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: \( 31.0493228289 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.956804208\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.383669525\) \(a_{7}=-0.148586845\) \(a_{8}=+0.353553391\) \(a_{9}=+2.829082707\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.565275638\) \(a_{12}=+0.978402104\) \(a_{13}=+0.558131310\) \(a_{14}=-0.105066766\) \(a_{15}=-0.875109445\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.383180556\) \(a_{18}=+2.000463567\) \(a_{19}=-1.177336147\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.290755363\) \(a_{22}=+0.399710237\) \(a_{23}=+1.820851461\) \(a_{24}=+0.691834762\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.394658434\) \(a_{27}=+3.579156738\) \(a_{28}=-0.074293422\) \(a_{29}=-0.449602152\) \(a_{30}=-0.618795823\)
\(a_{31}=-0.888143641\) \(a_{32}=+0.176776695\) \(a_{33}=+1.106133748\) \(a_{34}=+0.270949569\) \(a_{35}=+0.066450057\)
\(a_{36}=+1.414541354\) \(a_{37}=+1.449144299\) \(a_{38}=-0.832502373\) \(a_{39}=+1.092153695\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.094351302\) \(a_{42}=-0.205595089\) \(a_{43}=-1.906086713\) \(a_{44}=+0.282637819\) \(a_{45}=-1.265204249\)
\(a_{46}=+1.287536415\) \(a_{47}=+0.487304983\) \(a_{48}=+0.489201052\) \(a_{49}=-0.977921949\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.749809323\) \(a_{52}=+0.279065655\) \(a_{53}=-0.404097012\) \(a_{54}=+2.530846000\) \(a_{55}=-0.252798951\)
\(a_{56}=-0.052533383\) \(a_{57}=-2.303816326\) \(a_{58}=-0.317916731\) \(a_{59}=-0.032287870\) \(a_{60}=-0.437554723\)
\(a_{61}=+0.110797673\) \(a_{62}=-0.628012391\) \(a_{63}=-0.420364473\) \(a_{64}=+0.125000000\) \(a_{65}=-0.249603910\)
\(a_{66}=+0.782154674\) \(a_{67}=-0.300971488\) \(a_{68}=+0.191590278\) \(a_{69}=+3.563049800\) \(a_{70}=+0.046987286\)
\(a_{71}=-0.091730476\) \(a_{72}=+1.000231783\) \(a_{73}=+1.050962235\) \(a_{74}=+1.024699760\) \(a_{75}=+0.391360842\)
\(a_{76}=-0.588668073\) \(a_{77}=-0.083992524\) \(a_{78}=+0.772269284\) \(a_{79}=-0.424858854\) \(a_{80}=-0.111803399\)
\(a_{81}=+4.174626257\) \(a_{82}=+0.773823227\) \(a_{83}=+1.245996519\) \(a_{84}=-0.145377682\) \(a_{85}=-0.171363554\)
\(a_{86}=-1.347806840\) \(a_{87}=-0.879783383\) \(a_{88}=+0.199855119\) \(a_{89}=+1.777776851\) \(a_{90}=-0.894634504\)
\(a_{91}=-0.082930970\) \(a_{92}=+0.910425730\) \(a_{93}=-1.737923213\) \(a_{94}=+0.344576658\) \(a_{95}=+0.526520731\)
\(a_{96}=+0.345917381\) \(a_{97}=-0.318924925\) \(a_{98}=-0.691495242\) \(a_{99}=+1.599211534\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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