Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 10.9135396775 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.412244843\) \(a_{3}=+0.577350269\) \(a_{4}=-0.830054190\) \(a_{5}=-0.254508244\)
\(a_{6}=-0.238009671\) \(a_{7}=+1.435382977\) \(a_{8}=+0.754430402\) \(a_{9}=+0.333333333\) \(a_{10}=+0.104919711\)
\(a_{11}=+1.083759485\) \(a_{12}=-0.479232010\) \(a_{13}=+0.516784827\) \(a_{14}=-0.591729229\) \(a_{15}=-0.146940403\)
\(a_{16}=+0.519044147\) \(a_{17}=+0.693266926\) \(a_{18}=-0.137414948\) \(a_{19}=-1.381357834\) \(a_{20}=+0.211255635\)
\(a_{21}=+0.828718748\) \(a_{22}=-0.446774259\) \(a_{23}=+0.604563888\) \(a_{24}=+0.435570595\) \(a_{25}=-0.935225554\)
\(a_{26}=-0.213041880\) \(a_{27}=+0.192450090\) \(a_{28}=-1.191445653\) \(a_{29}=+1.752611461\) \(a_{30}=+0.060575423\)
\(a_{31}=+0.217432123\) \(a_{32}=-0.968403675\) \(a_{33}=+0.625708831\) \(a_{34}=-0.285795715\) \(a_{35}=-0.365316801\)
\(a_{36}=-0.276684730\) \(a_{37}=-0.096869969\) \(a_{38}=+0.569457643\) \(a_{39}=+0.298365859\) \(a_{40}=-0.192008757\)
\(a_{41}=+0.993458186\) \(a_{42}=-0.341635030\) \(a_{43}=-0.209976233\) \(a_{44}=-0.899579101\) \(a_{45}=-0.084836081\)
\(a_{46}=-0.249228345\) \(a_{47}=-0.169047834\) \(a_{48}=+0.299670278\) \(a_{49}=+1.060324289\) \(a_{50}=+0.385541911\)
\(a_{51}=+0.400257846\) \(a_{52}=-0.428959411\) \(a_{53}=-0.983024544\) \(a_{54}=-0.079336557\) \(a_{55}=-0.275825724\)
\(a_{56}=+1.082896555\) \(a_{57}=-0.797527317\) \(a_{58}=-0.722505036\) \(a_{59}=+0.234656727\) \(a_{60}=+0.121968497\)
\(a_{61}=+1.120751498\) \(a_{62}=-0.089635271\) \(a_{63}=+0.478460992\) \(a_{64}=-0.119824727\) \(a_{65}=-0.131525999\)
\(a_{66}=-0.257945238\) \(a_{67}=-0.461977853\) \(a_{68}=-0.575449116\) \(a_{69}=+0.349045124\) \(a_{70}=+0.150599967\)
\(a_{71}=-0.479559444\) \(a_{72}=+0.251476801\) \(a_{73}=+0.010870268\) \(a_{74}=+0.039934145\) \(a_{75}=-0.539952725\)
\(a_{76}=+1.146601858\) \(a_{77}=+1.555609916\) \(a_{78}=-0.122999787\) \(a_{79}=-1.304389788\) \(a_{80}=-0.132101015\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.409548014\) \(a_{83}=-0.470165477\) \(a_{84}=-0.687881469\) \(a_{85}=-0.176442148\)
\(a_{86}=+0.086561619\) \(a_{87}=+1.011870699\) \(a_{88}=+0.817621104\) \(a_{89}=-0.324494496\) \(a_{90}=+0.034973237\)
\(a_{91}=+0.741784143\) \(a_{92}=-0.501820788\) \(a_{93}=+0.125534495\) \(a_{94}=+0.069689098\) \(a_{95}=+0.351566957\)
\(a_{96}=-0.559108122\) \(a_{97}=-1.192048303\) \(a_{98}=-0.437113220\) \(a_{99}=+0.361253162\) \(a_{100}=+0.776287889\)

Showing 100 of 1228 available coefficients

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