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: \( 28.8123294116 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.849724582\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.307952796\) \(a_{7}=+0.522890792\) \(a_{8}=+0.353553391\) \(a_{9}=+2.421481031\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.615676263\) \(a_{12}=-0.924862291\) \(a_{13}=-1.283817031\) \(a_{14}=+0.369739625\) \(a_{15}=+0.827221981\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.232253538\) \(a_{18}=+1.712245658\) \(a_{19}=-1.447766656\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.967203952\) \(a_{22}=+0.435348861\) \(a_{23}=-1.682280331\) \(a_{24}=-0.653976398\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.907795729\) \(a_{27}=-2.629348407\) \(a_{28}=+0.261445396\) \(a_{29}=+1.282715879\) \(a_{30}=+0.584934272\)
\(a_{31}=+0.721077888\) \(a_{32}=+0.176776695\) \(a_{33}=-1.138831519\) \(a_{34}=+0.164228051\) \(a_{35}=-0.233843871\)
\(a_{36}=+1.210740516\) \(a_{37}=+0.914761971\) \(a_{38}=-1.023725620\) \(a_{39}=+2.374707922\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.817789338\) \(a_{42}=-0.683916473\) \(a_{43}=+1.504748079\) \(a_{44}=+0.307838132\) \(a_{45}=-1.082919238\)
\(a_{46}=-1.189551830\) \(a_{47}=+0.314282622\) \(a_{48}=-0.462431146\) \(a_{49}=-0.726585220\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.429605078\) \(a_{52}=-0.641908516\) \(a_{53}=-0.065891909\) \(a_{54}=-1.859230089\) \(a_{55}=-0.275338795\)
\(a_{56}=+0.184869812\) \(a_{57}=+2.677969574\) \(a_{58}=+0.907017096\) \(a_{59}=-1.045149197\) \(a_{60}=+0.413610991\)
\(a_{61}=+0.933913594\) \(a_{62}=+0.509879064\) \(a_{63}=+1.266170134\) \(a_{64}=+0.125000000\) \(a_{65}=+0.574140431\)
\(a_{66}=-0.805275490\) \(a_{67}=-0.692089579\) \(a_{68}=+0.116126769\) \(a_{69}=+3.111755283\) \(a_{70}=-0.165352587\)
\(a_{71}=+1.802353394\) \(a_{72}=+0.856122829\) \(a_{73}=-0.750806037\) \(a_{74}=+0.646834393\) \(a_{75}=-0.369944916\)
\(a_{76}=-0.723883328\) \(a_{77}=+0.321931449\) \(a_{78}=+1.679172075\) \(a_{79}=-0.099321239\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.442089353\) \(a_{82}=+0.578264386\) \(a_{83}=-0.163814229\) \(a_{84}=-0.483601976\) \(a_{85}=-0.103866940\)
\(a_{86}=+1.064017570\) \(a_{87}=-2.372671093\) \(a_{88}=+0.217674430\) \(a_{89}=-0.567156160\) \(a_{90}=-0.765739537\)
\(a_{91}=-0.671296104\) \(a_{92}=-0.841140166\) \(a_{93}=-1.333795495\) \(a_{94}=+0.222231374\) \(a_{95}=+0.647460932\)
\(a_{96}=-0.326988199\) \(a_{97}=+0.180717361\) \(a_{98}=-0.513773336\) \(a_{99}=+1.490848393\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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