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: \( 22.9632098523 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.473151165\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.334568397\) \(a_{7}=-0.343145116\) \(a_{8}=-0.353553391\) \(a_{9}=-0.776127976\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.203139618\) \(a_{12}=+0.236575582\) \(a_{13}=+0.565074909\) \(a_{14}=+0.242640239\) \(a_{15}=+0.211599633\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.407612615\) \(a_{18}=+0.548805355\) \(a_{19}=+0.241096675\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.162359511\) \(a_{22}=+0.143641401\) \(a_{23}=+0.386681515\) \(a_{24}=-0.167284198\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.399568300\) \(a_{27}=-0.840377020\) \(a_{28}=-0.171572558\) \(a_{29}=+0.029985391\) \(a_{30}=-0.149623536\)
\(a_{31}=+0.371010553\) \(a_{32}=-0.176776695\) \(a_{33}=-0.096115747\) \(a_{34}=-0.288225644\) \(a_{35}=-0.153459161\)
\(a_{36}=-0.388063988\) \(a_{37}=-0.442136887\) \(a_{38}=-0.170481094\) \(a_{39}=+0.267365851\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.009093770\) \(a_{42}=+0.114805512\) \(a_{43}=-0.421943784\) \(a_{44}=-0.101569809\) \(a_{45}=-0.347094983\)
\(a_{46}=-0.273425122\) \(a_{47}=-1.164956369\) \(a_{48}=+0.118287791\) \(a_{49}=-0.882251429\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.192862383\) \(a_{52}=+0.282537454\) \(a_{53}=+0.318063987\) \(a_{54}=+0.594236290\) \(a_{55}=-0.090846799\)
\(a_{56}=+0.121320119\) \(a_{57}=+0.114075173\) \(a_{58}=-0.021202873\) \(a_{59}=+1.150991910\) \(a_{60}=+0.105799817\)
\(a_{61}=+1.554017716\) \(a_{62}=-0.262344078\) \(a_{63}=+0.266324525\) \(a_{64}=+0.125000000\) \(a_{65}=+0.252709182\)
\(a_{66}=+0.067964096\) \(a_{67}=+0.594082134\) \(a_{68}=+0.203806307\) \(a_{69}=+0.182958809\) \(a_{70}=+0.108512014\)
\(a_{71}=-1.469685426\) \(a_{72}=+0.274402677\) \(a_{73}=-1.862808495\) \(a_{74}=+0.312637991\) \(a_{75}=+0.094630233\)
\(a_{76}=+0.120548338\) \(a_{77}=+0.069706368\) \(a_{78}=-0.189056206\) \(a_{79}=+0.631856044\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.378502610\) \(a_{82}=-0.006430266\) \(a_{83}=+1.674662143\) \(a_{84}=-0.081179756\) \(a_{85}=+0.182289903\)
\(a_{86}=+0.298359311\) \(a_{87}=+0.014187622\) \(a_{88}=+0.071820701\) \(a_{89}=-0.685319837\) \(a_{90}=+0.245433216\)
\(a_{91}=-0.193902695\) \(a_{92}=+0.193340758\) \(a_{93}=+0.175544075\) \(a_{94}=+0.823748549\) \(a_{95}=+0.107821711\)
\(a_{96}=-0.083642099\) \(a_{97}=+0.959152125\) \(a_{98}=+0.623845968\) \(a_{99}=+0.157662340\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

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