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: \( 31.4294214363 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.413790635\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.292594164\) \(a_{7}=+1.456634463\) \(a_{8}=-0.353553391\) \(a_{9}=-0.828777310\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.559858664\) \(a_{12}=-0.206895318\) \(a_{13}=-1.871911143\) \(a_{14}=-1.029996106\) \(a_{15}=-0.185052798\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.400401726\) \(a_{18}=+0.586034056\) \(a_{19}=+0.960183288\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.602741700\) \(a_{22}=-0.395879858\) \(a_{23}=+0.550588725\) \(a_{24}=+0.146297082\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.323641063\) \(a_{27}=+0.756730925\) \(a_{28}=+0.728317231\) \(a_{29}=-1.086533276\) \(a_{30}=+0.130852088\)
\(a_{31}=-0.143068738\) \(a_{32}=-0.176776695\) \(a_{33}=-0.231664273\) \(a_{34}=-0.990233557\) \(a_{35}=+0.651426735\)
\(a_{36}=-0.414388655\) \(a_{37}=-1.069202882\) \(a_{38}=-0.678952114\) \(a_{39}=+0.774579301\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.674817877\) \(a_{42}=+0.426202743\) \(a_{43}=-1.021658407\) \(a_{44}=+0.279929332\) \(a_{45}=-0.370640481\)
\(a_{46}=-0.389325021\) \(a_{47}=+0.083660071\) \(a_{48}=-0.103447659\) \(a_{49}=+1.121783957\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.579473120\) \(a_{52}=-0.935955572\) \(a_{53}=+0.207274287\) \(a_{54}=-0.535089569\) \(a_{55}=+0.250376406\)
\(a_{56}=-0.514998053\) \(a_{57}=-0.397314853\) \(a_{58}=+0.768295048\) \(a_{59}=-1.213948455\) \(a_{60}=-0.092526399\)
\(a_{61}=+1.034413333\) \(a_{62}=+0.101164875\) \(a_{63}=-1.207225591\) \(a_{64}=+0.125000000\) \(a_{65}=-0.837144113\)
\(a_{66}=+0.163811378\) \(a_{67}=-1.304138066\) \(a_{68}=+0.700200863\) \(a_{69}=-0.227828458\) \(a_{70}=-0.460628262\)
\(a_{71}=+0.455851092\) \(a_{72}=+0.293017028\) \(a_{73}=+0.158849759\) \(a_{74}=+0.756040608\) \(a_{75}=-0.082758127\)
\(a_{76}=+0.480091644\) \(a_{77}=+0.815509424\) \(a_{78}=-0.547710277\) \(a_{79}=+1.261751163\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.515649140\) \(a_{82}=+0.477168297\) \(a_{83}=-1.836444824\) \(a_{84}=-0.301370850\) \(a_{85}=+0.626278691\)
\(a_{86}=+0.722421587\) \(a_{87}=+0.449597295\) \(a_{88}=-0.197939929\) \(a_{89}=-1.212869578\) \(a_{90}=+0.262082397\)
\(a_{91}=-2.726690282\) \(a_{92}=+0.275294363\) \(a_{93}=+0.059200504\) \(a_{94}=-0.059156603\) \(a_{95}=+0.429407020\)
\(a_{96}=+0.073148541\) \(a_{97}=+1.882509163\) \(a_{98}=-0.793221043\) \(a_{99}=-0.463998158\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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