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: \( 12.9433745145 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.424107352\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.006995966\) \(a_{7}=-0.659730656\) \(a_{8}=+0.353553391\) \(a_{9}=+1.028081751\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.379756391\) \(a_{12}=-0.712053676\) \(a_{13}=-1.181514907\) \(a_{14}=-0.466500020\) \(a_{15}=+0.636880169\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.424027551\) \(a_{18}=+0.726963578\) \(a_{19}=-0.572099021\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.939527277\) \(a_{22}=-0.975635100\) \(a_{23}=+0.910339734\) \(a_{24}=-0.503497983\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.835457203\) \(a_{27}=-0.039991428\) \(a_{28}=-0.329865328\) \(a_{29}=-0.508591217\) \(a_{30}=+0.450342287\)
\(a_{31}=+1.585752412\) \(a_{32}=+0.176776695\) \(a_{33}=+1.964921221\) \(a_{34}=+0.299832757\) \(a_{35}=+0.295040519\)
\(a_{36}=+0.514040875\) \(a_{37}=-1.782397877\) \(a_{38}=-0.404535097\) \(a_{39}=+1.682604066\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.232120904\) \(a_{42}=+0.664346109\) \(a_{43}=+1.358058346\) \(a_{44}=-0.689878196\) \(a_{45}=-0.459772136\)
\(a_{46}=+0.643707399\) \(a_{47}=+1.590786783\) \(a_{48}=-0.356026838\) \(a_{49}=-0.564755462\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.603860753\) \(a_{52}=-0.590757454\) \(a_{53}=+1.257092683\) \(a_{54}=-0.028278210\) \(a_{55}=+0.617045817\)
\(a_{56}=-0.233250010\) \(a_{57}=+0.814730422\) \(a_{58}=-0.359628298\) \(a_{59}=-1.792294083\) \(a_{60}=+0.318440085\)
\(a_{61}=-0.015434112\) \(a_{62}=+1.121296284\) \(a_{63}=-0.678257048\) \(a_{64}=+0.125000000\) \(a_{65}=+0.528389530\)
\(a_{66}=+1.389409120\) \(a_{67}=+0.521040716\) \(a_{68}=+0.212013775\) \(a_{69}=-1.296421508\) \(a_{70}=+0.208625151\)
\(a_{71}=-0.695454934\) \(a_{72}=+0.363481789\) \(a_{73}=-0.820935381\) \(a_{74}=-1.260345626\) \(a_{75}=-0.284821470\)
\(a_{76}=-0.286049510\) \(a_{77}=+0.910267590\) \(a_{78}=+1.189780745\) \(a_{79}=+0.544755599\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.971129663\) \(a_{82}=+0.871241047\) \(a_{83}=-1.126419785\) \(a_{84}=+0.469763639\) \(a_{85}=-0.189630886\)
\(a_{86}=+0.960292266\) \(a_{87}=+0.724288484\) \(a_{88}=-0.487817550\) \(a_{89}=-0.006049447\) \(a_{90}=-0.325107995\)
\(a_{91}=+0.779481622\) \(a_{92}=+0.455169867\) \(a_{93}=-2.258281655\) \(a_{94}=+1.124856122\) \(a_{95}=+0.255850460\)
\(a_{96}=-0.251748991\) \(a_{97}=+0.444692196\) \(a_{98}=-0.399342417\) \(a_{99}=-1.418502353\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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