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: \( 20.7113415288 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.445997535\) \(a_{3}=+0.577350269\) \(a_{4}=+1.090908872\) \(a_{5}=-0.645489817\)
\(a_{6}=-0.834847066\) \(a_{7}=+0.993779459\) \(a_{8}=-0.131454004\) \(a_{9}=+0.333333333\) \(a_{10}=+0.933376685\)
\(a_{11}=+1.238934389\) \(a_{12}=+0.629836531\) \(a_{13}=-1.615962521\) \(a_{14}=-1.437002648\) \(a_{15}=-0.372673720\)
\(a_{16}=-0.900826705\) \(a_{17}=+0.608760538\) \(a_{18}=-0.481999178\) \(a_{19}=-0.708134305\) \(a_{20}=-0.704170568\)
\(a_{21}=+0.573758838\) \(a_{22}=-1.791496073\) \(a_{23}=+0.325576139\) \(a_{24}=-0.075895005\) \(a_{25}=-0.583342896\)
\(a_{26}=+2.336677823\) \(a_{27}=+0.192450090\) \(a_{28}=+1.084122829\) \(a_{29}=-0.977323739\) \(a_{30}=+0.538885280\)
\(a_{31}=+1.660696140\) \(a_{32}=+1.434047200\) \(a_{33}=+0.715299103\) \(a_{34}=-0.880266238\) \(a_{35}=-0.641474522\)
\(a_{36}=+0.363636291\) \(a_{37}=+1.069075238\) \(a_{38}=+1.023960460\) \(a_{39}=-0.932976397\) \(a_{40}=+0.084852221\)
\(a_{41}=+1.070053672\) \(a_{42}=-0.829653866\) \(a_{43}=-0.990410523\) \(a_{44}=+1.351564516\) \(a_{45}=-0.215163272\)
\(a_{46}=-0.470782295\) \(a_{47}=+0.747105316\) \(a_{48}=-0.520092541\) \(a_{49}=-0.012402386\) \(a_{50}=+0.843512390\)
\(a_{51}=+0.351468061\) \(a_{52}=-1.762867851\) \(a_{53}=+1.263661519\) \(a_{54}=-0.278282355\) \(a_{55}=-0.799719532\)
\(a_{56}=-0.130636289\) \(a_{57}=-0.408841532\) \(a_{58}=+1.413207718\) \(a_{59}=+0.778990182\) \(a_{60}=-0.406553067\)
\(a_{61}=+1.358509075\) \(a_{62}=-2.401362526\) \(a_{63}=+0.331259820\) \(a_{64}=-1.172802011\) \(a_{65}=+1.043087353\)
\(a_{66}=-1.034320740\) \(a_{67}=+0.672264074\) \(a_{68}=+0.664102272\) \(a_{69}=+0.187971472\) \(a_{70}=+0.927570577\)
\(a_{71}=-0.016757989\) \(a_{72}=-0.043818001\) \(a_{73}=-0.432205383\) \(a_{74}=-1.545880159\) \(a_{75}=-0.336793178\)
\(a_{76}=-0.772509996\) \(a_{77}=+1.231227547\) \(a_{78}=+1.349081570\) \(a_{79}=-0.270486063\) \(a_{80}=+0.581474465\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.547294972\) \(a_{83}=-0.124603519\) \(a_{84}=+0.625918607\) \(a_{85}=-0.392948729\)
\(a_{86}=+1.432131176\) \(a_{87}=-0.564258124\) \(a_{88}=-0.162862887\) \(a_{89}=-0.283287027\) \(a_{90}=+0.311125562\)
\(a_{91}=-1.605910361\) \(a_{92}=+0.355173899\) \(a_{93}=+0.958803364\) \(a_{94}=-1.080312446\) \(a_{95}=+0.457093483\)
\(a_{96}=+0.827947537\) \(a_{97}=+0.518840852\) \(a_{98}=+0.017933820\) \(a_{99}=+0.412978130\) \(a_{100}=-0.636373940\)

Showing 100 of 1228 available coefficients

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