Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 25.8810477463 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.453684226\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.320803193\) \(a_{7}=+0.710689116\) \(a_{8}=-0.353553391\) \(a_{9}=-0.794170623\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.826091742\) \(a_{12}=+0.226842113\) \(a_{13}=-1.296446399\) \(a_{14}=-0.502533093\) \(a_{15}=+0.202893754\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.172202543\) \(a_{18}=+0.561563433\) \(a_{19}=+0.167607010\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.322428442\) \(a_{22}=-1.291241854\) \(a_{23}=+0.336240411\) \(a_{24}=-0.160401596\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.916726040\) \(a_{27}=-0.813986911\) \(a_{28}=+0.355344558\) \(a_{29}=+0.196753060\) \(a_{30}=-0.143467549\)
\(a_{31}=-1.360050448\) \(a_{32}=-0.176776695\) \(a_{33}=+0.828469019\) \(a_{34}=+0.121765586\) \(a_{35}=+0.317829835\)
\(a_{36}=-0.397085311\) \(a_{37}=-0.629859642\) \(a_{38}=-0.118516053\) \(a_{39}=-0.588177281\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.061290099\) \(a_{42}=-0.227991338\) \(a_{43}=+1.167745819\) \(a_{44}=+0.913045871\) \(a_{45}=-0.355163900\)
\(a_{46}=-0.237757874\) \(a_{47}=-0.520924746\) \(a_{48}=+0.113421057\) \(a_{49}=-0.494920981\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.078125577\) \(a_{52}=-0.648223199\) \(a_{53}=-1.137523222\) \(a_{54}=+0.575575665\) \(a_{55}=+0.816653054\)
\(a_{56}=-0.251266547\) \(a_{57}=+0.076040657\) \(a_{58}=-0.139125423\) \(a_{59}=-1.665982015\) \(a_{60}=+0.101446877\)
\(a_{61}=-0.383671068\) \(a_{62}=+0.961700894\) \(a_{63}=-0.564408418\) \(a_{64}=+0.125000000\) \(a_{65}=-0.579788455\)
\(a_{66}=-0.585816062\) \(a_{67}=+1.720089468\) \(a_{68}=-0.086101271\) \(a_{69}=+0.152546971\) \(a_{70}=-0.224739631\)
\(a_{71}=-1.460089291\) \(a_{72}=+0.280781716\) \(a_{73}=-0.132716663\) \(a_{74}=+0.445378024\) \(a_{75}=+0.090736845\)
\(a_{76}=+0.083803505\) \(a_{77}=+1.297783526\) \(a_{78}=+0.415904144\) \(a_{79}=+1.482102520\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.424877601\) \(a_{82}=+0.750445426\) \(a_{83}=+0.932031663\) \(a_{84}=+0.161214221\) \(a_{85}=-0.077011318\)
\(a_{86}=-0.825720987\) \(a_{87}=+0.089263760\) \(a_{88}=-0.645620927\) \(a_{89}=+0.883772177\) \(a_{90}=+0.251138802\)
\(a_{91}=-0.921370345\) \(a_{92}=+0.168120205\) \(a_{93}=-0.617033435\) \(a_{94}=+0.368349421\) \(a_{95}=+0.074956133\)
\(a_{96}=-0.080200798\) \(a_{97}=+0.440702059\) \(a_{98}=+0.349961982\) \(a_{99}=-1.450228416\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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