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: \( 21.0284013311 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.155719812\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.817217316\) \(a_{7}=+1.705157749\) \(a_{8}=+0.353553391\) \(a_{9}=+0.335688283\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.289702231\) \(a_{12}=+0.577859906\) \(a_{13}=+0.841152749\) \(a_{14}=+1.205728607\) \(a_{15}=+0.516853612\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.550280527\) \(a_{18}=+0.237367461\) \(a_{19}=+1.344448766\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.970684592\) \(a_{22}=-0.911957194\) \(a_{23}=-1.384664526\) \(a_{24}=+0.408608658\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.594784813\) \(a_{27}=-0.767758213\) \(a_{28}=+0.852578874\) \(a_{29}=+1.244944180\) \(a_{30}=+0.365470694\)
\(a_{31}=+1.198020906\) \(a_{32}=+0.176776695\) \(a_{33}=-1.490534420\) \(a_{34}=+0.389107092\) \(a_{35}=+0.762569728\)
\(a_{36}=+0.167844141\) \(a_{37}=+0.094708505\) \(a_{38}=+0.950668840\) \(a_{39}=+0.972136897\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.158378444\) \(a_{42}=+1.393484439\) \(a_{43}=+0.245851337\) \(a_{44}=-0.644851116\) \(a_{45}=+0.150124364\)
\(a_{46}=-0.979105676\) \(a_{47}=+0.276031677\) \(a_{48}=+0.288929953\) \(a_{49}=+1.907562949\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.635970106\) \(a_{52}=+0.420576375\) \(a_{53}=-1.023601862\) \(a_{54}=-0.542887038\) \(a_{55}=-0.576772372\)
\(a_{56}=+0.602864304\) \(a_{57}=+1.553806075\) \(a_{58}=+0.880308472\) \(a_{59}=+1.450819423\) \(a_{60}=+0.258426806\)
\(a_{61}=-1.010074140\) \(a_{62}=+0.847128707\) \(a_{63}=+0.572401477\) \(a_{64}=+0.125000000\) \(a_{65}=+0.376174945\)
\(a_{66}=-1.053966996\) \(a_{67}=-0.725647205\) \(a_{68}=+0.275140263\) \(a_{69}=-1.600284225\) \(a_{70}=+0.539218226\)
\(a_{71}=-1.287304282\) \(a_{72}=+0.118683731\) \(a_{73}=+0.514956958\) \(a_{74}=+0.066969026\) \(a_{75}=+0.231143962\)
\(a_{76}=+0.672224383\) \(a_{77}=-2.199145754\) \(a_{78}=+0.687404592\) \(a_{79}=+0.127817875\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.223001660\) \(a_{82}=-0.819097253\) \(a_{83}=+0.694691871\) \(a_{84}=+0.985342296\) \(a_{85}=+0.246092933\)
\(a_{86}=+0.173843147\) \(a_{87}=+1.438806653\) \(a_{88}=-0.455978597\) \(a_{89}=-1.714161246\) \(a_{90}=+0.106153956\)
\(a_{91}=+1.434298129\) \(a_{92}=-0.692332263\) \(a_{93}=+1.384576496\) \(a_{94}=+0.195183871\) \(a_{95}=+0.601255767\)
\(a_{96}=+0.204304329\) \(a_{97}=+0.712545594\) \(a_{98}=+1.348850697\) \(a_{99}=-0.432937927\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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