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: \( 18.570584434 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.201736403\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.849755960\) \(a_{7}=-1.714563336\) \(a_{8}=-0.353553391\) \(a_{9}=+0.444170383\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.649833072\) \(a_{12}=-0.600868202\) \(a_{13}=+0.161306127\) \(a_{14}=+1.212379362\) \(a_{15}=+0.537432858\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.177537823\) \(a_{18}=-0.314075890\) \(a_{19}=-1.469469653\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.060453177\) \(a_{22}=-0.459501372\) \(a_{23}=+0.340103671\) \(a_{24}=+0.424877980\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.114060656\) \(a_{27}=+0.667960685\) \(a_{28}=-0.857281668\) \(a_{29}=+0.500773890\) \(a_{30}=-0.380022418\)
\(a_{31}=+1.903520188\) \(a_{32}=-0.176776695\) \(a_{33}=-0.780928058\) \(a_{34}=+0.832644979\) \(a_{35}=+0.766776034\)
\(a_{36}=+0.222085192\) \(a_{37}=+1.096648315\) \(a_{38}=+1.039071956\) \(a_{39}=-0.193847445\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.101068202\) \(a_{42}=-1.456960414\) \(a_{43}=-0.272612609\) \(a_{44}=+0.324916536\) \(a_{45}=-0.198639034\)
\(a_{46}=-0.240489612\) \(a_{47}=+0.819045243\) \(a_{48}=-0.300434101\) \(a_{49}=+1.939727434\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.415090068\) \(a_{52}=+0.080653063\) \(a_{53}=-1.088177599\) \(a_{54}=-0.472319530\) \(a_{55}=-0.290614184\)
\(a_{56}=+0.606189681\) \(a_{57}=+1.765915175\) \(a_{58}=-0.354100613\) \(a_{59}=+0.272841684\) \(a_{60}=+0.268716429\)
\(a_{61}=+1.736415638\) \(a_{62}=-1.345992033\) \(a_{63}=-0.761558254\) \(a_{64}=+0.125000000\) \(a_{65}=-0.072138293\)
\(a_{66}=+0.552199526\) \(a_{67}=-0.913924909\) \(a_{68}=-0.588768911\) \(a_{69}=-0.408714962\) \(a_{70}=-0.542192534\)
\(a_{71}=+1.199314281\) \(a_{72}=-0.157037945\) \(a_{73}=-1.261074071\) \(a_{74}=-0.775447460\) \(a_{75}=-0.240347281\)
\(a_{76}=-0.734734826\) \(a_{77}=-1.114179959\) \(a_{78}=+0.137070843\) \(a_{79}=-0.769354922\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.246883054\) \(a_{82}=-0.071466011\) \(a_{83}=-0.027637895\) \(a_{84}=+1.030226589\) \(a_{85}=+0.526610923\)
\(a_{86}=+0.192766224\) \(a_{87}=-0.601798213\) \(a_{88}=-0.229750686\) \(a_{89}=-1.754072635\) \(a_{90}=+0.140459008\)
\(a_{91}=-0.276569571\) \(a_{92}=+0.170051835\) \(a_{93}=-2.287529505\) \(a_{94}=-0.579152445\) \(a_{95}=+0.657166807\)
\(a_{96}=+0.212438990\) \(a_{97}=+0.858141132\) \(a_{98}=-1.371594422\) \(a_{99}=+0.288636603\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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