Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 19.7788534901 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.073397522\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.759006667\) \(a_{7}=+0.529490153\) \(a_{8}=+0.353553391\) \(a_{9}=+0.152182241\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.934861799\) \(a_{12}=-0.536698761\) \(a_{13}=+0.382560700\) \(a_{14}=+0.374406078\) \(a_{15}=-0.480037965\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.532679672\) \(a_{18}=+0.107609095\) \(a_{19}=-0.533430568\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.568353418\) \(a_{22}=-0.661047117\) \(a_{23}=-1.165883011\) \(a_{24}=-0.379503333\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.270511265\) \(a_{27}=+0.910045482\) \(a_{28}=+0.264745076\) \(a_{29}=+0.914051599\) \(a_{30}=-0.339438101\)
\(a_{31}=+0.406820534\) \(a_{32}=+0.176776695\) \(a_{33}=+1.003478339\) \(a_{34}=+0.376661408\) \(a_{35}=+0.236795195\)
\(a_{36}=+0.076091121\) \(a_{37}=-0.233164341\) \(a_{38}=-0.377192372\) \(a_{39}=-0.410639707\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.105221046\) \(a_{42}=-0.401886556\) \(a_{43}=+0.850765822\) \(a_{44}=-0.467430899\) \(a_{45}=+0.068057967\)
\(a_{46}=-0.824403783\) \(a_{47}=-1.881634076\) \(a_{48}=-0.268349381\) \(a_{49}=-0.719640178\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.571777040\) \(a_{52}=+0.191280350\) \(a_{53}=-1.032786143\) \(a_{54}=+0.643499331\) \(a_{55}=-0.418082906\)
\(a_{56}=+0.187203039\) \(a_{57}=+0.572583050\) \(a_{58}=+0.646332084\) \(a_{59}=-0.572102727\) \(a_{60}=-0.240018983\)
\(a_{61}=+0.630634198\) \(a_{62}=+0.287665559\) \(a_{63}=+0.080578998\) \(a_{64}=+0.125000000\) \(a_{65}=+0.171086346\)
\(a_{66}=+0.709566338\) \(a_{67}=-1.566592077\) \(a_{68}=+0.266339836\) \(a_{69}=+1.251455935\) \(a_{70}=+0.167439488\)
\(a_{71}=+1.426421607\) \(a_{72}=+0.053804547\) \(a_{73}=-0.589953645\) \(a_{74}=-0.164872086\) \(a_{75}=-0.214679504\)
\(a_{76}=-0.266715284\) \(a_{77}=-0.495000117\) \(a_{78}=-0.290366122\) \(a_{79}=-1.695548107\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.129022807\) \(a_{82}=+0.781509297\) \(a_{83}=-1.675995982\) \(a_{84}=-0.284176709\) \(a_{85}=+0.238221591\)
\(a_{86}=+0.601582282\) \(a_{87}=-0.981140722\) \(a_{88}=-0.330523559\) \(a_{89}=+0.301826766\) \(a_{90}=+0.048124250\)
\(a_{91}=+0.202562123\) \(a_{92}=-0.582941505\) \(a_{93}=-0.436680154\) \(a_{94}=-1.330516215\) \(a_{95}=-0.238557402\)
\(a_{96}=-0.189751667\) \(a_{97}=-1.534682420\) \(a_{98}=-0.508862450\) \(a_{99}=-0.142269363\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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