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: \( 30.9231048721 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.825666909\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.583834670\) \(a_{7}=+1.261123726\) \(a_{8}=-0.353553391\) \(a_{9}=-0.318274156\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.915184925\) \(a_{12}=-0.412833454\) \(a_{13}=+1.580268516\) \(a_{14}=-0.891749138\) \(a_{15}=+0.369249467\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.046050534\) \(a_{18}=+0.225053814\) \(a_{19}=-1.616433019\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.041268128\) \(a_{22}=-1.354240248\) \(a_{23}=+0.364596734\) \(a_{24}=+0.291917335\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.117418583\) \(a_{27}=+1.088455347\) \(a_{28}=+0.630561863\) \(a_{29}=-0.372992250\) \(a_{30}=-0.261098802\)
\(a_{31}=+0.170347076\) \(a_{32}=-0.176776695\) \(a_{33}=-1.581304817\) \(a_{34}=+0.032562645\) \(a_{35}=-0.563991676\)
\(a_{36}=-0.159137078\) \(a_{37}=-1.236017136\) \(a_{38}=+1.142990749\) \(a_{39}=-1.304775420\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.080949648\) \(a_{42}=+0.736287754\) \(a_{43}=-0.088811938\) \(a_{44}=+0.957592463\) \(a_{45}=+0.142336530\)
\(a_{46}=-0.257808823\) \(a_{47}=+0.310873214\) \(a_{48}=-0.206416727\) \(a_{49}=+0.590433051\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.038022402\) \(a_{52}=+0.790134258\) \(a_{53}=-0.515769232\) \(a_{54}=-0.769654157\) \(a_{55}=-0.856496736\)
\(a_{56}=-0.445874569\) \(a_{57}=+1.334635254\) \(a_{58}=+0.263745349\) \(a_{59}=-1.358726478\) \(a_{60}=+0.184624733\)
\(a_{61}=-0.842680565\) \(a_{62}=-0.120453573\) \(a_{63}=-0.401383089\) \(a_{64}=+0.125000000\) \(a_{65}=-0.706717565\)
\(a_{66}=+1.118151359\) \(a_{67}=-1.251435933\) \(a_{68}=-0.023025267\) \(a_{69}=-0.301035458\) \(a_{70}=+0.398802338\)
\(a_{71}=+1.451216585\) \(a_{72}=+0.112526907\) \(a_{73}=+1.695098907\) \(a_{74}=+0.873996099\) \(a_{75}=-0.165133382\)
\(a_{76}=-0.808216510\) \(a_{77}=+2.415285148\) \(a_{78}=+0.922615548\) \(a_{79}=-1.491564877\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.580427406\) \(a_{82}=+0.764346826\) \(a_{83}=-0.520191695\) \(a_{84}=-0.520634064\) \(a_{85}=+0.020594425\)
\(a_{86}=+0.062799524\) \(a_{87}=+0.307967358\) \(a_{88}=-0.677120124\) \(a_{89}=-1.215279024\) \(a_{90}=-0.100647125\)
\(a_{91}=+1.992914118\) \(a_{92}=+0.182298367\) \(a_{93}=-0.140649944\) \(a_{94}=-0.219820557\) \(a_{95}=+0.722890822\)
\(a_{96}=+0.145958668\) \(a_{97}=+0.221469225\) \(a_{98}=-0.417499214\) \(a_{99}=-0.609553865\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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