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: \( 28.2148889919 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.019186501\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.720673686\) \(a_{7}=-0.855137701\) \(a_{8}=-0.353553391\) \(a_{9}=+0.038741125\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.827057176\) \(a_{12}=+0.509593251\) \(a_{13}=+1.877586847\) \(a_{14}=+0.604673667\) \(a_{15}=+0.455794060\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.527273357\) \(a_{18}=-0.027394112\) \(a_{19}=-0.969308944\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.871544802\) \(a_{22}=+1.291924519\) \(a_{23}=-0.436754126\) \(a_{24}=-0.360336843\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.327654392\) \(a_{27}=-0.979702070\) \(a_{28}=-0.427568851\) \(a_{29}=+1.292159482\) \(a_{30}=-0.322295071\)
\(a_{31}=-0.877078644\) \(a_{32}=-0.176776695\) \(a_{33}=-1.862112012\) \(a_{34}=+0.372838567\) \(a_{35}=-0.382429206\)
\(a_{36}=+0.019370562\) \(a_{37}=+0.045761193\) \(a_{38}=+0.685404927\) \(a_{39}=+1.913611170\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.647255160\) \(a_{42}=+0.616275240\) \(a_{43}=+0.948974750\) \(a_{44}=-0.913528588\) \(a_{45}=+0.017325558\)
\(a_{46}=+0.308831804\) \(a_{47}=-0.107871713\) \(a_{48}=+0.254796625\) \(a_{49}=-0.268739512\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.537389889\) \(a_{52}=+0.938793423\) \(a_{53}=+1.849084078\) \(a_{54}=+0.692753977\) \(a_{55}=-0.817084809\)
\(a_{56}=+0.302336834\) \(a_{57}=-0.987906591\) \(a_{58}=-0.913694732\) \(a_{59}=+0.233078713\) \(a_{60}=+0.227897030\)
\(a_{61}=+1.374002400\) \(a_{62}=+0.620188257\) \(a_{63}=-0.033128996\) \(a_{64}=+0.125000000\) \(a_{65}=+0.839682365\)
\(a_{66}=+1.316712031\) \(a_{67}=+1.618283465\) \(a_{68}=-0.263636679\) \(a_{69}=-0.445133910\) \(a_{70}=+0.270418285\)
\(a_{71}=-0.952810387\) \(a_{72}=-0.013697056\) \(a_{73}=+1.310249781\) \(a_{74}=-0.032358050\) \(a_{75}=+0.203837300\)
\(a_{76}=-0.484654472\) \(a_{77}=+1.562385474\) \(a_{78}=-1.353127435\) \(a_{79}=+0.229234666\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.037240250\) \(a_{82}=+1.164785294\) \(a_{83}=+0.033712380\) \(a_{84}=-0.435772401\) \(a_{85}=-0.235803814\)
\(a_{86}=-0.671026481\) \(a_{87}=+1.316951502\) \(a_{88}=+0.645962260\) \(a_{89}=-0.174378565\) \(a_{90}=-0.012251019\)
\(a_{91}=-1.605595300\) \(a_{92}=-0.218377063\) \(a_{93}=-0.893906715\) \(a_{94}=+0.076276820\) \(a_{95}=-0.433488138\)
\(a_{96}=-0.180168422\) \(a_{97}=-0.383203139\) \(a_{98}=+0.190027531\) \(a_{99}=-0.070782250\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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