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: \( 20.8896134485 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.557028041\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.393878305\) \(a_{7}=-0.158247852\) \(a_{8}=+0.353553391\) \(a_{9}=-0.689719762\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.975923395\) \(a_{12}=+0.278514020\) \(a_{13}=-0.585915331\) \(a_{14}=-0.111898129\) \(a_{15}=-0.249110513\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.581182712\) \(a_{18}=-0.487705521\) \(a_{19}=-0.133886473\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.088148491\) \(a_{22}=+0.690082051\) \(a_{23}=+0.324524379\) \(a_{24}=+0.196939152\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.414304703\) \(a_{27}=-0.941221288\) \(a_{28}=-0.079123926\) \(a_{29}=-0.706512982\) \(a_{30}=-0.176147733\)
\(a_{31}=-0.441327097\) \(a_{32}=+0.176776695\) \(a_{33}=+0.543616697\) \(a_{34}=+0.410958237\) \(a_{35}=+0.070770591\)
\(a_{36}=-0.344859881\) \(a_{37}=-1.186102551\) \(a_{38}=-0.094672033\) \(a_{39}=-0.326371269\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.253706331\) \(a_{42}=-0.062330396\) \(a_{43}=-0.053288774\) \(a_{44}=+0.487961697\) \(a_{45}=+0.308452055\)
\(a_{46}=+0.229473389\) \(a_{47}=-1.748446177\) \(a_{48}=+0.139257010\) \(a_{49}=-0.974957617\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.323735068\) \(a_{52}=-0.292957665\) \(a_{53}=+0.118127071\) \(a_{54}=-0.665543956\) \(a_{55}=-0.436446210\)
\(a_{56}=-0.055949065\) \(a_{57}=-0.074578520\) \(a_{58}=-0.499580121\) \(a_{59}=-1.411033304\) \(a_{60}=-0.124555256\)
\(a_{61}=-0.916945940\) \(a_{62}=-0.312065383\) \(a_{63}=+0.109146671\) \(a_{64}=+0.125000000\) \(a_{65}=+0.262029302\)
\(a_{66}=+0.384395053\) \(a_{67}=+1.158459826\) \(a_{68}=+0.290591356\) \(a_{69}=+0.180769179\) \(a_{70}=+0.050042365\)
\(a_{71}=+1.238855566\) \(a_{72}=-0.243852760\) \(a_{73}=+0.293329927\) \(a_{74}=-0.838701157\) \(a_{75}=+0.111405608\)
\(a_{76}=-0.066943236\) \(a_{77}=-0.154437781\) \(a_{78}=-0.230779337\) \(a_{79}=+1.503058697\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.165433111\) \(a_{82}=+0.179397467\) \(a_{83}=-0.582735425\) \(a_{84}=-0.044074245\) \(a_{85}=-0.259912810\)
\(a_{86}=-0.037680854\) \(a_{87}=-0.393547542\) \(a_{88}=+0.345041025\) \(a_{89}=-1.739484216\) \(a_{90}=+0.218108539\)
\(a_{91}=+0.092719843\) \(a_{92}=+0.162262189\) \(a_{93}=-0.245831568\) \(a_{94}=-1.236338148\) \(a_{95}=+0.059875851\)
\(a_{96}=+0.098469576\) \(a_{97}=-1.806097815\) \(a_{98}=-0.689399143\) \(a_{99}=-0.673113651\) \(a_{100}=+0.099975586\)

Showing 100 of 205 available coefficients

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