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: \( 9.46193719273 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.106378715\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.075221111\) \(a_{7}=+1.332746900\) \(a_{8}=-0.353553391\) \(a_{9}=-0.988683569\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.605483567\) \(a_{12}=+0.053189358\) \(a_{13}=+1.442939525\) \(a_{14}=-0.942394371\) \(a_{15}=+0.047574008\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.256744244\) \(a_{18}=+0.699104856\) \(a_{19}=+1.592329055\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.141775903\) \(a_{22}=+1.135248317\) \(a_{23}=+0.341091738\) \(a_{24}=-0.037610555\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.020312323\) \(a_{27}=-0.211553603\) \(a_{28}=+0.666373450\) \(a_{29}=+0.518897892\) \(a_{30}=-0.033639903\)
\(a_{31}=+1.117147212\) \(a_{32}=-0.176776695\) \(a_{33}=-0.170789279\) \(a_{34}=+0.181545596\) \(a_{35}=+0.596022533\)
\(a_{36}=-0.494341784\) \(a_{37}=-0.021074563\) \(a_{38}=-1.125946673\) \(a_{39}=+0.153498053\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.356648233\) \(a_{42}=-0.100250702\) \(a_{43}=-0.215277374\) \(a_{44}=-0.802741783\) \(a_{45}=-0.442152734\)
\(a_{46}=-0.241188281\) \(a_{47}=+1.050945431\) \(a_{48}=+0.026594679\) \(a_{49}=+0.776214300\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.027312123\) \(a_{52}=+0.721469762\) \(a_{53}=-0.227201499\) \(a_{54}=+0.149590987\) \(a_{55}=-0.717994078\)
\(a_{56}=-0.471197185\) \(a_{57}=+0.169389919\) \(a_{58}=-0.366916218\) \(a_{59}=+0.465395736\) \(a_{60}=+0.023787004\)
\(a_{61}=-0.107251416\) \(a_{62}=-0.789942369\) \(a_{63}=-1.317664962\) \(a_{64}=+0.125000000\) \(a_{65}=+0.645302173\)
\(a_{66}=+0.120766257\) \(a_{67}=+1.782242732\) \(a_{68}=-0.128372122\) \(a_{69}=+0.036284901\) \(a_{70}=-0.421451575\)
\(a_{71}=+0.354755847\) \(a_{72}=+0.349552428\) \(a_{73}=+0.773365039\) \(a_{74}=+0.014901967\) \(a_{75}=+0.021275743\)
\(a_{76}=+0.796164528\) \(a_{77}=-2.139703247\) \(a_{78}=-0.108539514\) \(a_{79}=-1.151449320\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.966178768\) \(a_{82}=-0.959295165\) \(a_{83}=-0.451680020\) \(a_{84}=+0.070887951\) \(a_{85}=-0.114819516\)
\(a_{86}=+0.152224091\) \(a_{87}=+0.055199691\) \(a_{88}=+0.567624159\) \(a_{89}=-0.750827330\) \(a_{90}=+0.312649196\)
\(a_{91}=+1.923073179\) \(a_{92}=+0.170545869\) \(a_{93}=+0.118840685\) \(a_{94}=-0.743130641\) \(a_{95}=+0.712111202\)
\(a_{96}=-0.018805278\) \(a_{97}=-1.254113300\) \(a_{98}=-0.548866395\) \(a_{99}=+1.587315223\) \(a_{100}=+0.099975586\)

Showing 100 of 148 available coefficients

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