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: \( 30.0124030308 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.773665202\) \(a_{3}=+0.577350269\) \(a_{4}=-0.401442155\) \(a_{5}=-0.257361532\)
\(a_{6}=+0.446675813\) \(a_{7}=+0.164149758\) \(a_{8}=-1.084247028\) \(a_{9}=+0.333333333\) \(a_{10}=-0.199111662\)
\(a_{11}=+0.636935305\) \(a_{12}=-0.231772736\) \(a_{13}=-0.021506822\) \(a_{14}=+0.126996956\) \(a_{15}=-0.148587750\)
\(a_{16}=-0.437402042\) \(a_{17}=-1.159215780\) \(a_{18}=+0.257888401\) \(a_{19}=+0.638864743\) \(a_{20}=+0.103315768\)
\(a_{21}=+0.094771907\) \(a_{22}=+0.492774681\) \(a_{23}=+1.180630915\) \(a_{24}=-0.625990314\) \(a_{25}=-0.933765042\)
\(a_{26}=-0.016639080\) \(a_{27}=+0.192450090\) \(a_{28}=-0.065896633\) \(a_{29}=+0.953733957\) \(a_{30}=-0.114957172\)
\(a_{31}=+1.652578392\) \(a_{32}=+0.745844289\) \(a_{33}=+0.367734770\) \(a_{34}=-0.896844911\) \(a_{35}=-0.042245833\)
\(a_{36}=-0.133814052\) \(a_{37}=+0.461496622\) \(a_{38}=+0.494267421\) \(a_{39}=-0.012416970\) \(a_{40}=+0.279043476\)
\(a_{41}=+1.223927371\) \(a_{42}=+0.073321727\) \(a_{43}=-0.083482288\) \(a_{44}=-0.255692681\) \(a_{45}=-0.085787177\)
\(a_{46}=+0.913413056\) \(a_{47}=-1.190210859\) \(a_{48}=-0.252534187\) \(a_{49}=-0.973054857\) \(a_{50}=-0.722421520\)
\(a_{51}=-0.669273543\) \(a_{52}=+0.008633745\) \(a_{53}=+1.166425232\) \(a_{54}=+0.148891938\) \(a_{55}=-0.163922646\)
\(a_{56}=-0.177978887\) \(a_{57}=+0.368848732\) \(a_{58}=+0.737870775\) \(a_{59}=+0.039105682\) \(a_{60}=+0.059649386\)
\(a_{61}=+1.924208433\) \(a_{62}=+1.278542396\) \(a_{63}=+0.054716586\) \(a_{64}=+1.014435815\) \(a_{65}=+0.005535029\)
\(a_{66}=+0.284503595\) \(a_{67}=-0.123785981\) \(a_{68}=+0.465358080\) \(a_{69}=+0.681637577\) \(a_{70}=-0.032684131\)
\(a_{71}=+1.944917175\) \(a_{72}=-0.361415676\) \(a_{73}=+0.550420547\) \(a_{74}=+0.357043877\) \(a_{75}=-0.539109498\)
\(a_{76}=-0.256467239\) \(a_{77}=+0.104552776\) \(a_{78}=-0.009606577\) \(a_{79}=+0.390934840\) \(a_{80}=+0.112570460\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.946910017\) \(a_{83}=-0.666373206\) \(a_{84}=-0.038045439\) \(a_{85}=+0.298337549\)
\(a_{86}=-0.064587342\) \(a_{87}=+0.550638557\) \(a_{88}=-0.690595211\) \(a_{89}=-0.035323096\) \(a_{90}=-0.066370554\)
\(a_{91}=-0.003530340\) \(a_{92}=-0.473955019\) \(a_{93}=+0.954116579\) \(a_{94}=-0.920824725\) \(a_{95}=-0.164419209\)
\(a_{96}=+0.430613401\) \(a_{97}=+1.942540052\) \(a_{98}=-0.752818683\) \(a_{99}=+0.212311768\) \(a_{100}=+0.374852650\)

Showing 100 of 1228 available coefficients

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