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: \( 26.8954926454 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.737771249\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.228789834\) \(a_{7}=+1.943660614\) \(a_{8}=+0.353553391\) \(a_{9}=+2.019848912\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.934475317\) \(a_{12}=-0.868885624\) \(a_{13}=+0.488303659\) \(a_{14}=+1.374375600\) \(a_{15}=-0.777154928\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.515430386\) \(a_{18}=+1.428248863\) \(a_{19}=-1.027271655\) \(a_{20}=+0.223606798\)
\(a_{21}=-3.377637531\) \(a_{22}=-0.660773834\) \(a_{23}=-0.551336383\) \(a_{24}=-0.614394917\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.345282828\) \(a_{27}=-1.772264118\) \(a_{28}=+0.971830307\) \(a_{29}=+0.954052983\) \(a_{30}=-0.549531520\)
\(a_{31}=-1.422045597\) \(a_{32}=+0.176776695\) \(a_{33}=+1.623904339\) \(a_{34}=-0.364464321\) \(a_{35}=+0.869231451\)
\(a_{36}=+1.009924456\) \(a_{37}=-0.889078110\) \(a_{38}=-0.726390753\) \(a_{39}=-0.848560059\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.448300856\) \(a_{42}=-2.388350403\) \(a_{43}=-0.290362827\) \(a_{44}=-0.467237659\) \(a_{45}=+0.903303894\)
\(a_{46}=-0.389853695\) \(a_{47}=-1.976156851\) \(a_{48}=-0.434442812\) \(a_{49}=+2.777816581\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.895700106\) \(a_{52}=+0.244151829\) \(a_{53}=+0.780714751\) \(a_{54}=-1.253179976\) \(a_{55}=-0.417910067\)
\(a_{56}=+0.687187800\) \(a_{57}=+1.785163147\) \(a_{58}=+0.674617334\) \(a_{59}=+0.742739682\) \(a_{60}=-0.388577464\)
\(a_{61}=+0.102558439\) \(a_{62}=-1.005538085\) \(a_{63}=+3.925900776\) \(a_{64}=+0.125000000\) \(a_{65}=+0.218376035\)
\(a_{66}=+1.148273770\) \(a_{67}=-0.156398667\) \(a_{68}=-0.257715193\) \(a_{69}=+0.958096515\) \(a_{70}=+0.614639454\)
\(a_{71}=-0.454158257\) \(a_{72}=+0.714124431\) \(a_{73}=-0.878424569\) \(a_{74}=-0.628673161\) \(a_{75}=-0.347554250\)
\(a_{76}=-0.513635828\) \(a_{77}=-1.816302869\) \(a_{78}=-0.600022572\) \(a_{79}=+0.278608427\) \(a_{80}=+0.111803399\)
\(a_{81}=+1.059940716\) \(a_{82}=+0.316996575\) \(a_{83}=+1.692529942\) \(a_{84}=-1.688818766\) \(a_{85}=-0.230507476\)
\(a_{86}=-0.205317524\) \(a_{87}=-1.657925843\) \(a_{88}=-0.330386917\) \(a_{89}=-1.065145231\) \(a_{90}=+0.638732309\)
\(a_{91}=+0.949096589\) \(a_{92}=-0.275668191\) \(a_{93}=+2.471189952\) \(a_{94}=-1.397353910\) \(a_{95}=-0.459409850\)
\(a_{96}=-0.307197459\) \(a_{97}=+0.286218346\) \(a_{98}=+1.964212941\) \(a_{99}=-1.887498953\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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