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: \( 24.4197154423 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.965540640\) \(a_{3}=-0.690260078\) \(a_{4}=-0.067731273\) \(a_{5}=+1.315803633\)
\(a_{6}=-0.666474157\) \(a_{7}=-0.545495994\) \(a_{8}=-1.030937936\) \(a_{9}=-0.523541024\) \(a_{10}=+1.270461881\)
\(a_{11}=-0.156969214\) \(a_{12}=+0.046752194\) \(a_{13}=-1.894282085\) \(a_{14}=-0.526698550\) \(a_{15}=-0.908246719\)
\(a_{16}=-0.927681201\) \(a_{17}=+0.344746218\) \(a_{18}=-0.505500136\) \(a_{19}=-0.100628587\) \(a_{20}=-0.089121055\)
\(a_{21}=+0.376534107\) \(a_{22}=-0.151560156\) \(a_{23}=-0.704050570\) \(a_{24}=+0.711615301\) \(a_{25}=+0.731339201\)
\(a_{26}=-1.829006336\) \(a_{27}=+1.051639547\) \(a_{28}=+0.036947138\) \(a_{29}=+0.339890304\) \(a_{30}=-0.876949118\)
\(a_{31}=+0.267400547\) \(a_{32}=+0.135224036\) \(a_{33}=+0.108349582\) \(a_{34}=+0.332866484\) \(a_{35}=-0.717765610\)
\(a_{36}=+0.035460100\) \(a_{37}=+0.161243716\) \(a_{38}=-0.097160990\) \(a_{39}=+1.307547300\) \(a_{40}=-1.356511882\)
\(a_{41}=-0.553884435\) \(a_{42}=+0.363558983\) \(a_{43}=+1.063778730\) \(a_{44}=+0.010631725\) \(a_{45}=-0.688877182\)
\(a_{46}=-0.679789438\) \(a_{47}=+0.494065756\) \(a_{48}=+0.640341299\) \(a_{49}=-0.702434121\) \(a_{50}=+0.706137720\)
\(a_{51}=-0.237964551\) \(a_{52}=+0.128302137\) \(a_{53}=-1.301960318\) \(a_{54}=+1.015400721\) \(a_{55}=-0.206540662\)
\(a_{56}=+0.562372514\) \(a_{57}=+0.069459896\) \(a_{58}=+0.328177900\) \(a_{59}=-1.669271791\) \(a_{60}=+0.061516705\)
\(a_{61}=+0.747162097\) \(a_{62}=+0.258186113\) \(a_{63}=+0.285589531\) \(a_{64}=+1.058245504\) \(a_{65}=-2.492503249\)
\(a_{66}=+0.104615925\) \(a_{67}=+0.850184860\) \(a_{68}=-0.023350100\) \(a_{69}=+0.485978001\) \(a_{70}=-0.693031866\)
\(a_{71}=+0.445158119\) \(a_{72}=+0.539738303\) \(a_{73}=-0.951680600\) \(a_{74}=+0.155687361\) \(a_{75}=-0.504814254\)
\(a_{76}=+0.006815702\) \(a_{77}=+0.085626077\) \(a_{78}=+1.262490057\) \(a_{79}=+0.486542417\) \(a_{80}=-1.220646295\)
\(a_{81}=-0.202363771\) \(a_{82}=-0.534797932\) \(a_{83}=+0.137628428\) \(a_{84}=-0.025503134\) \(a_{85}=+0.453618326\)
\(a_{86}=+1.027121595\) \(a_{87}=-0.234612708\) \(a_{88}=+0.161825518\) \(a_{89}=-1.292996151\) \(a_{90}=-0.665138915\)
\(a_{91}=+1.033323288\) \(a_{92}=+0.047686241\) \(a_{93}=-0.184575923\) \(a_{94}=+0.477040566\) \(a_{95}=-0.132407461\)
\(a_{96}=-0.093339753\) \(a_{97}=+0.713772122\) \(a_{98}=-0.678228690\) \(a_{99}=+0.082179823\) \(a_{100}=-0.049534534\)

Showing 100 of 5000 available coefficients

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