Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 31.5265821968 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.758953383\) \(a_{3}=+1.643895687\) \(a_{4}=-0.423989763\) \(a_{5}=+0.849860836\)
\(a_{6}=-1.247640193\) \(a_{7}=+0.973606574\) \(a_{8}=+1.080741848\) \(a_{9}=+1.702393028\) \(a_{10}=-0.645004756\)
\(a_{11}=-0.120212990\) \(a_{12}=-0.696994942\) \(a_{13}=-0.822651179\) \(a_{14}=-0.738922003\) \(a_{15}=+1.397082562\)
\(a_{16}=-0.396242915\) \(a_{17}=+0.155930140\) \(a_{18}=-1.292036948\) \(a_{19}=-0.230083795\) \(a_{20}=-0.360332294\)
\(a_{21}=+1.600507647\) \(a_{22}=+0.091236055\) \(a_{23}=+1.259555184\) \(a_{24}=+1.776626861\) \(a_{25}=-0.277736560\)
\(a_{26}=+0.624353896\) \(a_{27}=+1.154660869\) \(a_{28}=-0.412799220\) \(a_{29}=+0.602720830\) \(a_{30}=-1.060320537\)
\(a_{31}=+1.748344957\) \(a_{32}=-0.780011944\) \(a_{33}=-0.197617615\) \(a_{34}=-0.118343734\) \(a_{35}=+0.827430096\)
\(a_{36}=-0.721797216\) \(a_{37}=+0.450086357\) \(a_{38}=+0.174622875\) \(a_{39}=-1.352352725\) \(a_{40}=+0.918480170\)
\(a_{41}=+1.196653696\) \(a_{42}=-1.214710693\) \(a_{43}=-0.554835822\) \(a_{44}=+0.050969077\) \(a_{45}=+1.446797162\)
\(a_{46}=-0.955943668\) \(a_{47}=+0.450771912\) \(a_{48}=-0.651382025\) \(a_{49}=-0.052090239\) \(a_{50}=+0.210789102\)
\(a_{51}=+0.256332943\) \(a_{52}=+0.348795678\) \(a_{53}=-0.108916623\) \(a_{54}=-0.876333773\) \(a_{55}=-0.102164312\)
\(a_{56}=+1.052217366\) \(a_{57}=-0.378233756\) \(a_{58}=-0.457437015\) \(a_{59}=+1.265945313\) \(a_{60}=-0.592348690\)
\(a_{61}=-0.494686638\) \(a_{62}=-1.326912314\) \(a_{63}=+1.657461098\) \(a_{64}=+0.988235466\) \(a_{65}=-0.699138844\)
\(a_{66}=+0.149982558\) \(a_{67}=-1.602582227\) \(a_{68}=-0.066112798\) \(a_{69}=+2.070577335\) \(a_{70}=-0.627980871\)
\(a_{71}=-1.201473245\) \(a_{72}=+1.839847387\) \(a_{73}=-0.662574021\) \(a_{74}=-0.341594563\) \(a_{75}=-0.456569933\)
\(a_{76}=+0.097553174\) \(a_{77}=-0.117040157\) \(a_{78}=+1.026372676\) \(a_{79}=+0.023743611\) \(a_{80}=-0.336751338\)
\(a_{81}=+0.195748995\) \(a_{82}=-0.908204371\) \(a_{83}=+0.551389332\) \(a_{84}=-0.678598857\) \(a_{85}=+0.132518949\)
\(a_{86}=+0.421094524\) \(a_{87}=+0.990810173\) \(a_{88}=-0.129919209\) \(a_{89}=-0.060167602\) \(a_{90}=-1.098051600\)
\(a_{91}=-0.800938596\) \(a_{92}=-0.534038504\) \(a_{93}=+2.874096733\) \(a_{94}=-0.342114867\) \(a_{95}=-0.195539206\)
\(a_{96}=-1.282258271\) \(a_{97}=+0.850225346\) \(a_{98}=+0.039534065\) \(a_{99}=-0.204649757\) \(a_{100}=+0.117757454\)

Showing 100 of 5000 available coefficients

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