Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 31.1067821239 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.446989681\) \(a_{3}=-0.577350269\) \(a_{4}=+1.093779137\) \(a_{5}=+0.025905159\)
\(a_{6}=+0.835419882\) \(a_{7}=+0.171387498\) \(a_{8}=-0.135697443\) \(a_{9}=+0.333333333\) \(a_{10}=-0.037484497\)
\(a_{11}=-0.988589118\) \(a_{12}=-0.631493679\) \(a_{13}=+0.679691561\) \(a_{14}=-0.247995941\) \(a_{15}=-0.014956350\)
\(a_{16}=-0.897426337\) \(a_{17}=-0.235737078\) \(a_{18}=-0.482329894\) \(a_{19}=-1.647840629\) \(a_{20}=+0.028334522\)
\(a_{21}=-0.098950618\) \(a_{22}=+1.430478252\) \(a_{23}=+1.392379897\) \(a_{24}=+0.078344955\) \(a_{25}=-0.999328923\)
\(a_{26}=-0.983506675\) \(a_{27}=-0.192450090\) \(a_{28}=+0.187460070\) \(a_{29}=+0.455923626\) \(a_{30}=+0.021641684\)
\(a_{31}=+0.553131469\) \(a_{32}=+1.434264092\) \(a_{33}=+0.570762193\) \(a_{34}=+0.341109119\) \(a_{35}=+0.004439820\)
\(a_{36}=+0.364593046\) \(a_{37}=+1.828766350\) \(a_{38}=+2.384408386\) \(a_{39}=-0.392420106\) \(a_{40}=-0.003515264\)
\(a_{41}=-0.802686422\) \(a_{42}=+0.143180524\) \(a_{43}=+1.566453502\) \(a_{44}=-1.081298152\) \(a_{45}=+0.008635053\)
\(a_{46}=-2.014759343\) \(a_{47}=+0.839468619\) \(a_{48}=+0.518129337\) \(a_{49}=-0.970626325\) \(a_{50}=+1.446018639\)
\(a_{51}=+0.136102865\) \(a_{52}=+0.743432449\) \(a_{53}=+0.578614932\) \(a_{54}=+0.278473294\) \(a_{55}=-0.025609558\)
\(a_{56}=-0.023256845\) \(a_{57}=+0.951381231\) \(a_{58}=-0.659716783\) \(a_{59}=-0.107172629\) \(a_{60}=-0.016358944\)
\(a_{61}=-0.292893103\) \(a_{62}=-0.800375527\) \(a_{63}=+0.057129166\) \(a_{64}=-1.177939004\) \(a_{65}=+0.017607518\)
\(a_{66}=-0.825887004\) \(a_{67}=-1.779717629\) \(a_{68}=-0.257844298\) \(a_{69}=-0.803890908\) \(a_{70}=-0.006424374\)
\(a_{71}=+0.283183100\) \(a_{72}=-0.045232481\) \(a_{73}=+0.157260575\) \(a_{74}=-2.646206037\) \(a_{75}=+0.576962823\)
\(a_{76}=-1.802373701\) \(a_{77}=-0.169431816\) \(a_{78}=+0.567827844\) \(a_{79}=-0.153259398\) \(a_{80}=-0.023247972\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.161478970\) \(a_{83}=-0.870710125\) \(a_{84}=-0.108230122\) \(a_{85}=-0.006106806\)
\(a_{86}=-2.266642053\) \(a_{87}=-0.263227628\) \(a_{88}=+0.134149016\) \(a_{89}=+1.252031479\) \(a_{90}=-0.012494832\)
\(a_{91}=+0.116490636\) \(a_{92}=+1.522956082\) \(a_{93}=-0.319350602\) \(a_{94}=-1.214702430\) \(a_{95}=-0.042687573\)
\(a_{96}=-0.828072760\) \(a_{97}=-0.417750940\) \(a_{98}=+1.404486277\) \(a_{99}=-0.329529706\) \(a_{100}=-1.093045127\)

Showing 100 of 1228 available coefficients

Rows: Cols: