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: \( 30.7377364898 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.090857686\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.771352867\) \(a_{7}=-0.249888696\) \(a_{8}=+0.353553391\) \(a_{9}=+0.189970491\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.370451129\) \(a_{12}=+0.545428843\) \(a_{13}=-1.666927688\) \(a_{14}=-0.176697992\) \(a_{15}=+0.487846388\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.028574385\) \(a_{18}=+0.134329422\) \(a_{19}=+0.963102401\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.272593005\) \(a_{22}=-0.261948505\) \(a_{23}=+0.000386587\) \(a_{24}=+0.385676434\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.178695872\) \(a_{27}=-0.883626916\) \(a_{28}=-0.124944348\) \(a_{29}=+1.566458956\) \(a_{30}=+0.344959489\)
\(a_{31}=-0.685375923\) \(a_{32}=+0.176776695\) \(a_{33}=-0.404109461\) \(a_{34}=-0.020205141\) \(a_{35}=-0.111753622\)
\(a_{36}=+0.094985245\) \(a_{37}=-0.808207077\) \(a_{38}=+0.681016239\) \(a_{39}=-1.818380880\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.409648553\) \(a_{42}=-0.192752362\) \(a_{43}=+0.250830201\) \(a_{44}=-0.185225564\) \(a_{45}=+0.084957386\)
\(a_{46}=+0.000273358\) \(a_{47}=-1.018319725\) \(a_{48}=+0.272714421\) \(a_{49}=-0.937555640\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.031170587\) \(a_{52}=-0.833463844\) \(a_{53}=-0.328182634\) \(a_{54}=-0.624818584\) \(a_{55}=-0.165670781\)
\(a_{56}=-0.088348996\) \(a_{57}=+1.050607657\) \(a_{58}=+1.107653750\) \(a_{59}=-0.776819237\) \(a_{60}=+0.243923194\)
\(a_{61}=+0.997908312\) \(a_{62}=-0.484633963\) \(a_{63}=-0.047471478\) \(a_{64}=+0.125000000\) \(a_{65}=-0.745472725\)
\(a_{66}=-0.285748540\) \(a_{67}=-1.528174049\) \(a_{68}=-0.014287192\) \(a_{69}=+0.000421711\) \(a_{70}=-0.079021744\)
\(a_{71}=-1.700950552\) \(a_{72}=+0.067164711\) \(a_{73}=+0.151556585\) \(a_{74}=-0.571488704\) \(a_{75}=+0.218171537\)
\(a_{76}=+0.481551201\) \(a_{77}=+0.092571550\) \(a_{78}=-1.285789451\) \(a_{79}=-1.586425278\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.153881703\) \(a_{82}=+0.289665270\) \(a_{83}=-0.412027651\) \(a_{84}=-0.136296502\) \(a_{85}=-0.012778853\)
\(a_{86}=+0.177363736\) \(a_{87}=+1.708783791\) \(a_{88}=-0.130974253\) \(a_{89}=+0.058900395\) \(a_{90}=+0.060073944\)
\(a_{91}=+0.416546387\) \(a_{92}=+0.000193293\) \(a_{93}=-0.747647593\) \(a_{94}=-0.720060783\) \(a_{95}=+0.430712488\)
\(a_{96}=+0.192838217\) \(a_{97}=+0.546166550\) \(a_{98}=-0.662951950\) \(a_{99}=-0.070374783\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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