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: \( 21.3157959402 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.287528378\) \(a_{3}=+1.251772631\) \(a_{4}=+0.657729325\) \(a_{5}=+1.169901767\)
\(a_{6}=+1.611692786\) \(a_{7}=-0.559463903\) \(a_{8}=-0.440683207\) \(a_{9}=+0.566934720\) \(a_{10}=+1.506281725\)
\(a_{11}=+0.678117899\) \(a_{12}=+0.823327568\) \(a_{13}=+0.532574742\) \(a_{14}=-0.720325652\) \(a_{15}=+1.464451013\)
\(a_{16}=-1.225121460\) \(a_{17}=+0.333856645\) \(a_{18}=+0.729944540\) \(a_{19}=-1.054160741\) \(a_{20}=+0.769478700\)
\(a_{21}=-0.700321602\) \(a_{22}=+0.873096039\) \(a_{23}=-0.375145855\) \(a_{24}=-0.551635177\) \(a_{25}=+0.368670144\)
\(a_{26}=+0.685705085\) \(a_{27}=-0.542099265\) \(a_{28}=-0.367975816\) \(a_{29}=-0.444995783\) \(a_{30}=+1.885522238\)
\(a_{31}=-0.850129631\) \(a_{32}=-1.136695440\) \(a_{33}=+0.848849427\) \(a_{34}=+0.429849905\) \(a_{35}=-0.654517809\)
\(a_{36}=+0.372889591\) \(a_{37}=+0.484109308\) \(a_{38}=-1.357261869\) \(a_{39}=+0.666662477\) \(a_{40}=-0.515556062\)
\(a_{41}=+1.894323126\) \(a_{42}=-0.901683937\) \(a_{43}=-1.307675743\) \(a_{44}=+0.446018028\) \(a_{45}=+0.663257930\)
\(a_{46}=-0.483010934\) \(a_{47}=+1.687633536\) \(a_{48}=-1.533573513\) \(a_{49}=-0.687000141\) \(a_{50}=+0.474673273\)
\(a_{51}=+0.417912611\) \(a_{52}=+0.350290021\) \(a_{53}=-0.163173293\) \(a_{54}=-0.697968188\) \(a_{55}=+0.793331328\)
\(a_{56}=+0.246546347\) \(a_{57}=-1.319569562\) \(a_{58}=-0.572944706\) \(a_{59}=+1.566169418\) \(a_{60}=+0.963212354\)
\(a_{61}=-0.472115895\) \(a_{62}=-1.094566025\) \(a_{63}=-0.317179511\) \(a_{64}=-0.238406177\) \(a_{65}=+0.623060123\)
\(a_{66}=+1.092917726\) \(a_{67}=-0.514680634\) \(a_{68}=+0.219587306\) \(a_{69}=-0.469597314\) \(a_{70}=-0.842710253\)
\(a_{71}=+0.742390029\) \(a_{72}=-0.249838610\) \(a_{73}=-0.074418553\) \(a_{74}=+0.623304472\) \(a_{75}=+0.461491196\)
\(a_{76}=-0.693352433\) \(a_{77}=-0.379382487\) \(a_{78}=+0.858346858\) \(a_{79}=+0.076560060\) \(a_{80}=-1.433271761\)
\(a_{81}=-1.245519743\) \(a_{82}=+2.438994783\) \(a_{83}=+0.893105662\) \(a_{84}=-0.460622055\) \(a_{85}=+0.390579479\)
\(a_{86}=-1.683669629\) \(a_{87}=-0.557033542\) \(a_{88}=-0.298835170\) \(a_{89}=+1.326241265\) \(a_{90}=+0.853963407\)
\(a_{91}=-0.297956340\) \(a_{92}=-0.246744430\) \(a_{93}=-1.064169005\) \(a_{94}=+2.172876070\) \(a_{95}=-1.233264512\)
\(a_{96}=-1.422884241\) \(a_{97}=+1.574244586\) \(a_{98}=-0.884532180\) \(a_{99}=+0.384448582\) \(a_{100}=+0.242485165\)

Showing 100 of 5000 available coefficients

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