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: \( 28.5102777031 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.314094605\) \(a_{3}=-1.410042845\) \(a_{4}=+0.726844631\) \(a_{5}=-1.325850202\)
\(a_{6}=+1.852929696\) \(a_{7}=+0.083864475\) \(a_{8}=+0.358951997\) \(a_{9}=+0.988220825\) \(a_{10}=+1.742292597\)
\(a_{11}=+0.774435792\) \(a_{12}=-1.024882071\) \(a_{13}=+0.693444809\) \(a_{14}=-0.110205854\) \(a_{15}=+1.869505591\)
\(a_{16}=-1.198541511\) \(a_{17}=-0.000414264\) \(a_{18}=-1.298615655\) \(a_{19}=-1.173992561\) \(a_{20}=-0.963687101\)
\(a_{21}=-0.118252503\) \(a_{22}=-1.017681896\) \(a_{23}=+0.062495786\) \(a_{24}=-0.506137695\) \(a_{25}=+0.757878758\)
\(a_{26}=-0.911252083\) \(a_{27}=+0.016609141\) \(a_{28}=+0.060956444\) \(a_{29}=+1.440407537\) \(a_{30}=-2.456707211\)
\(a_{31}=+0.882693040\) \(a_{32}=+1.216044940\) \(a_{33}=-1.091987648\) \(a_{34}=+0.000544382\) \(a_{35}=-0.111191731\)
\(a_{36}=+0.718283001\) \(a_{37}=-1.098709376\) \(a_{38}=+1.542737291\) \(a_{39}=-0.977786892\) \(a_{40}=-0.475916577\)
\(a_{41}=+0.536729084\) \(a_{42}=+0.155394977\) \(a_{43}=+0.032353723\) \(a_{44}=+0.562894497\) \(a_{45}=-1.310232781\)
\(a_{46}=-0.082125375\) \(a_{47}=+0.330091475\) \(a_{48}=+1.689994886\) \(a_{49}=-0.992966750\) \(a_{50}=-0.995924387\)
\(a_{51}=+0.000584130\) \(a_{52}=+0.504026637\) \(a_{53}=+0.708806577\) \(a_{54}=-0.021825982\) \(a_{55}=-1.026785851\)
\(a_{56}=+0.030103321\) \(a_{57}=+1.655379811\) \(a_{58}=-1.892831774\) \(a_{59}=-0.392400259\) \(a_{60}=+1.358840103\)
\(a_{61}=+0.887577697\) \(a_{62}=-1.159942164\) \(a_{63}=+0.082876634\) \(a_{64}=-0.399456591\) \(a_{65}=-0.919403941\)
\(a_{66}=+1.434975076\) \(a_{67}=+0.277172174\) \(a_{68}=-0.000301106\) \(a_{69}=-0.088121736\) \(a_{70}=+0.146116454\)
\(a_{71}=-1.871047668\) \(a_{72}=+0.354723839\) \(a_{73}=+0.966505000\) \(a_{74}=+1.443808063\) \(a_{75}=-1.068641520\)
\(a_{76}=-0.853310190\) \(a_{77}=+0.064947651\) \(a_{78}=+1.284904480\) \(a_{79}=-1.855119354\) \(a_{80}=+1.589086507\)
\(a_{81}=-1.011640426\) \(a_{82}=-0.705312793\) \(a_{83}=+1.909805260\) \(a_{84}=-0.085951197\) \(a_{85}=+0.000549252\)
\(a_{86}=-0.042515853\) \(a_{87}=-2.031036342\) \(a_{88}=+0.277985274\) \(a_{89}=+0.232820005\) \(a_{90}=+1.721769829\)
\(a_{91}=+0.058155385\) \(a_{92}=+0.045424727\) \(a_{93}=-1.244635005\) \(a_{94}=-0.433771426\) \(a_{95}=+1.556538274\)
\(a_{96}=-1.714675467\) \(a_{97}=-0.454744811\) \(a_{98}=+1.304852249\) \(a_{99}=+0.765313577\) \(a_{100}=+0.550860106\)

Showing 100 of 5000 available coefficients

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