Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 17.5005568024 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.974644775\) \(a_{3}=-0.577350269\) \(a_{4}=-0.050067563\) \(a_{5}=+0.813294363\)
\(a_{6}=-0.562711423\) \(a_{7}=-0.211255153\) \(a_{8}=-1.023442864\) \(a_{9}=+0.333333333\) \(a_{10}=+0.792673101\)
\(a_{11}=+1.487036529\) \(a_{12}=+0.028906521\) \(a_{13}=+0.093937951\) \(a_{14}=-0.205898731\) \(a_{15}=-0.469555719\)
\(a_{16}=-0.947425676\) \(a_{17}=+1.254025537\) \(a_{18}=+0.324881592\) \(a_{19}=+1.307122290\) \(a_{20}=-0.040719667\)
\(a_{21}=+0.121968219\) \(a_{22}=+1.449332382\) \(a_{23}=+0.923662102\) \(a_{24}=+0.590885013\) \(a_{25}=-0.338552280\)
\(a_{26}=+0.091556133\) \(a_{27}=-0.192450090\) \(a_{28}=+0.010577031\) \(a_{29}=+1.949318354\) \(a_{30}=-0.457650028\)
\(a_{31}=-0.662677167\) \(a_{32}=+0.100039379\) \(a_{33}=-0.858540940\) \(a_{34}=+1.222229437\) \(a_{35}=-0.171812625\)
\(a_{36}=-0.016689188\) \(a_{37}=-0.711144464\) \(a_{38}=+1.273979910\) \(a_{39}=-0.054235101\) \(a_{40}=-0.832360311\)
\(a_{41}=+0.491331578\) \(a_{42}=+0.118875687\) \(a_{43}=-1.109709678\) \(a_{44}=-0.074452295\) \(a_{45}=+0.271098121\)
\(a_{46}=+0.900242441\) \(a_{47}=+0.413449320\) \(a_{48}=+0.546996469\) \(a_{49}=-0.955371261\) \(a_{50}=-0.329968210\)
\(a_{51}=-0.724011981\) \(a_{52}=-0.004703244\) \(a_{53}=+0.088899083\) \(a_{54}=-0.187570474\) \(a_{55}=+1.209398426\)
\(a_{56}=+0.216207578\) \(a_{57}=-0.754667406\) \(a_{58}=+1.899892948\) \(a_{59}=-1.444210208\) \(a_{60}=+0.023509511\)
\(a_{61}=-0.691000950\) \(a_{62}=-0.645874838\) \(a_{63}=-0.070418384\) \(a_{64}=+1.044928534\) \(a_{65}=+0.076399206\)
\(a_{66}=-0.836772441\) \(a_{67}=+1.671800420\) \(a_{68}=-0.062786003\) \(a_{69}=-0.533276563\) \(a_{70}=-0.167456277\)
\(a_{71}=+0.084080641\) \(a_{72}=-0.341147621\) \(a_{73}=+0.545000669\) \(a_{74}=-0.693113236\) \(a_{75}=+0.195463250\)
\(a_{76}=-0.065444428\) \(a_{77}=-0.314144129\) \(a_{78}=-0.052859958\) \(a_{79}=+0.587438196\) \(a_{80}=-0.770535961\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.478873755\) \(a_{83}=+1.210862818\) \(a_{84}=-0.006106652\) \(a_{85}=+1.019891900\)
\(a_{86}=-1.081572739\) \(a_{87}=-1.125439476\) \(a_{88}=-1.521896923\) \(a_{89}=+0.544407203\) \(a_{90}=+0.264224367\)
\(a_{91}=-0.019844876\) \(a_{92}=-0.046245511\) \(a_{93}=+0.382596841\) \(a_{94}=+0.402966220\) \(a_{95}=+1.063075190\)
\(a_{96}=-0.057757763\) \(a_{97}=+0.460101734\) \(a_{98}=-0.931147607\) \(a_{99}=+0.495678843\) \(a_{100}=+0.016950488\)

Showing 100 of 1228 available coefficients

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