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: \( 24.6159903788 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.845335197\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.304849031\) \(a_{7}=+0.042921763\) \(a_{8}=+0.353553391\) \(a_{9}=+2.405261988\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.884249346\) \(a_{12}=-0.922667598\) \(a_{13}=-1.272808310\) \(a_{14}=+0.030350270\) \(a_{15}=+0.825258988\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.223294235\) \(a_{18}=+1.700777062\) \(a_{19}=-0.544867884\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.079205041\) \(a_{22}=-0.625258709\) \(a_{23}=+1.130286070\) \(a_{24}=-0.652424516\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.900011387\) \(a_{27}=-2.593179406\) \(a_{28}=+0.021460882\) \(a_{29}=-0.367765309\) \(a_{30}=+0.583546227\)
\(a_{31}=-1.108056580\) \(a_{32}=+0.176776695\) \(a_{33}=+1.631736442\) \(a_{34}=+0.864999649\) \(a_{35}=-0.019195196\)
\(a_{36}=+1.202630994\) \(a_{37}=-1.937489056\) \(a_{38}=-0.385279775\) \(a_{39}=+2.348757972\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.569101864\) \(a_{42}=-0.056006421\) \(a_{43}=-1.008722970\) \(a_{44}=-0.442124673\) \(a_{45}=-1.075665862\)
\(a_{46}=+0.799232945\) \(a_{47}=-0.729900209\) \(a_{48}=-0.461333799\) \(a_{49}=-0.998157722\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.257387907\) \(a_{52}=-0.636404155\) \(a_{53}=-1.264700434\) \(a_{54}=-1.833654743\) \(a_{55}=+0.395448330\)
\(a_{56}=+0.015175135\) \(a_{57}=+1.005463883\) \(a_{58}=-0.260049344\) \(a_{59}=+1.622099664\) \(a_{60}=+0.412629494\)
\(a_{61}=-0.919754841\) \(a_{62}=-0.783514321\) \(a_{63}=+0.103238086\) \(a_{64}=+0.125000000\) \(a_{65}=+0.569217181\)
\(a_{66}=+1.153811903\) \(a_{67}=-0.339360905\) \(a_{68}=+0.611647117\) \(a_{69}=-2.085756668\) \(a_{70}=-0.013573053\)
\(a_{71}=+1.101744645\) \(a_{72}=+0.850388531\) \(a_{73}=+1.052751488\) \(a_{74}=-1.370011650\) \(a_{75}=-0.369067039\)
\(a_{76}=-0.272433942\) \(a_{77}=-0.037953541\) \(a_{78}=+1.660822690\) \(a_{79}=-0.956020089\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.380023242\) \(a_{82}=-0.402415787\) \(a_{83}=+1.481966495\) \(a_{84}=-0.039602520\) \(a_{85}=-0.547073813\)
\(a_{86}=-0.713274852\) \(a_{87}=+0.678650268\) \(a_{88}=-0.312629355\) \(a_{89}=+1.230380285\) \(a_{90}=-0.760610625\)
\(a_{91}=-0.054631177\) \(a_{92}=+0.565143035\) \(a_{93}=+2.044735806\) \(a_{94}=-0.516117387\) \(a_{95}=+0.243672325\)
\(a_{96}=-0.326212258\) \(a_{97}=+0.421426698\) \(a_{98}=-0.705804094\) \(a_{99}=-2.126851341\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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