046109\) \(a_{25}=+0.947554031\)
\(a_{26}=-0.591096824\) \(a_{27}=-0.367988752\) \(a_{28}=-0.203789844\) \(a_{29}=+1.237350804\) \(a_{30}=-0.224465221\)
\(a_{31}=-1.134588808\) \(a_{32}=+0.509816413\) \(a_{33}=-0.072543471\) \(a_{34}=+1.060329190\) \(a_{35}=-1.083915177\)
\(a_{36}=+0.253178213\) \(a_{37}=-0.160679766\) \(a_{38}=-0.081384174\) \(a_{39}=-0.128893405\) \(a_{40}=+1.513042903\)
\(a_{41}=-1.310824309\) \(a_{42}=+0.124926577\) \(a_{43}=-0.615803108\) \(a_{44}=+0.101634731\) \(a_{45}=+1.346601490\)
\(a_{46}=-0.029047570\) \(a_{47}=-0.967537802\) \(a_{48}=-0.125247361\) \(a_{49}=-0.396744792\) \(a_{50}=+0.813804523\)
\(a_{51}=+0.231213287\) \(a_{52}=+0.180582020\) \(a_{53}=-0.463642431\) \(a_{54}=-0.316046264\) \(a_{55}=+0.540573689\)
\(a_{56}=-0.842087120\) \(a_{57}=-0.017746470\) \(a_{58}=+1.062695793\) \(a_{59}=-0.048716740\) \(a_{60}=+0.068574852\)
\(a_{61}=-0.066486211\) \(a_{62}=-0.974438897\) \(a_{63}=-0.749453812\) \(a_{64}=+1.106630179\) \(a_{65}=+0.960477659\)
\(a_{66}=-0.062303788\) \(a_{67}=-0.422301548\) \(a_{68}=-0.323934048\) \(a_{69}=-0.006334056\) \(a_{70}=-0.930917969\)
\(a_{71}=+0.512965796\) \(a_{72}=+1.046166522\) \(a_{73}=-0.335104766\) \(a_{74}=-0.137999434\) \(a_{75}=+0.177456605\)
\(a_{76}=+0.024863132\) \(a_{77}=-0.300857392\) \(a_{78}=-0.110699794\) \(a_{79}=-1.100955176\) \(a_{80}=+0.933308358\)
\(a_{81}=+0.896010297\) \(a_{82}=-1.125798337\) \(a_{83}=+1.777964527\) \(a_{84}=-0.038165479\) \(a_{85}=-1.722936847\)
\(a_{86}=-0.528881033\) \(a_{87}=+0.231729343\) \(a_{88}=+0.419968418\) \(a_{89}=+0.208095279\) \(a_{90}=+1.156525483\)
\(a_{91}=-0.534555805\) \(a_{92}=+0.008874128\) \(a_{93}=-0.212484219\) \(a_{94}=-0.830967537\) \(a_{95}=+0.132241753\)
\(a_{96}=+0.095477710\) \(a_{97}=+0.349957391\) \(a_{98}=-0.340743320\) \(a_{99}=+0.373770036\) \(a_{100}=-0.248619954\)

Showing 100 of 5000 available coefficients

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