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: \( 7.56348983462 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.339300157\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.239921442\) \(a_{7}=+0.139947614\) \(a_{8}=+0.353553391\) \(a_{9}=-0.884875404\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.354417236\) \(a_{12}=-0.169650078\) \(a_{13}=-1.151271487\) \(a_{14}=+0.098957907\) \(a_{15}=+0.151739643\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.631270843\) \(a_{18}=-0.625701398\) \(a_{19}=+0.028302559\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.047484247\) \(a_{22}=-0.957717612\) \(a_{23}=+0.918653886\) \(a_{24}=-0.119960721\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.814071876\) \(a_{27}=+0.639538520\) \(a_{28}=+0.069973807\) \(a_{29}=+1.101272764\) \(a_{30}=+0.107296131\)
\(a_{31}=-1.534506156\) \(a_{32}=+0.176776695\) \(a_{33}=+0.459553980\) \(a_{34}=-0.446375894\) \(a_{35}=-0.062586476\)
\(a_{36}=-0.442437702\) \(a_{37}=-0.544979648\) \(a_{38}=+0.020012932\) \(a_{39}=+0.390626596\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.587445229\) \(a_{42}=-0.033576433\) \(a_{43}=+1.653581446\) \(a_{44}=-0.677208618\) \(a_{45}=+0.395728311\)
\(a_{46}=+0.649586392\) \(a_{47}=-0.781004251\) \(a_{48}=-0.084825039\) \(a_{49}=-0.980414665\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.214190296\) \(a_{52}=-0.575635744\) \(a_{53}=-1.840894208\) \(a_{54}=+0.452222024\) \(a_{55}=+0.605713802\)
\(a_{56}=+0.049478953\) \(a_{57}=-0.009603063\) \(a_{58}=+0.778717439\) \(a_{59}=+0.119196638\) \(a_{60}=+0.075869822\)
\(a_{61}=+1.875984822\) \(a_{62}=-1.085059708\) \(a_{63}=-0.123836201\) \(a_{64}=+0.125000000\) \(a_{65}=+0.514864261\)
\(a_{66}=+0.324953736\) \(a_{67}=-1.212148666\) \(a_{68}=-0.315635422\) \(a_{69}=-0.311699407\) \(a_{70}=-0.044255321\)
\(a_{71}=+0.460179576\) \(a_{72}=-0.312850699\) \(a_{73}=+0.519610781\) \(a_{74}=-0.385358805\) \(a_{75}=-0.067860031\)
\(a_{76}=+0.014151280\) \(a_{77}=-0.189547460\) \(a_{78}=+0.276214715\) \(a_{79}=-1.576740100\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.667879884\) \(a_{82}=+0.415386505\) \(a_{83}=+0.123591990\) \(a_{84}=-0.023742124\) \(a_{85}=+0.282312904\)
\(a_{86}=+1.169258654\) \(a_{87}=-0.373662021\) \(a_{88}=-0.478858806\) \(a_{89}=+0.341120300\) \(a_{90}=+0.279822172\)
\(a_{91}=-0.161117697\) \(a_{92}=+0.459326943\) \(a_{93}=+0.520658179\) \(a_{94}=-0.552253402\) \(a_{95}=-0.012657289\)
\(a_{96}=-0.059980360\) \(a_{97}=-1.000589000\) \(a_{98}=-0.693257858\) \(a_{99}=+1.198490498\) \(a_{100}=+0.099975586\)

Showing 100 of 136 available coefficients

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