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: \( 15.6281191067 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.739669760\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.230132284\) \(a_{7}=+0.061599084\) \(a_{8}=+0.353553391\) \(a_{9}=+2.026450875\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.698193210\) \(a_{12}=+0.869834880\) \(a_{13}=-0.083660938\) \(a_{14}=+0.043557130\) \(a_{15}=+0.778003968\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.538321743\) \(a_{18}=+1.432917155\) \(a_{19}=-0.347323741\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.107162063\) \(a_{22}=-0.493697154\) \(a_{23}=+1.421168566\) \(a_{24}=+0.615066142\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.059157217\) \(a_{27}=+1.785685547\) \(a_{28}=+0.030799542\) \(a_{29}=+1.933741496\) \(a_{30}=+0.550131882\)
\(a_{31}=-1.810051728\) \(a_{32}=+0.176776695\) \(a_{33}=-1.214625615\) \(a_{34}=+1.087757736\) \(a_{35}=+0.027547948\)
\(a_{36}=+1.013225437\) \(a_{37}=-1.017280646\) \(a_{38}=-0.245594973\) \(a_{39}=-0.145542405\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.160248328\) \(a_{42}=+0.075775021\) \(a_{43}=-0.188879645\) \(a_{44}=-0.349096605\) \(a_{45}=+0.906256382\)
\(a_{46}=+1.004917930\) \(a_{47}=+0.703645608\) \(a_{48}=+0.434917440\) \(a_{49}=-0.996205553\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.676171819\) \(a_{52}=-0.041830469\) \(a_{53}=-0.466029183\) \(a_{54}=+1.262670359\) \(a_{55}=-0.312241496\)
\(a_{56}=+0.021778565\) \(a_{57}=-0.604228610\) \(a_{58}=+1.367361725\) \(a_{59}=+1.324851021\) \(a_{60}=+0.389001984\)
\(a_{61}=+0.793453420\) \(a_{62}=-1.279899851\) \(a_{63}=+0.124827517\) \(a_{64}=+0.125000000\) \(a_{65}=-0.037414309\)
\(a_{66}=-0.858870009\) \(a_{67}=+0.846186364\) \(a_{68}=+0.769160872\) \(a_{69}=+2.472363978\) \(a_{70}=+0.019479341\)
\(a_{71}=+0.120773155\) \(a_{72}=+0.716458578\) \(a_{73}=-1.125710106\) \(a_{74}=-0.719326043\) \(a_{75}=+0.347933952\)
\(a_{76}=-0.173661871\) \(a_{77}=-0.043008062\) \(a_{78}=-0.102914021\) \(a_{79}=-1.797416059\) \(a_{80}=+0.111803399\)
\(a_{81}=+1.080052272\) \(a_{82}=-0.820419461\) \(a_{83}=+0.433314921\) \(a_{84}=+0.053581031\) \(a_{85}=+0.687958398\)
\(a_{86}=-0.133558078\) \(a_{87}=+3.364071605\) \(a_{88}=-0.246848577\) \(a_{89}=-1.113134788\) \(a_{90}=+0.640820033\)
\(a_{91}=-0.005153436\) \(a_{92}=+0.710584283\) \(a_{93}=-3.148892255\) \(a_{94}=+0.497552581\) \(a_{95}=-0.155327899\)
\(a_{96}=+0.307533071\) \(a_{97}=+0.313340346\) \(a_{98}=-0.704423702\) \(a_{99}=-1.414854252\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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