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: \( 18.0189772589 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.448563155\) \(a_{3}=-0.577350269\) \(a_{4}=+1.098335215\) \(a_{5}=-1.114252893\)
\(a_{6}=+0.836328328\) \(a_{7}=-0.930969403\) \(a_{8}=-0.142444769\) \(a_{9}=+0.333333333\) \(a_{10}=+1.614065687\)
\(a_{11}=+1.119868886\) \(a_{12}=-0.634124132\) \(a_{13}=+0.787177939\) \(a_{14}=+1.348567976\) \(a_{15}=+0.643314208\)
\(a_{16}=-0.891994971\) \(a_{17}=+1.834128537\) \(a_{18}=-0.482854385\) \(a_{19}=-0.819068091\) \(a_{20}=-1.223823191\)
\(a_{21}=+0.537495436\) \(a_{22}=-1.622200807\) \(a_{23}=-1.062195406\) \(a_{24}=+0.082240526\) \(a_{25}=+0.241559510\)
\(a_{26}=-1.140276960\) \(a_{27}=-0.192450090\) \(a_{28}=-1.022516480\) \(a_{29}=+0.774548187\) \(a_{30}=-0.931881259\)
\(a_{31}=+0.589295531\) \(a_{32}=+1.434555818\) \(a_{33}=-0.646556603\) \(a_{34}=-2.656851021\) \(a_{35}=+1.037335351\)
\(a_{36}=+0.366111738\) \(a_{37}=-0.019041903\) \(a_{38}=+1.186471858\) \(a_{39}=-0.454477395\) \(a_{40}=+0.158719496\)
\(a_{41}=-0.476085571\) \(a_{42}=-0.778596084\) \(a_{43}=-0.678489699\) \(a_{44}=+1.229991433\) \(a_{45}=-0.371417631\)
\(a_{46}=+1.538657128\) \(a_{47}=-1.122596508\) \(a_{48}=+0.514993537\) \(a_{49}=-0.133295970\) \(a_{50}=-0.349914207\)
\(a_{51}=-1.058934605\) \(a_{52}=+0.864585251\) \(a_{53}=+0.522376366\) \(a_{54}=+0.278776109\) \(a_{55}=-1.247817146\)
\(a_{56}=+0.132611722\) \(a_{57}=+0.472889183\) \(a_{58}=-1.121981965\) \(a_{59}=+1.642234651\) \(a_{60}=+0.706574649\)
\(a_{61}=+0.139681921\) \(a_{62}=-0.853631794\) \(a_{63}=-0.310323134\) \(a_{64}=-1.186049732\) \(a_{65}=-0.877115297\)
\(a_{66}=+0.936578073\) \(a_{67}=-0.217394814\) \(a_{68}=+2.014487961\) \(a_{69}=+0.613258803\) \(a_{70}=-1.502645770\)
\(a_{71}=+1.057294088\) \(a_{72}=-0.047481590\) \(a_{73}=-0.847704527\) \(a_{74}=+0.027583400\) \(a_{75}=-0.139464448\)
\(a_{76}=-0.899611328\) \(a_{77}=-1.042563669\) \(a_{78}=+0.658339210\) \(a_{79}=+0.853181119\) \(a_{80}=+0.993907977\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.689640017\) \(a_{83}=-0.850017074\) \(a_{84}=+0.590350165\) \(a_{85}=-2.043683029\)
\(a_{86}=+0.982835180\) \(a_{87}=-0.447185604\) \(a_{88}=-0.159519465\) \(a_{89}=+0.732607548\) \(a_{90}=+0.538021896\)
\(a_{91}=-0.732838577\) \(a_{92}=-1.166646619\) \(a_{93}=-0.340229934\) \(a_{94}=+1.626151940\) \(a_{95}=+0.912648990\)
\(a_{96}=-0.828241188\) \(a_{97}=-0.601532358\) \(a_{98}=+0.193087631\) \(a_{99}=+0.373289629\) \(a_{100}=+0.265313317\)

Showing 100 of 1228 available coefficients

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