Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.83080665145 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.307193464\) \(a_{3}=-0.421777502\) \(a_{4}=+0.708754753\) \(a_{5}=+0.080220810\)
\(a_{6}=+0.551344793\) \(a_{7}=-1.446416435\) \(a_{8}=+0.380713883\) \(a_{9}=-0.822103739\) \(a_{10}=-0.104864118\)
\(a_{11}=+0.915235204\) \(a_{12}=-0.298936809\) \(a_{13}=-0.277350098\) \(a_{14}=+1.890746110\) \(a_{15}=-0.033835333\)
\(a_{16}=-1.206421453\) \(a_{17}=-1.365895245\) \(a_{18}=+1.074648635\) \(a_{19}=+0.684307711\) \(a_{20}=+0.056856880\)
\(a_{21}=+0.610065910\) \(a_{22}=-1.196389477\) \(a_{23}=-0.237745114\) \(a_{24}=-0.160576551\) \(a_{25}=-0.993564622\)
\(a_{26}=+0.362550236\) \(a_{27}=+0.768522363\) \(a_{28}=-1.025154523\) \(a_{29}=+0.582577277\) \(a_{30}=+0.044229326\)
\(a_{31}=+0.686886563\) \(a_{32}=+1.196312355\) \(a_{33}=-0.386025618\) \(a_{34}=+1.785489337\) \(a_{35}=-0.116032698\)
\(a_{36}=-0.582669933\) \(a_{37}=-1.432927625\) \(a_{38}=-0.894522568\) \(a_{39}=+0.116980031\) \(a_{40}=+0.030541176\)
\(a_{41}=-0.126610014\) \(a_{42}=-0.797474170\) \(a_{43}=-0.857128903\) \(a_{44}=+0.648677301\) \(a_{45}=-0.065949828\)
\(a_{46}=+0.310778860\) \(a_{47}=-0.859416385\) \(a_{48}=+0.508841426\) \(a_{49}=+1.092120503\) \(a_{50}=+1.298781180\)
\(a_{51}=+0.576103884\) \(a_{52}=-0.196573200\) \(a_{53}=+1.142325413\) \(a_{54}=-1.004607410\) \(a_{55}=+0.073420909\)
\(a_{56}=-0.550670818\) \(a_{57}=-0.288625597\) \(a_{58}=-0.761541209\) \(a_{59}=+1.096837025\) \(a_{60}=-0.023980953\)
\(a_{61}=-1.452550767\) \(a_{62}=-0.897893626\) \(a_{63}=+1.189104359\) \(a_{64}=-0.357390239\) \(a_{65}=-0.022249249\)
\(a_{66}=+0.504610164\) \(a_{67}=+0.689029583\) \(a_{68}=-0.968084747\) \(a_{69}=+0.100275540\) \(a_{70}=+0.151677184\)
\(a_{71}=-0.782074988\) \(a_{72}=-0.312986307\) \(a_{73}=-0.829569642\) \(a_{74}=+1.873113627\) \(a_{75}=+0.419063204\)
\(a_{76}=+0.485006343\) \(a_{77}=-1.323811240\) \(a_{78}=-0.152915533\) \(a_{79}=+0.162107495\) \(a_{80}=-0.096780106\)
\(a_{81}=+0.497958297\) \(a_{82}=+0.165503783\) \(a_{83}=+0.117345706\) \(a_{84}=+0.432387113\) \(a_{85}=-0.109573223\)
\(a_{86}=+1.120433300\) \(a_{87}=-0.245717988\) \(a_{88}=+0.348442749\) \(a_{89}=-1.470590837\) \(a_{90}=+0.086209184\)
\(a_{91}=+0.401163740\) \(a_{92}=-0.168502980\) \(a_{93}=-0.289713298\) \(a_{94}=+1.123423482\) \(a_{95}=+0.054895719\)
\(a_{96}=-0.504577636\) \(a_{97}=+1.602480997\) \(a_{98}=-1.427612783\) \(a_{99}=-0.752418283\) \(a_{100}=-0.704193648\)

Showing 100 of 546 available coefficients

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